main_mtm_fontanelli_mdh.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Robot Dynamic Model Identification\n",
    "=======\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1 - Praparing work"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "# enable auto-reload modules\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "#interactive plotting in separate window\n",
    "%matplotlib qt \n",
    "#%matplotlib inline\n",
    "\n",
    "from sympy import init_printing\n",
    "init_printing()\n",
    "    \n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.figsize'] = [12, 8]\n",
    "plt.rcParams['pdf.fonttype'] = 42\n",
    "plt.rcParams['ps.fonttype'] = 42\n",
    "plt.rcParams.update({'font.size': 12})\n",
    "\n",
    "import numpy as np\n",
    "import sympy\n",
    "from robot_def import RobotDef\n",
    "from kinematics import Geometry\n",
    "from dynamics import Dynamics\n",
    "from trajectory_optimization import TrajOptimizer\n",
    "from trajectory_optimization import TrajPlotter\n",
    "from utils import new_sym\n",
    "from utils import save_data, load_data\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Folder dir for saving and loading files"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#model_name = 'mtm_2spring_tendon'\n",
    "model_name = 'mtm_fontanelli'\n",
    "\n",
    "model_folder = 'data/' + model_name + '/model/'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "# 2 - Robot modelling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Robot geometry definition in following order"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Joint number | prev link | succ links | $a$ | $\\alpha$ | $d$ | $\\theta$ | link inertia | motor inertia | friction "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mtm_fontanelli\n"
     ]
    }
   ],
   "source": [
    "q0, q1, q2, q3, q4, q5, q6, q7, q8, q9, q10 = new_sym('q:11')\n",
    "_pi = sympy.pi\n",
    "\n",
    "# define paralelogram coordinate relation\n",
    "# qd -> coordinate for dvrk_ros package\n",
    "# qmd -> coordinate for the modeling joints\n",
    "# q -> coordinate for motors\n",
    "qd2 = q2\n",
    "qd3 = -q2 + q3\n",
    "qd4 = 0.6697*q2 - 0.6697*q3 + q4\n",
    "\n",
    "\n",
    "qmd1 = q1\n",
    "qmd2 = qd2\n",
    "qmd30 = qd3\n",
    "qmd31 = qd3 + qd2 \n",
    "qmd32 = -qd3\n",
    "qmd33 = q3\n",
    "qmd4 = qd4\n",
    "qmd5 = q5\n",
    "qmd6 = q6\n",
    "qmd7 = q7\n",
    "\n",
    "# q31 = q3 + q2 \n",
    "# q32 = -q3\n",
    "\n",
    "l_b2p = 215.4 * 0.001\n",
    "l_arm = 279.4 * 0.001\n",
    "l_b2f = 100 * 0.001\n",
    "l_fa = 364.5 * 0.001\n",
    "h =105.6 * 0.001\n",
    "\n",
    "# define link number\n",
    "L_b = 0\n",
    "L_1 = 1\n",
    "L_2 = 2\n",
    "L_30 = 3\n",
    "L_31 = 4\n",
    "L_32 = 5\n",
    "L_4 = 6\n",
    "L_5 = 7\n",
    "L_6 = 8\n",
    "L_7 = 9\n",
    "\n",
    "# define spring delta L\n",
    "dlN = None\n",
    "dl1 = -qmd1\n",
    "dl4 = -qmd4\n",
    "dl5 = -qmd5\n",
    "dl6 = -qmd6\n",
    "\n",
    "# DH\n",
    "# dh = [(L_b,  -1,   [L_1],       0,     0,      0,       0,           False, False, False, dlN),\n",
    "#       (L_1,  L_b,  [L_2, L_31], 0,     0,      -l_b2p,  qmd1,        True,  False, True, dl1),\n",
    "#       (L_2,  L_1,  [L_30],      0,     -_pi/2, 0,       qmd2+_pi/2,  True,  False, True, dlN),\n",
    "#       (L_30, L_2,  [L_4],       l_arm, 0,      0,       qmd30+_pi/2, True,  False, True, dlN),\n",
    "#       (L_31, L_1,  [L_32],      0,     -_pi/2, 0,       qmd31+_pi,   True,  False, True, dlN),\n",
    "#       (L_32, L_31, [],          l_b2f, 0,      0,       qmd32-_pi/2, True,  False, True, dlN),\n",
    "#       (L_4,  L_30, [L_5],       l_fa,  -_pi/2, 0.151,   qmd4,        True,  False, True, dl4),\n",
    "#       (L_5,  L_4,  [L_6],       0,     _pi/2,  0,       qmd5,        True,  False, True, dl5),\n",
    "#       (L_6,  L_5,  [L_7],       0,     -_pi/2, 0,       qmd6+_pi/2,  True,  False, True, dl6),\n",
    "#       (L_7,  L_6,  [],          0,     -_pi/2, 0,       qmd7+_pi,    True,  False, True, dlN)]\n",
    "dh = [(L_b,  -1,   [L_1],       0,     0,      0,       0,           False, False, False, dlN),\n",
    "      (L_1,  L_b,  [L_2, L_31], 0,     0,      -l_b2p,  qmd1,        True,  False, True, dl1),\n",
    "      (L_2,  L_1,  [L_30],      0,     -_pi/2, 0,       qmd2+_pi/2,  True,  False, True, dlN),\n",
    "      (L_30, L_2,  [L_4],       l_arm, 0,      0,       qmd30+_pi/2, True,  False, True, dlN),\n",
    "      (L_31, L_1,  [L_32],      0,     -_pi/2, 0,       qmd31+_pi,   True,  False, True, dlN),\n",
    "      (L_32, L_31, [],          l_b2f, 0,      0,       qmd32-_pi/2, True,  False, True, dlN),\n",
    "      (L_4,  L_30, [L_5],       l_fa,  -_pi/2, 0.151,   qmd4,        True,  False, True, dl4),\n",
    "      (L_5,  L_4,  [L_6],       0,     _pi/2,  0,       qmd5,        True,  False, True, dl5),\n",
    "      (L_6,  L_5,  [L_7],       0,     -_pi/2, 0,       qmd6+_pi/2,  True,  False, True, dl6),\n",
    "      (L_7,  L_6,  [],          0,     -_pi/2, 0,       qmd7+_pi,    True,  False, True, dlN)]\n",
    "\n",
    "\n",
    "# Friction\n",
    "friction_type = ['Coulomb', 'viscous']\n",
    "print(model_name)\n",
    "\n",
    "robot_def = RobotDef(dh, dh_convention='mdh', friction_type=friction_type)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$$\\left [ 0, \\quad dq_{1}, \\quad dq_{2}, \\quad - dq_{2} + dq_{3}, \\quad dq_{3}, \\quad dq_{2} - dq_{3}, \\quad 0.6697 dq_{2} - 0.6697 dq_{3} + dq_{4}, \\quad dq_{5}, \\quad dq_{6}, \\quad dq_{7}\\right ]$$"
      ],
      "text/plain": [
       "[0, dq₁, dq₂, -dq₂ + dq₃, dq₃, dq₂ - dq₃, 0.6697⋅dq₂ - 0.6697⋅dq₃ + dq₄, dq₅, \n",
       "dq₆, dq₇]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "robot_def.dq_for_frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['R', 'R', 'R', 'R', 'R', 'R', 'R']"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "robot_def.coordinates_joint_type"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$$\\left [ L1xx, \\quad L1xy, \\quad L1xz, \\quad L1yy, \\quad L1yz, \\quad L1zz, \\quad l1x, \\quad l1y, \\quad l1z, \\quad m_{1}, \\quad Fc_{1}, \\quad Fv_{1}, \\quad K_{1}, \\quad L2xx, \\quad L2xy, \\quad L2xz, \\quad L2yy, \\quad L2yz, \\quad L2zz, \\quad l2x, \\quad l2y, \\quad l2z, \\quad m_{2}, \\quad Fc_{2}, \\quad Fv_{2}, \\quad L3xx, \\quad L3xy, \\quad L3xz, \\quad L3yy, \\quad L3yz, \\quad L3zz, \\quad l3x, \\quad l3y, \\quad l3z, \\quad m_{3}, \\quad Fc_{3}, \\quad Fv_{3}, \\quad L4xx, \\quad L4xy, \\quad L4xz, \\quad L4yy, \\quad L4yz, \\quad L4zz, \\quad l4x, \\quad l4y, \\quad l4z, \\quad m_{4}, \\quad Fc_{4}, \\quad Fv_{4}, \\quad L5xx, \\quad L5xy, \\quad L5xz, \\quad L5yy, \\quad L5yz, \\quad L5zz, \\quad l5x, \\quad l5y, \\quad l5z, \\quad m_{5}, \\quad Fc_{5}, \\quad Fv_{5}, \\quad L6xx, \\quad L6xy, \\quad L6xz, \\quad L6yy, \\quad L6yz, \\quad L6zz, \\quad l6x, \\quad l6y, \\quad l6z, \\quad m_{6}, \\quad Fc_{6}, \\quad Fv_{6}, \\quad K_{6}, \\quad L7xx, \\quad L7xy, \\quad L7xz, \\quad L7yy, \\quad L7yz, \\quad L7zz, \\quad l7x, \\quad l7y, \\quad l7z, \\quad m_{7}, \\quad Fc_{7}, \\quad Fv_{7}, \\quad K_{7}, \\quad L8xx, \\quad L8xy, \\quad L8xz, \\quad L8yy, \\quad L8yz, \\quad L8zz, \\quad l8x, \\quad l8y, \\quad l8z, \\quad m_{8}, \\quad Fc_{8}, \\quad Fv_{8}, \\quad K_{8}, \\quad L9xx, \\quad L9xy, \\quad L9xz, \\quad L9yy, \\quad L9yz, \\quad L9zz, \\quad l9x, \\quad l9y, \\quad l9z, \\quad m_{9}, \\quad Fc_{9}, \\quad Fv_{9}\\right ]$$"
      ],
      "text/plain": [
       "[L1xx, L1xy, L1xz, L1yy, L1yz, L1zz, l1x, l1y, l1z, m₁, Fc₁, Fv₁, K₁, L2xx, L2\n",
       "xy, L2xz, L2yy, L2yz, L2zz, l2x, l2y, l2z, m₂, Fc₂, Fv₂, L3xx, L3xy, L3xz, L3y\n",
       "y, L3yz, L3zz, l3x, l3y, l3z, m₃, Fc₃, Fv₃, L4xx, L4xy, L4xz, L4yy, L4yz, L4zz\n",
       ", l4x, l4y, l4z, m₄, Fc₄, Fv₄, L5xx, L5xy, L5xz, L5yy, L5yz, L5zz, l5x, l5y, l\n",
       "5z, m₅, Fc₅, Fv₅, L6xx, L6xy, L6xz, L6yy, L6yz, L6zz, l6x, l6y, l6z, m₆, Fc₆, \n",
       "Fv₆, K₆, L7xx, L7xy, L7xz, L7yy, L7yz, L7zz, l7x, l7y, l7z, m₇, Fc₇, Fv₇, K₇, \n",
       "L8xx, L8xy, L8xz, L8yy, L8yz, L8zz, l8x, l8y, l8z, m₈, Fc₈, Fv₈, K₈, L9xx, L9x\n",
       "y, L9xz, L9yy, L9yz, L9zz, l9x, l9y, l9z, m₉, Fc₉, Fv₉]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "robot_def.bary_params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create kinematics chain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Frame: 0\n",
      "Frame: 1\n",
      "Frame: 2\n",
      "Frame: 3\n",
      "Frame: 4\n",
      "Frame: 5\n",
      "Frame: 6\n",
      "Frame: 7\n",
      "Frame: 8\n",
      "Frame: 9\n",
      "CPU times: user 56min 29s, sys: 7.16 s, total: 56min 36s\n",
      "Wall time: 56min 27s\n"
     ]
    }
   ],
   "source": [
    "%time geom = Geometry(robot_def)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "angle = [0.5, 0.3, -0.5, 0, 0, 0, 0]\n",
    "geom.draw_geom(angle)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create dynamics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calculating Lagrangian...\n",
      "Calculating the link kinetic energy of 1/9\n",
      "Calculating the link kinetic energy of 2/9\n",
      "Calculating the link kinetic energy of 3/9\n",
      "Calculating the link kinetic energy of 4/9\n",
      "Calculating the link kinetic energy of 5/9\n",
      "Calculating the link kinetic energy of 6/9\n",
      "Calculating the link kinetic energy of 7/9\n",
      "Calculating the link kinetic energy of 8/9\n",
      "Calculating the link kinetic energy of 9/9\n",
      "Calculating joint torques...\n",
      "tau of q1\n",
      "tau of q2\n",
      "tau of q3\n",
      "tau of q4\n",
      "tau of q5\n",
      "tau of q6\n",
      "tau of q7\n",
      "Adding frictions and springs...\n",
      "Add motor inertia...\n",
      "Calculating regressor...\n",
      "Calculating M, C and G...\n",
      "Calculating base parameter...\n",
      "base parameter number: 66\n",
      "Creating H_b function...\n",
      "Finished creating robot dynamics\n",
      "CPU times: user 31min 24s, sys: 4.53 s, total: 31min 29s\n",
      "Wall time: 31min 20s\n"
     ]
    }
   ],
   "source": [
    "%time dyn = Dynamics(robot_def, geom)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$$\\left [ L1xx, \\quad L1xy, \\quad L1xz, \\quad L1yy, \\quad L1yz, \\quad L1zz, \\quad l1x, \\quad l1y, \\quad l1z, \\quad m_{1}, \\quad Fc_{1}, \\quad Fv_{1}, \\quad K_{1}, \\quad L2xx, \\quad L2xy, \\quad L2xz, \\quad L2yy, \\quad L2yz, \\quad L2zz, \\quad l2x, \\quad l2y, \\quad l2z, \\quad m_{2}, \\quad Fc_{2}, \\quad Fv_{2}, \\quad L3xx, \\quad L3xy, \\quad L3xz, \\quad L3yy, \\quad L3yz, \\quad L3zz, \\quad l3x, \\quad l3y, \\quad l3z, \\quad m_{3}, \\quad Fc_{3}, \\quad Fv_{3}, \\quad L4xx, \\quad L4xy, \\quad L4xz, \\quad L4yy, \\quad L4yz, \\quad L4zz, \\quad l4x, \\quad l4y, \\quad l4z, \\quad m_{4}, \\quad Fc_{4}, \\quad Fv_{4}, \\quad L5xx, \\quad L5xy, \\quad L5xz, \\quad L5yy, \\quad L5yz, \\quad L5zz, \\quad l5x, \\quad l5y, \\quad l5z, \\quad m_{5}, \\quad Fc_{5}, \\quad Fv_{5}, \\quad L6xx, \\quad L6xy, \\quad L6xz, \\quad L6yy, \\quad L6yz, \\quad L6zz, \\quad l6x, \\quad l6y, \\quad l6z, \\quad m_{6}, \\quad Fc_{6}, \\quad Fv_{6}, \\quad K_{6}, \\quad L7xx, \\quad L7xy, \\quad L7xz, \\quad L7yy, \\quad L7yz, \\quad L7zz, \\quad l7x, \\quad l7y, \\quad l7z, \\quad m_{7}, \\quad Fc_{7}, \\quad Fv_{7}, \\quad K_{7}, \\quad L8xx, \\quad L8xy, \\quad L8xz, \\quad L8yy, \\quad L8yz, \\quad L8zz, \\quad l8x, \\quad l8y, \\quad l8z, \\quad m_{8}, \\quad Fc_{8}, \\quad Fv_{8}, \\quad K_{8}, \\quad L9xx, \\quad L9xy, \\quad L9xz, \\quad L9yy, \\quad L9yz, \\quad L9zz, \\quad l9x, \\quad l9y, \\quad l9z, \\quad m_{9}, \\quad Fc_{9}, \\quad Fv_{9}\\right ]$$"
      ],
      "text/plain": [
       "[L1xx, L1xy, L1xz, L1yy, L1yz, L1zz, l1x, l1y, l1z, m₁, Fc₁, Fv₁, K₁, L2xx, L2\n",
       "xy, L2xz, L2yy, L2yz, L2zz, l2x, l2y, l2z, m₂, Fc₂, Fv₂, L3xx, L3xy, L3xz, L3y\n",
       "y, L3yz, L3zz, l3x, l3y, l3z, m₃, Fc₃, Fv₃, L4xx, L4xy, L4xz, L4yy, L4yz, L4zz\n",
       ", l4x, l4y, l4z, m₄, Fc₄, Fv₄, L5xx, L5xy, L5xz, L5yy, L5yz, L5zz, l5x, l5y, l\n",
       "5z, m₅, Fc₅, Fv₅, L6xx, L6xy, L6xz, L6yy, L6yz, L6zz, l6x, l6y, l6z, m₆, Fc₆, \n",
       "Fv₆, K₆, L7xx, L7xy, L7xz, L7yy, L7yz, L7zz, l7x, l7y, l7z, m₇, Fc₇, Fv₇, K₇, \n",
       "L8xx, L8xy, L8xz, L8yy, L8yz, L8zz, l8x, l8y, l8z, m₈, Fc₈, Fv₈, K₈, L9xx, L9x\n",
       "y, L9xz, L9yy, L9yz, L9zz, l9x, l9y, l9z, m₉, Fc₉, Fv₉]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "robot_def.bary_params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}1.0 L9xy\\\\1.0 L9xz\\\\1.0 L9yz\\\\1.0 L8yz\\\\1.0 L8xy\\\\1.0 L8xz\\\\1.0 L7xy\\\\1.0 L8xx - 1.0 L8yy + 1.0 L9yy\\\\1.0 L9zz\\\\1.0 L7xz\\\\1.0 L7yz\\\\1.0 l9x\\\\1.0 L8xx - 1.0 L8yy + 1.0 L9xx\\\\1.0 l9y\\\\1.0 l8y + 1.0 l9z\\\\1.0 l8x\\\\1.0 L6xz\\\\- 1.0 L8xx + 1.0 L8yy + 1.0 L8zz\\\\1.0 l7y + 1.0 l8z\\\\1.0 L6xy\\\\1.0 L6yz\\\\1.0 l7x\\\\1.0 l6x\\\\1.0 l6y - 1.0 l7z\\\\1.0 L7zz + 1.0 L8yy\\\\1.0 L3zz + 1.0 L4zz + 1.0 L6xx + 1.0 L7xx + 1.0 L8yy - 0.302 l3y + 0.01 m_{5} + 0.11005925 m_{6} + 0.11005925 m_{7} + 0.11005925 m_{8} + 0.11005925 m_{9}\\\\- 0.35790981 l2x + 1.0 l3x - 0.1 m_{3} + 0.2645 m_{6} + 0.2645 m_{7} + 0.2645 m_{8} + 0.2645 m_{9}\\\\1.0 l3y + 1.0 l6z + 0.151 m_{6} + 0.151 m_{7} + 0.151 m_{8} + 0.151 m_{9}\\\\1.0 l5y\\\\1.0 l2x + 1.0 l5x + 0.2794 m_{3} + 0.2794 m_{6} + 0.2794 m_{7} + 0.2794 m_{8} + 0.2794 m_{9}\\\\- 1.0 L3zz - 1.0 L4zz - 1.0 L6xx + 1.0 L6zz + 0.302 l3y - 0.01 m_{5} - 0.11005925 m_{6} - 0.11005925 m_{7} - 0.11005925 m_{8} - 0.11005925 m_{9}\\\\1.0 L2xy + 1.0 L5xy\\\\1.0 L3xy + 1.0 L4xy + 0.3645 l3y\\\\1.0 L3zz + 1.0 L4zz + 1.0 L6yy - 0.302 l3y + 0.01 m_{5} + 0.11005925 m_{6} + 0.11005925 m_{7} + 0.11005925 m_{8} + 0.11005925 m_{9}\\\\1.0 Fv_{3} + 1.0 Fv_{5}\\\\1.0 L2yz + 1.0 L5yz\\\\1.0 K_{6}\\\\1.0 L2xz + 1.0 L5xz - 0.2794 l3z\\\\1.0 L3xz + 1.0 L4xz - 0.1 l5z\\\\1.0 L3yz + 1.0 L4yz\\\\1.0 Fv_{6}\\\\1.0 L1zz + 1.0 L2xx + 1.0 L3xx - 1.0 L3zz + 1.0 L4xx - 1.0 L4zz + 1.0 L5xx - 0.01 m_{5} - 0.13286025 m_{6} - 0.13286025 m_{7} - 0.13286025 m_{8} - 0.13286025 m_{9}\\\\1.0 L3zz + 1.0 L4zz + 1.0 L6xx + 1.0 L7yy - 0.302 l3y + 0.01 m_{5} + 0.11005925 m_{6} + 0.11005925 m_{7} + 0.11005925 m_{8} + 0.11005925 m_{9}\\\\1.0 l4y\\\\0.35790981 l2x + 1.0 l4x + 0.1 m_{3} + 0.1 m_{5} + 0.1 m_{6} + 0.1 m_{7} + 0.1 m_{8} + 0.1 m_{9}\\\\1.0 Fv_{9}\\\\1.0 Fv_{7}\\\\- 1.0 L3xx + 1.0 L3yy + 1.0 L3zz - 1.0 L4xx + 1.0 L4yy + 1.0 L4zz + 0.02 m_{5} + 0.2657205 m_{6} + 0.2657205 m_{7} + 0.2657205 m_{8} + 0.2657205 m_{9}\\\\1.0 Fv_{8}\\\\1.0 K_{8}\\\\1.0 L2zz + 1.0 L5zz + 0.07806436 m_{3} + 0.07806436 m_{6} + 0.07806436 m_{7} + 0.07806436 m_{8} + 0.07806436 m_{9}\\\\1.0 K_{7}\\\\1.0 Fv_{1}\\\\1.0 K_{1}\\\\1.0 Fv_{2}\\\\1.0 Fv_{4}\\\\1.0 L1zz + 1.0 L2yy + 1.0 L3xx - 1.0 L3zz + 1.0 L4xx - 1.0 L4zz + 1.0 L5yy + 0.07806436 m_{3} - 0.01 m_{5} - 0.05479589 m_{6} - 0.05479589 m_{7} - 0.05479589 m_{8} - 0.05479589 m_{9}\\\\1.0 Fc_{3} + 1.0 Fc_{5}\\\\1.0 Fc_{6}\\\\1.0 l2y\\\\1.0 Fc_{8}\\\\1.0 Fc_{9}\\\\1.0 Fc_{2}\\\\1.0 Fc_{1}\\\\1.0 Fc_{4}\\\\1.0 Fc_{7}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                   1.0⋅L8xx -\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                   1.0⋅L8xx -\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                         1.0⋅\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                  -1.0⋅L8xx +\n",
       "⎢                                                                             \n",
       "⎢                                                                         1.0⋅\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                         1.0⋅\n",
       "⎢                                                                             \n",
       "⎢                                                                        1.0⋅L\n",
       "⎢                                                                             \n",
       "⎢             1.0⋅L3zz + 1.0⋅L4zz + 1.0⋅L6xx + 1.0⋅L7xx + 1.0⋅L8yy - 0.302⋅l3y\n",
       "⎢                                                                             \n",
       "⎢                                         -0.35790981⋅l2x + 1.0⋅l3x - 0.1⋅m₃ +\n",
       "⎢                                                                             \n",
       "⎢                                                   1.0⋅l3y + 1.0⋅l6z + 0.151⋅\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                           1.0⋅l2x + 1.0⋅l5x + 0.2794⋅m₃ + 0.\n",
       "⎢                                                                             \n",
       "⎢                  -1.0⋅L3zz - 1.0⋅L4zz - 1.0⋅L6xx + 1.0⋅L6zz + 0.302⋅l3y - 0.\n",
       "⎢                                                                             \n",
       "⎢                                                                        1.0⋅L\n",
       "⎢                                                                             \n",
       "⎢                                                                  1.0⋅L3xy + \n",
       "⎢                                                                             \n",
       "⎢                        1.0⋅L3zz + 1.0⋅L4zz + 1.0⋅L6yy - 0.302⋅l3y + 0.01⋅m₅ \n",
       "⎢                                                                             \n",
       "⎢                                                                         1.0⋅\n",
       "⎢                                                                             \n",
       "⎢                                                                        1.0⋅L\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                  1.0⋅L2xz + \n",
       "⎢                                                                             \n",
       "⎢                                                                   1.0⋅L3xz +\n",
       "⎢                                                                             \n",
       "⎢                                                                        1.0⋅L\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢        1.0⋅L1zz + 1.0⋅L2xx + 1.0⋅L3xx - 1.0⋅L3zz + 1.0⋅L4xx - 1.0⋅L4zz + 1.0\n",
       "⎢                                                                             \n",
       "⎢                  1.0⋅L3zz + 1.0⋅L4zz + 1.0⋅L6xx + 1.0⋅L7yy - 0.302⋅l3y + 0.0\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                           0.35790981⋅l2x + 1.0⋅l4x + 0.1⋅m₃ \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢               -1.0⋅L3xx + 1.0⋅L3yy + 1.0⋅L3zz - 1.0⋅L4xx + 1.0⋅L4yy + 1.0⋅L4\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                1.0⋅L2zz + 1.0⋅L5zz + 0.07806436⋅m₃ + 0.07806\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢1.0⋅L1zz + 1.0⋅L2yy + 1.0⋅L3xx - 1.0⋅L3zz + 1.0⋅L4xx - 1.0⋅L4zz + 1.0⋅L5yy + \n",
       "⎢                                                                             \n",
       "⎢                                                                         1.0⋅\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎣                                                                             \n",
       "\n",
       " 1.0⋅L9xy                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L9xz                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L9yz                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L8yz                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L8xy                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L8xz                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L7xy                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L8yy + 1.0⋅L9yy                                                          \n",
       "                                                                              \n",
       " 1.0⋅L9zz                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L7xz                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L7yz                                                                     \n",
       "                                                                              \n",
       " 1.0⋅l9x                                                                      \n",
       "                                                                              \n",
       " 1.0⋅L8yy + 1.0⋅L9xx                                                          \n",
       "                                                                              \n",
       " 1.0⋅l9y                                                                      \n",
       "                                                                              \n",
       "l8y + 1.0⋅l9z                                                                 \n",
       "                                                                              \n",
       " 1.0⋅l8x                                                                      \n",
       "                                                                              \n",
       " 1.0⋅L6xz                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L8yy + 1.0⋅L8zz                                                          \n",
       "                                                                              \n",
       "l7y + 1.0⋅l8z                                                                 \n",
       "                                                                              \n",
       " 1.0⋅L6xy                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L6yz                                                                     \n",
       "                                                                              \n",
       " 1.0⋅l7x                                                                      \n",
       "                                                                              \n",
       " 1.0⋅l6x                                                                      \n",
       "                                                                              \n",
       "l6y - 1.0⋅l7z                                                                 \n",
       "                                                                              \n",
       "7zz + 1.0⋅L8yy                                                                \n",
       "                                                                              \n",
       " + 0.01⋅m₅ + 0.11005925⋅m₆ + 0.11005925⋅m₇ + 0.11005925⋅m₈ + 0.11005925⋅m₉    \n",
       "                                                                              \n",
       " 0.2645⋅m₆ + 0.2645⋅m₇ + 0.2645⋅m₈ + 0.2645⋅m₉                                \n",
       "                                                                              \n",
       "m₆ + 0.151⋅m₇ + 0.151⋅m₈ + 0.151⋅m₉                                           \n",
       "                                                                              \n",
       " 1.0⋅l5y                                                                      \n",
       "                                                                              \n",
       "2794⋅m₆ + 0.2794⋅m₇ + 0.2794⋅m₈ + 0.2794⋅m₉                                   \n",
       "                                                                              \n",
       "01⋅m₅ - 0.11005925⋅m₆ - 0.11005925⋅m₇ - 0.11005925⋅m₈ - 0.11005925⋅m₉         \n",
       "                                                                              \n",
       "2xy + 1.0⋅L5xy                                                                \n",
       "                                                                              \n",
       "1.0⋅L4xy + 0.3645⋅l3y                                                         \n",
       "                                                                              \n",
       "+ 0.11005925⋅m₆ + 0.11005925⋅m₇ + 0.11005925⋅m₈ + 0.11005925⋅m₉               \n",
       "                                                                              \n",
       "Fv₃ + 1.0⋅Fv₅                                                                 \n",
       "                                                                              \n",
       "2yz + 1.0⋅L5yz                                                                \n",
       "                                                                              \n",
       "  1.0⋅K₆                                                                      \n",
       "                                                                              \n",
       "1.0⋅L5xz - 0.2794⋅l3z                                                         \n",
       "                                                                              \n",
       " 1.0⋅L4xz - 0.1⋅l5z                                                           \n",
       "                                                                              \n",
       "3yz + 1.0⋅L4yz                                                                \n",
       "                                                                              \n",
       " 1.0⋅Fv₆                                                                      \n",
       "                                                                              \n",
       "⋅L5xx - 0.01⋅m₅ - 0.13286025⋅m₆ - 0.13286025⋅m₇ - 0.13286025⋅m₈ - 0.13286025⋅m\n",
       "                                                                              \n",
       "1⋅m₅ + 0.11005925⋅m₆ + 0.11005925⋅m₇ + 0.11005925⋅m₈ + 0.11005925⋅m₉          \n",
       "                                                                              \n",
       " 1.0⋅l4y                                                                      \n",
       "                                                                              \n",
       "+ 0.1⋅m₅ + 0.1⋅m₆ + 0.1⋅m₇ + 0.1⋅m₈ + 0.1⋅m₉                                  \n",
       "                                                                              \n",
       " 1.0⋅Fv₉                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fv₇                                                                      \n",
       "                                                                              \n",
       "zz + 0.02⋅m₅ + 0.2657205⋅m₆ + 0.2657205⋅m₇ + 0.2657205⋅m₈ + 0.2657205⋅m₉      \n",
       "                                                                              \n",
       " 1.0⋅Fv₈                                                                      \n",
       "                                                                              \n",
       "  1.0⋅K₈                                                                      \n",
       "                                                                              \n",
       "436⋅m₆ + 0.07806436⋅m₇ + 0.07806436⋅m₈ + 0.07806436⋅m₉                        \n",
       "                                                                              \n",
       "  1.0⋅K₇                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fv₁                                                                      \n",
       "                                                                              \n",
       "  1.0⋅K₁                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fv₂                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fv₄                                                                      \n",
       "                                                                              \n",
       "0.07806436⋅m₃ - 0.01⋅m₅ - 0.05479589⋅m₆ - 0.05479589⋅m₇ - 0.05479589⋅m₈ - 0.05\n",
       "                                                                              \n",
       "Fc₃ + 1.0⋅Fc₅                                                                 \n",
       "                                                                              \n",
       " 1.0⋅Fc₆                                                                      \n",
       "                                                                              \n",
       " 1.0⋅l2y                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fc₈                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fc₉                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fc₂                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fc₁                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fc₄                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fc₇                                                                      \n",
       "\n",
       "         ⎤\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "₉        ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "479589⋅m₉⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎥\n",
       "         ⎦"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.Matrix(dyn.base_param)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saved 66 parameters\n"
     ]
    }
   ],
   "source": [
    "from data import RobotModel\n",
    "\n",
    "# Data to be saved\n",
    "robot_model = RobotModel(dyn)\n",
    "\n",
    "# Save\n",
    "save_data(model_folder, model_name, robot_model)\n",
    "print('Saved {} parameters'.format(len(robot_model.base_param)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "# 3 - Excitation trajectory optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_name = 'mtm'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from utils import load_data\n",
    "model_folder = 'data/' + model_name + '/model/'\n",
    "robot_model = load_data(model_folder, model_name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create trajectory optimizer object, with H matrix, foourier order, base frequency, joint constraints and cartisian constraints as input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#trajectory_name = 'one'\n",
    "# trajectory_name = 'two'\n",
    "trajectory_name = 'three'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "joint constraint number: 8\n",
      "cartesian constraint number: 0\n",
      "constraint number: 32\n",
      "frames_constrained: []\n",
      "Condition number: 90.9681102027\n",
      "Condition number: 90.9681090284\n",
      "Condition number: 78.2257954513\n",
      "Condition number: 52.2442858246\n",
      "Condition number: 47.7568001076\n",
      "Condition number: 52.3999783674\n",
      "Condition number: 59.4557245605\n",
      "Condition number: 69.3717483911\n",
      "Condition number: 127.007508549\n",
      "Condition number: 381.132708489\n",
      "Condition number: 293.37927514\n",
      "Condition number: 274.475499215\n",
      "Condition number: 271.652179114\n",
      "Condition number: 263.05927703\n",
      "Condition number: 258.306014397\n",
      "Condition number: 256.771012941\n",
      "Condition number: 256.739417144\n",
      "Condition number: 256.406138908\n",
      "Condition number: 254.176811067\n",
      "Condition number: 252.539061631\n",
      "Condition number: 251.169946299\n",
      "Condition number: 250.063250132\n",
      "Condition number: 249.92688399\n",
      "Condition number: 249.739872645\n",
      "Condition number: 249.325158671\n",
      "Condition number: 249.123159558\n",
      "Condition number: 249.005872155\n",
      "Condition number: 248.685794372\n",
      "Condition number: 248.67606807\n",
      "Condition number: 248.664912322\n",
      "Condition number: 248.63641503\n",
      "Condition number: 248.633642022\n",
      "Condition number: 248.61892738\n",
      "Condition number: 291.544681772\n",
      "Condition number: 248.617254529\n",
      "Condition number: 248.614253659\n",
      "Condition number: 248.613951805\n",
      "Condition number: 248.340148586\n",
      "Condition number: 247.945827997\n",
      "Condition number: 247.930522168\n",
      "Condition number: 247.922263116\n",
      "Condition number: 247.758988453\n",
      "Condition number: 247.755633165\n",
      "Condition number: 247.420842019\n",
      "Condition number: 247.417409359\n",
      "Condition number: 247.391615359\n",
      "Condition number: 247.377784585\n",
      "Condition number: 246.94345011\n",
      "Condition number: 246.879941705\n",
      "Condition number: 246.83944852\n",
      "Condition number: 246.834160631\n",
      "Condition number: 246.815976507\n",
      "Condition number: 246.815937021\n",
      "x: [-0.16713219 -0.055767    0.19451049 -0.34817693  0.38810819 -0.09429936\n",
      "  1.09407854  0.08059524 -0.07370908 -0.08347017  0.43251408 -0.85211213\n",
      " -2.0013609   0.32964011  0.12384932  0.11871307  0.10557705 -0.47659694\n",
      " -0.4631624   0.76330089  0.10537441  0.25501539 -0.21327137 -0.25374023\n",
      "  0.10320046 -0.88105194  0.28723604 -0.03797165  0.08326475  0.1957296\n",
      " -0.02838298 -0.5617864   0.52091285  0.02031051  0.19811357  0.14338303\n",
      "  0.44615244 -0.06574065  0.05387045  1.23720411 -0.51134555  0.17103669\n",
      " -0.71715279  0.14151604 -0.41510082 -1.8732809   0.37471788  0.20545907\n",
      " -1.10919323 -1.07879143  0.29156735  0.63337166  1.20936595  0.19697491\n",
      " -0.94986599 -0.39747053 -1.36475216 -0.62923632  1.94574031  0.05470338\n",
      " -1.01791797  0.34213888 -1.44878223 -0.06891586  1.59377626 -0.05733615\n",
      " -0.02414178 -0.05134831  0.02239576 -0.08165929 -0.14344892  0.12886094\n",
      "  0.05970928  0.16321728  0.15032425  0.14517555  0.02699639  0.21080956\n",
      "  1.77784309  1.6753215   3.27616227 -0.95319742  0.4474786   0.53490816\n",
      "  1.26683539  2.28294894  1.45825319 -3.5573126  -1.35351573 -4.77463665\n",
      "  0.18962812]\n"
     ]
    }
   ],
   "source": [
    "from numpy import deg2rad\n",
    "\n",
    "optimal_trajectory_folder = 'data/optimal_trajectory/'\n",
    "trajectory_folder = 'data/' + model_name +'/optimal_trajectory/'\n",
    "\n",
    "base_freq = 0.1\n",
    "fourier_order = 6\n",
    "\n",
    "cartesian_constraints = []\n",
    "\n",
    "\n",
    "joint_constraints = [(qmd1,  deg2rad(-57), deg2rad(29), deg2rad(-160), deg2rad(160)),\n",
    "                     (qmd2,  deg2rad(-10), deg2rad(60), deg2rad(-180), deg2rad(180)),\n",
    "                     (qmd30, deg2rad(-30), deg2rad(30), deg2rad(-180), deg2rad(180)),\n",
    "                     (qmd4,  deg2rad(-40), deg2rad(195), deg2rad(-360), deg2rad(360)),\n",
    "                     (qmd5,  deg2rad(-87), deg2rad(180), deg2rad(-360), deg2rad(360)),\n",
    "                     (qmd6,  deg2rad(-40), deg2rad(38), deg2rad(-360), deg2rad(360)),\n",
    "                     (qmd7,  deg2rad(-460), deg2rad(450), deg2rad(-720), deg2rad(720)),\n",
    "                     (qmd31, deg2rad(-9), deg2rad(39), deg2rad(-360), deg2rad(360))]\n",
    "\n",
    "    \n",
    "traj_optimizer = TrajOptimizer(robot_model, fourier_order, base_freq,\n",
    "                               joint_constraints=joint_constraints,\n",
    "                               cartesian_constraints = cartesian_constraints)\n",
    "                                                                                                 \n",
    "                                                                                                                     \n",
    "traj_optimizer.optimize()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left [ q_{1}, \\quad q_{2}, \\quad q_{3}, \\quad q_{4}, \\quad q_{5}, \\quad q_{6}, \\quad q_{7}\\right ]$$"
      ],
      "text/plain": [
       "[q₁, q₂, q₃, q₄, q₅, q₆, q₇]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "robot_model.coordinates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "reg_norm_mat = traj_optimizer.calc_normalize_mat()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot optimal excitation trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "traj_optimizer.calc_frame_traj()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "traj_plotter = TrajPlotter(traj_optimizer.fourier_traj,traj_optimizer.frame_traj,\n",
    "                           traj_optimizer.const_frame_ind, robot_model.coordinates)\n",
    "traj_plotter.plot_desired_traj(traj_optimizer.x_result)\n",
    "\n",
    "# traj_plotter.plot_frame_traj(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Save trajectory for later use"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "dof_order_bf_x_norm = (traj_optimizer.fourier_traj.dof, fourier_order,\n",
    "                       base_freq, traj_optimizer.x_result, reg_norm_mat)\n",
    "save_data(trajectory_folder, trajectory_name, dof_order_bf_x_norm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "<tr><td>joint</td><td>qo     </td><td>a1     </td><td>a2     </td><td>a3     </td><td>a4     </td><td>a5     </td><td>a6     </td><td>b1    </td><td>b2     </td><td>b3     </td><td>b4     </td><td>b5     </td><td>b6     </td></tr>\n",
       "<tr><td>q1   </td><td>-0.1671</td><td>-0.0558</td><td>0.1945 </td><td>-0.3482</td><td>0.3881 </td><td>-0.0943</td><td>1.0941 </td><td>0.0806</td><td>-0.0737</td><td>-0.0835</td><td>0.4325 </td><td>-0.8521</td><td>-2.0014</td></tr>\n",
       "<tr><td>q2   </td><td>0.3296 </td><td>0.1238 </td><td>0.1187 </td><td>0.1056 </td><td>-0.4766</td><td>-0.4632</td><td>0.7633 </td><td>0.1054</td><td>0.255  </td><td>-0.2133</td><td>-0.2537</td><td>0.1032 </td><td>-0.8811</td></tr>\n",
       "<tr><td>q3   </td><td>0.2872 </td><td>-0.038 </td><td>0.0833 </td><td>0.1957 </td><td>-0.0284</td><td>-0.5618</td><td>0.5209 </td><td>0.0203</td><td>0.1981 </td><td>0.1434 </td><td>0.4462 </td><td>-0.0657</td><td>0.0539 </td></tr>\n",
       "<tr><td>q4   </td><td>1.2372 </td><td>-0.5113</td><td>0.171  </td><td>-0.7172</td><td>0.1415 </td><td>-0.4151</td><td>-1.8733</td><td>0.3747</td><td>0.2055 </td><td>-1.1092</td><td>-1.0788</td><td>0.2916 </td><td>0.6334 </td></tr>\n",
       "<tr><td>q5   </td><td>1.2094 </td><td>0.197  </td><td>-0.9499</td><td>-0.3975</td><td>-1.3648</td><td>-0.6292</td><td>1.9457 </td><td>0.0547</td><td>-1.0179</td><td>0.3421 </td><td>-1.4488</td><td>-0.0689</td><td>1.5938 </td></tr>\n",
       "<tr><td>q6   </td><td>-0.0573</td><td>-0.0241</td><td>-0.0513</td><td>0.0224 </td><td>-0.0817</td><td>-0.1434</td><td>0.1289 </td><td>0.0597</td><td>0.1632 </td><td>0.1503 </td><td>0.1452 </td><td>0.027  </td><td>0.2108 </td></tr>\n",
       "<tr><td>q7   </td><td>1.7778 </td><td>1.6753 </td><td>3.2762 </td><td>-0.9532</td><td>0.4475 </td><td>0.5349 </td><td>1.2668 </td><td>2.2829</td><td>1.4583 </td><td>-3.5573</td><td>-1.3535</td><td>-4.7746</td><td>0.1896 </td></tr>\n",
       "</tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import HTML, display\n",
    "import tabulate\n",
    "\n",
    "table = []\n",
    "table.append([\"joint\", 'qo'] +\n",
    "             [\"a\"+str(i+1) for i in range(fourier_order)] +\n",
    "             [\"b\"+str(i+1) for i in range(fourier_order)])\n",
    "for i in range(traj_optimizer.fourier_traj.dof):\n",
    "    line = []\n",
    "    line.append(robot_model.coordinates[i])\n",
    "    line += np.round(traj_optimizer.x_result[i*(1 + fourier_order*2): (i+1)*(1 + fourier_order*2)], 4).tolist()\n",
    "    table.append(line)\n",
    "\n",
    "display(HTML(tabulate.tabulate(table, tablefmt='html')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "# Data processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "ename": "ImportError",
     "evalue": "cannot import name plot_meas_2pred_tau",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m\u001b[0m",
      "\u001b[0;31mImportError\u001b[0mTraceback (most recent call last)",
      "\u001b[0;32m<ipython-input-61-f7d8b394c0de>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0midentification\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mload_trajectory_data\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdiff_and_filt_data\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mplot_trajectory_data\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mplot_meas_pred_tau\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mplot_meas_2pred_tau\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgen_regressor\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mImportError\u001b[0m: cannot import name plot_meas_2pred_tau"
     ]
    }
   ],
   "source": [
    "from identification import load_trajectory_data, diff_and_filt_data, plot_trajectory_data, plot_meas_pred_tau, plot_meas_2pred_tau, gen_regressor\n",
    "import copy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load robot model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dof: 7\n",
      "Fourier order: 6\n",
      "Base frequency: 0.1\n"
     ]
    }
   ],
   "source": [
    "# Names as Arguments\n",
    "model_name = 'mtm_fontanelli'\n",
    "#model_name = 'mtm_2spring_tendon'\n",
    "training_trajectory_name = 'one'\n",
    "\n",
    "\n",
    "model_folder = 'data/' + model_name + '/model/'\n",
    "robot_model = load_data(model_folder,model_name)\n",
    "\n",
    "\n",
    "trajectory_folder = 'data/' + model_name +'/optimal_trajectory/'\n",
    "dof, fourier_order, base_freq, traj_optimizer_result, reg_norm_mat = load_data(trajectory_folder,\n",
    "                                                                               training_trajectory_name)\n",
    "print(\"dof: {}\".format(dof))\n",
    "print(\"Fourier order: {}\".format(fourier_order))\n",
    "print(\"Base frequency: {}\".format(base_freq))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load traning data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(<type 'numpy.ndarray'>, (5999, 21))\n"
     ]
    }
   ],
   "source": [
    "# training_trajectory_name = 'one'\n",
    "\n",
    "results_folder = 'data/' + model_name +'/measured_trajectory/'\n",
    "training_results_data_file = results_folder + training_trajectory_name + '_results.csv'\n",
    "\n",
    "trajectory_sampling_rate = 200\n",
    "t_train, q_raw_train, dq_raw_train, tau_raw_train = load_trajectory_data(training_results_data_file,\n",
    "                                                                   trajectory_sampling_rate)\n",
    "# remove the cable part of the joint 4\n",
    "# from high to low\n",
    "p = np.array([0.0004877, -0.0037149, 0.0067497, 0.008519, -0.0201475, -0.025265, 0.048095, 0.00255])\n",
    "#p = p[::-1]\n",
    "\n",
    "# disable polynomial friction modeling\n",
    "# qm4_raw_train = 0.6697*q_raw_train[:,1] - 0.6697*q_raw_train[:,2] + q_raw_train[:,3]\n",
    "# tau_cable4_train = p[0]*qm4_raw_train**7 + p[1]*qm4_raw_train**6 + p[2]*qm4_raw_train**5\\\n",
    "# + p[3]*qm4_raw_train**4 + p[4]*qm4_raw_train**3 + p[5]*qm4_raw_train**2\\\n",
    "# + p[6]*qm4_raw_train + p[7]\n",
    "# tau_raw_train[:,1] -= 0.6697*tau_cable4_train\n",
    "# tau_raw_train[:,2] += 0.6697*tau_cable4_train\n",
    "# tau_raw_train[:,3] -= tau_cable4_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.    , -1.    ,  0.6697],\n",
       "       [ 0.    ,  1.    , -0.6697],\n",
       "       [ 0.    ,  0.    ,  1.    ]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([[1.0, 0, 0], [-1.0, 1.0, 0], [0.6697, -0.6697, 1.0]]).transpose()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from trajectory_optimization import FourierTraj\n",
    "fourier_traj_train = FourierTraj(dof, fourier_order, base_freq, sample_num_per_period=20)\n",
    "traj_plotter_train = TrajPlotter(fourier_traj_train, coordinates=robot_model.coordinates)\n",
    "traj_plotter_train.plot_desired_traj(traj_optimizer_result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load test data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(<type 'numpy.ndarray'>, (5999, 21))\n"
     ]
    }
   ],
   "source": [
    "test_trajectory_name = 'two'\n",
    "\n",
    "results_folder = 'data/' + model_name +'/measured_trajectory/'\n",
    "test_results_data_file = results_folder + test_trajectory_name + '_results.csv'\n",
    "\n",
    "trajectory_sampling_rate = 200\n",
    "t_test, q_raw_test, dq_raw_test, tau_raw_test = load_trajectory_data(test_results_data_file,\n",
    "                                                                trajectory_sampling_rate)\n",
    "# remove the cable part of the joint 4\n",
    "# from high to low\n",
    "p = np.array([0.0004877, -0.0037149, 0.0067497, 0.008519, -0.0201475, -0.025265, 0.048095, 0.00255])\n",
    "# p = p[::-1]\n",
    "\n",
    "#disable polynomial friction modeling\n",
    "# qm4_raw_test = 0.6697*q_raw_test[:,1] - 0.6697*q_raw_test[:,2] + q_raw_test[:,3]\n",
    "# tau_cable4_test = p[0]*qm4_raw_test**7 + p[1]*qm4_raw_test**6 + p[2]*qm4_raw_test**5\\\n",
    "# + p[3]*qm4_raw_test**4 + p[4]*qm4_raw_test**3 + p[5]*qm4_raw_test**2\\\n",
    "# + p[6]*qm4_raw_test + p[7]\n",
    "# tau_raw_test[:,1] -= 0.6697*tau_cable4_test\n",
    "# tau_raw_test[:,2] += 0.6697*tau_cable4_test\n",
    "# tau_raw_test[:,3] -= tau_cable4_test\n",
    "\n",
    "# plt.plot(qm4_raw_test, tau_cable4_test)\n",
    "# plt.xlabel('Time (s)')\n",
    "# plt.ylabel('Joint torque (Nm)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate filter cut-off frequency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cut frequency: [1.8]\n"
     ]
    }
   ],
   "source": [
    "# times of the highest frequency in the Fourier series\n",
    "\n",
    "fc_mult = [3]\n",
    "#fc_mult = [5, 5, 5, 3, 4, 4, 4]\n",
    "\n",
    "#fc_mult = 4\n",
    "fc = np.array(fc_mult)*base_freq* fourier_order \n",
    "\n",
    "print(\"Cut frequency: {}\".format(fc))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Differentiation and filtering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Traning data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "q_raw shape: (5999, 7)\n",
      "plot shape: 470\n"
     ]
    }
   ],
   "source": [
    "cut_num = 200\n",
    "t_cut_train, q_f_train, dq_f_train, ddq_f_train, tau_f_train, q_raw_cut_train, tau_raw_cut_train =\\\n",
    "    diff_and_filt_data(dof, 1.0/trajectory_sampling_rate,\n",
    "                       t_train, q_raw_train, dq_raw_train, tau_raw_train, fc, fc, fc, fc, cut_num)\n",
    "plot_trajectory_data(t_cut_train, q_raw_cut_train, q_f_train, dq_f_train, ddq_f_train,\n",
    "                     tau_raw_cut_train, tau_f_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "q_raw shape: (5999, 7)\n",
      "plot shape: 470\n"
     ]
    }
   ],
   "source": [
    "t_cut_test, q_f_test, dq_f_test, ddq_f_test,tau_f_test, q_raw_cut_test, tau_raw_cut_test =\\\n",
    "    diff_and_filt_data(dof, 1.0/trajectory_sampling_rate,\n",
    "                       t_test, q_raw_test, dq_raw_test, tau_raw_test, fc, fc, fc, fc, cut_num)\n",
    "plot_trajectory_data(t_cut_test, q_raw_cut_test, q_f_test, dq_f_test, ddq_f_test,\n",
    "                     tau_raw_cut_test, tau_f_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "# Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ordinary Least Square (OLS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate regressor matrix for base parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "base_param_num = robot_model.base_num\n",
    "H_b_func = robot_model.H_b_func\n",
    "W_b_train, tau_s_train = gen_regressor(base_param_num, H_b_func, q_f_train,\n",
    "                                       dq_f_train, ddq_f_train, tau_f_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( \\left ( 39193, \\quad 66\\right ), \\quad \\left ( 39193\\right )\\right )$$"
      ],
      "text/plain": [
       "((39193, 66), (39193,))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W_b_train.shape, tau_s_train.shape\n",
    "#print np.linalg.cond(W_b_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/yan/anaconda2/envs/dynamics/lib/python2.7/site-packages/ipykernel_launcher.py:1: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    }
   ],
   "source": [
    "xb_ols = np.linalg.lstsq(W_b_train, tau_s_train)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<tbody>\n",
       "<tr><td>Base Parameter                                       </td><td>Value                  </td></tr>\n",
       "<tr><td>1.0*L9xy                                             </td><td>5.844136647811904e-05  </td></tr>\n",
       "<tr><td>1.0*L9xz                                             </td><td>6.78551845886752e-05   </td></tr>\n",
       "<tr><td>1.0*L9yz                                             </td><td>-1.4853632032201967e-05</td></tr>\n",
       "<tr><td>1.0*L8yz                                             </td><td>9.893430833028682e-05  </td></tr>\n",
       "<tr><td>1.0*L8xy                                             </td><td>-0.0003313111338781099 </td></tr>\n",
       "<tr><td>1.0*L8xz                                             </td><td>-0.0001919875016899537 </td></tr>\n",
       "<tr><td>1.0*L7xy                                             </td><td>-0.00010915975266017263</td></tr>\n",
       "<tr><td>1.0*L8xx - 1.0*L8yy + 1.0*L9yy                       </td><td>0.0010006615150471318  </td></tr>\n",
       "<tr><td>1.0*L9zz                                             </td><td>0.00016025100325793486 </td></tr>\n",
       "<tr><td>1.0*L7xz                                             </td><td>0.0004817356308339602  </td></tr>\n",
       "<tr><td>1.0*L7yz                                             </td><td>-0.00014557443718495478</td></tr>\n",
       "<tr><td>1.0*l9x                                              </td><td>-0.0002479850011651557 </td></tr>\n",
       "<tr><td>1.0*L8xx - 1.0*L8yy + 1.0*L9xx                       </td><td>0.0009952448683026773  </td></tr>\n",
       "<tr><td>1.0*l9y                                              </td><td>-0.0002610804393044404 </td></tr>\n",
       "<tr><td>1.0*l8y + 1.0*l9z                                    </td><td>0.004556155580413413   </td></tr>\n",
       "<tr><td>1.0*l8x                                              </td><td>-0.0010947599093391364 </td></tr>\n",
       "<tr><td>1.0*L6xz                                             </td><td>0.00010944617357332755 </td></tr>\n",
       "<tr><td>-1.0*L8xx + 1.0*L8yy + 1.0*L8zz                      </td><td>-0.0009537393333660946 </td></tr>\n",
       "<tr><td>1.0*l7y + 1.0*l8z                                    </td><td>-0.008718858934015548  </td></tr>\n",
       "<tr><td>1.0*L6xy                                             </td><td>-0.0005255601702960033 </td></tr>\n",
       "<tr><td>1.0*L6yz                                             </td><td>-0.000499553518391452  </td></tr>\n",
       "<tr><td>1.0*l7x                                              </td><td>0.0017304312006610686  </td></tr>\n",
       "<tr><td>1.0*l6x                                              </td><td>0.0004163710362558707  </td></tr>\n",
       "<tr><td>1.0*l6y - 1.0*l7z                                    </td><td>0.019546007805873317   </td></tr>\n",
       "<tr><td>1.0*L7zz + 1.0*L8yy                                  </td><td>-0.0008127836695423546 </td></tr>\n",
       "<tr><td>1.0*L3zz + 1.0*L4zz + 1.0*L6xx + 1.0*L7xx + 1.0*L8...</td><td>0.1387313922158547     </td></tr>\n",
       "<tr><td>-0.35790981*l2x + 1.0*l3x - 0.1*m3 + 0.2645*m6 + 0...</td><td>0.27716343678402433    </td></tr>\n",
       "<tr><td>1.0*l3y + 1.0*l6z + 0.151*m6 + 0.151*m7 + 0.151*m8...</td><td>-0.08610698255775832   </td></tr>\n",
       "<tr><td>1.0*l5y                                              </td><td>-0.22960159915480194   </td></tr>\n",
       "<tr><td>1.0*l2x + 1.0*l5x + 0.2794*m3 + 0.2794*m6 + 0.2794...</td><td>0.04824701728034167    </td></tr>\n",
       "<tr><td>-1.0*L3zz - 1.0*L4zz - 1.0*L6xx + 1.0*L6zz + 0.302...</td><td>-0.13769161402387853   </td></tr>\n",
       "<tr><td>1.0*L2xy + 1.0*L5xy                                  </td><td>0.006251992705141508   </td></tr>\n",
       "<tr><td>1.0*L3xy + 1.0*L4xy + 0.3645*l3y                     </td><td>-0.053561505627052385  </td></tr>\n",
       "<tr><td>1.0*L3zz + 1.0*L4zz + 1.0*L6yy - 0.302*l3y + 0.01*...</td><td>0.14053823757912556    </td></tr>\n",
       "<tr><td>1.0*Fv3 + 1.0*Fv5                                    </td><td>0.012409766859223249   </td></tr>\n",
       "<tr><td>1.0*L2yz + 1.0*L5yz                                  </td><td>0.005970987962788563   </td></tr>\n",
       "<tr><td>1.0*K6                                               </td><td>0.012511711719269175   </td></tr>\n",
       "<tr><td>1.0*L2xz + 1.0*L5xz - 0.2794*l3z                     </td><td>0.006178952049264743   </td></tr>\n",
       "<tr><td>1.0*L3xz + 1.0*L4xz - 0.1*l5z                        </td><td>-0.002232090326618943  </td></tr>\n",
       "<tr><td>1.0*L3yz + 1.0*L4yz                                  </td><td>-0.0027656938494838596 </td></tr>\n",
       "<tr><td>1.0*Fv6                                              </td><td>0.00557171424239223    </td></tr>\n",
       "<tr><td>1.0*L1zz + 1.0*L2xx + 1.0*L3xx - 1.0*L3zz + 1.0*L4...</td><td>-0.05705927368115067   </td></tr>\n",
       "<tr><td>1.0*L3zz + 1.0*L4zz + 1.0*L6xx + 1.0*L7yy - 0.302*...</td><td>0.1379378565312076     </td></tr>\n",
       "<tr><td>1.0*l4y                                              </td><td>0.1071883553668344     </td></tr>\n",
       "<tr><td>0.35790981*l2x + 1.0*l4x + 0.1*m3 + 0.1*m5 + 0.1*m...</td><td>-0.25087480290980335   </td></tr>\n",
       "<tr><td>1.0*Fv9                                              </td><td>7.852560885275464e-05  </td></tr>\n",
       "<tr><td>1.0*Fv7                                              </td><td>0.0008413118020786897  </td></tr>\n",
       "<tr><td>-1.0*L3xx + 1.0*L3yy + 1.0*L3zz - 1.0*L4xx + 1.0*L...</td><td>0.2851389802987026     </td></tr>\n",
       "<tr><td>1.0*Fv8                                              </td><td>-0.0029577172299799807 </td></tr>\n",
       "<tr><td>1.0*K8                                               </td><td>0.0048431738482986805  </td></tr>\n",
       "<tr><td>1.0*L2zz + 1.0*L5zz + 0.07806436*m3 + 0.07806436*m...</td><td>0.11112149789783884    </td></tr>\n",
       "<tr><td>1.0*K7                                               </td><td>-0.04382485099389834   </td></tr>\n",
       "<tr><td>1.0*Fv1                                              </td><td>0.06140646260664892    </td></tr>\n",
       "<tr><td>1.0*K1                                               </td><td>0.30493217552883933    </td></tr>\n",
       "<tr><td>1.0*Fv2                                              </td><td>0.09544920297444663    </td></tr>\n",
       "<tr><td>1.0*Fv4                                              </td><td>0.06745162785125487    </td></tr>\n",
       "<tr><td>1.0*L1zz + 1.0*L2yy + 1.0*L3xx - 1.0*L3zz + 1.0*L4...</td><td>0.0014920371159599316  </td></tr>\n",
       "<tr><td>1.0*Fc3 + 1.0*Fc5                                    </td><td>0.0021248377210211725  </td></tr>\n",
       "<tr><td>1.0*Fc6                                              </td><td>0.04274759924817436    </td></tr>\n",
       "<tr><td>1.0*l2y                                              </td><td>0.2399258091563413     </td></tr>\n",
       "<tr><td>1.0*Fc8                                              </td><td>0.005961012823807547   </td></tr>\n",
       "<tr><td>1.0*Fc9                                              </td><td>0.0011113210964038282  </td></tr>\n",
       "<tr><td>1.0*Fc2                                              </td><td>0.029266338836925015   </td></tr>\n",
       "<tr><td>1.0*Fc1                                              </td><td>0.04319114041337405    </td></tr>\n",
       "<tr><td>1.0*Fc4                                              </td><td>0.04412821037697757    </td></tr>\n",
       "<tr><td>1.0*Fc7                                              </td><td>0.007381450041830351   </td></tr>\n",
       "</tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#sympy.Matrix.hstack(sympy.Matrix(robot_model.base_param), sympy.Matrix(xb_ols))\n",
    "\n",
    "from IPython.display import HTML, display\n",
    "import tabulate\n",
    "\n",
    "table = [[\"Base Parameter\", \"Value\"]]\n",
    "\n",
    "for i in range(robot_model.base_num):\n",
    "    param_str = str(sympy.Matrix(robot_model.base_param)[i])\n",
    "    max_disp_len = 50\n",
    "    line = [param_str if len(param_str) <= max_disp_len \n",
    "            else param_str[:max_disp_len] + '...', xb_ols[i]]\n",
    "    #['%.7s ...'%b if len(str(b)) > 7 else str(b)\n",
    "    table.append(line)\n",
    "\n",
    "display(HTML(tabulate.tabulate(table, tablefmt='html')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare measured torque and predicted torque on the training set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate predicted torque"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "tau_p_train = np.zeros(tau_f_train.shape)\n",
    "tau_ps_train = W_b_train.dot(xb_ols)\n",
    "for i in range(dof):\n",
    "    tau_p_train[:, i] = tau_ps_train[i::dof]\n",
    "\n",
    "# add cable torque back\n",
    "# qm4_f_train = 0.6697*q_f_train[:,1] - 0.6697*q_f_train[:,2] + q_f_train[:,3]\n",
    "# tau_cable4_f_train = p[0]*qm4_f_train**7 + p[1]*qm4_f_train**6 + p[2]*qm4_f_train**5\\\n",
    "# + p[3]*qm4_f_train**4 + p[4]*qm4_f_train**3 + p[5]*qm4_f_train**2\\\n",
    "# + p[6]*qm4_f_train + p[7]\n",
    "tau_f_with_cable_train = copy.deepcopy(tau_f_train);\n",
    "# tau_f_with_cable_train[:,1] = tau_f_train[:,1] + 0.6697*tau_cable4_f_train\n",
    "# tau_f_with_cable_train[:,2] = tau_f_train[:,2] - 0.6697*tau_cable4_f_train\n",
    "# tau_f_with_cable_train[:,3] = tau_f_train[:,3] + tau_cable4_f_train\n",
    "tau_p_with_cable_train = copy.deepcopy(tau_p_train);\n",
    "# tau_p_with_cable_train[:,1] = tau_p_train[:,1] + 0.6697*tau_cable4_f_train\n",
    "# tau_p_with_cable_train[:,2] = tau_p_train[:,2] - 0.6697*tau_cable4_f_train\n",
    "# tau_p_with_cable_train[:,3] = tau_p_train[:,3] + tau_cable4_f_train"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluate regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variance of regression error using OLS:\n",
      "0.00015743546121234497\n",
      "standard deviation of xb using OLS:\n",
      "[3.75239888e-06 2.24965125e-06 2.22331934e-06 1.71854555e-05\n",
      " 1.60319036e-05 2.05884050e-05 1.98689121e-05 3.42780282e-05\n",
      " 5.80516994e-06 1.66539016e-05 2.30476322e-05 7.89100658e-06\n",
      " 3.42623830e-05 8.05135766e-06 4.96227365e-05 2.82956890e-05\n",
      " 4.18092278e-05 5.09140278e-05 2.46419957e-05 1.23828230e-04\n",
      " 3.58900596e-05 5.11132243e-05 3.82497109e-05 5.26402260e-05\n",
      " 3.85212314e-05 6.10323641e-04 7.04235328e-04 1.68055008e-03\n",
      " 5.19567075e-03 9.68111037e-05 6.11327625e-04 2.27832611e-04\n",
      " 6.43911286e-04 6.02392203e-04 5.30944353e-04 1.33081321e-04\n",
      " 1.33337668e-04 1.00821203e-04 2.69949971e-04 1.51776003e-04\n",
      " 1.15271989e-04 8.17293288e-04 6.10258411e-04 1.70285886e-03\n",
      " 7.01318878e-04 5.15791239e-05 1.25036537e-04 1.32773710e-03\n",
      " 6.89560486e-04 5.30174149e-04 1.53190727e-04 1.91372194e-04\n",
      " 4.90823323e-04 9.45001591e-04 4.74101672e-04 8.91630390e-04\n",
      " 1.29915549e-03 2.55390867e-04 2.07517728e-04 5.19740288e-03\n",
      " 3.52562085e-04 2.87326875e-04 2.80746527e-04 3.92165022e-04\n",
      " 3.30844222e-04 3.03699519e-04]\n",
      "percentage of standard deviation of xb using OLS: \n",
      "[0.06420793 0.03315371 0.14968186 0.17370572 0.04838927 0.10723826\n",
      " 0.18201683 0.03425537 0.03622548 0.03457062 0.15832197 0.0318205\n",
      " 0.03442608 0.03083861 0.01089136 0.02584648 0.38200721 0.05338359\n",
      " 0.00282629 0.2356119  0.07184427 0.02953785 0.09186449 0.00269314\n",
      " 0.0473942  0.00439932 0.00254087 0.019517   0.02262907 0.00200657\n",
      " 0.00443983 0.0364416  0.0120219  0.00428632 0.04278439 0.02228799\n",
      " 0.01065703 0.01631688 0.12094043 0.05487809 0.02068878 0.01432358\n",
      " 0.00442415 0.0158866  0.00279549 0.65684462 0.14862092 0.00465646\n",
      " 0.23313942 0.10946833 0.00137859 0.00436675 0.00799302 0.00309906\n",
      " 0.00496706 0.01321881 0.87072599 0.12019312 0.00485449 0.02166254\n",
      " 0.05914466 0.25854533 0.00959281 0.00907976 0.00749734 0.04114361]\n"
     ]
    }
   ],
   "source": [
    "var_regression_error_ols = np.linalg.norm(tau_ps_train - tau_s_train) / \\\n",
    "                        (tau_ps_train.size - base_param_num)\n",
    "print(\"variance of regression error using OLS:\")\n",
    "print(var_regression_error_ols)\n",
    "\n",
    "std_dev_xb_ols = np.sqrt(np.diag(var_regression_error_ols *\n",
    "                                 np.linalg.inv(W_b_train.transpose().dot(W_b_train))))\n",
    "print(\"standard deviation of xb using OLS:\")\n",
    "print(std_dev_xb_ols)\n",
    "\n",
    "pct_std_dev_xb_ols = std_dev_xb_ols / np.abs(xb_ols)\n",
    "print(\"percentage of standard deviation of xb using OLS: \")\n",
    "print(pct_std_dev_xb_ols)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot measured torque and predicted torque"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "plot_data_num = int(1 / base_freq * trajectory_sampling_rate)\n",
    "plot_meas_pred_tau(t_cut_train[:plot_data_num], tau_f_with_cable_train[:plot_data_num, :],\n",
    "                   tau_p_with_cable_train[:plot_data_num, :],\n",
    "                   robot_model.coordinates_joint_type,\n",
    "                   robot_model.coordinates)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare measured torque and predicted torque on the test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "W_b_test, tau_s_test = gen_regressor(base_param_num, H_b_func, q_f_test,\n",
    "                                       dq_f_test, ddq_f_test, tau_f_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "tau_p_test = np.zeros(tau_f_test.shape)\n",
    "tau_ps_test = W_b_test.dot(xb_ols)\n",
    "for i in range(dof):\n",
    "    tau_p_test[:, i] = tau_ps_test[i::dof]\n",
    "\n",
    "    # add cable torque back\n",
    "# qm4_f_test = 0.6697*q_f_test[:,1] - 0.6697*q_f_test[:,2] + q_f_test[:,3]\n",
    "# tau_cable4_f_test = p[0]*qm4_f_test**7 + p[1]*qm4_f_test**6 + p[2]*qm4_f_test**5\\\n",
    "# + p[3]*qm4_f_test**4 + p[4]*qm4_f_test**3 + p[5]*qm4_f_test**2\\\n",
    "# + p[6]*qm4_f_test + p[7]\n",
    "tau_f_with_cable_test = copy.deepcopy(tau_f_test);\n",
    "# tau_f_with_cable_test[:,1] = tau_f_test[:,1] + 0.6697*tau_cable4_f_test\n",
    "# tau_f_with_cable_test[:,2] = tau_f_test[:,2] - 0.6697*tau_cable4_f_test\n",
    "# tau_f_with_cable_test[:,3] = tau_f_test[:,3] + tau_cable4_f_test\n",
    "tau_p_with_cable_test = copy.deepcopy(tau_p_test);\n",
    "# tau_p_with_cable_test[:,1] = tau_p_test[:,1] + 0.6697*tau_cable4_f_test\n",
    "# tau_p_with_cable_test[:,2] = tau_p_test[:,2] - 0.6697*tau_cable4_f_test\n",
    "# tau_p_with_cable_test[:,3] = tau_p_test[:,3] + tau_cable4_f_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_data_num = int(1 / base_freq * trajectory_sampling_rate)\n",
    "plot_meas_pred_tau(t_cut_test[:plot_data_num], tau_f_test[:plot_data_num, :],\n",
    "                   tau_p_test[:plot_data_num, :],\n",
    "                   robot_model.coordinates_joint_type,\n",
    "                   robot_model.coordinates)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Weighted Least Square (WLS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# weight = np.sqrt(np.linalg.norm(tau_f - tau_p, axis=0)/(tau_f.shape[0] - base_param_num))\n",
    "weight = np.max(tau_f_train, axis=0) - np.min(tau_f_train, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( \\left ( 39193, \\quad 66\\right ), \\quad \\left ( 39193\\right )\\right )$$"
      ],
      "text/plain": [
       "((39193, 66), (39193,))"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W_b_train.shape, tau_s_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# repeat the weight to generate a large vecoter for all the data\n",
    "weights = 1.0/np.tile(weight, W_b_train.shape[0]/weight.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFAAAAAVCAYAAADRhGlyAAAABHNCSVQICAgIfAhkiAAAA1tJREFUWIXt2EuIHVUQBuDPcdQMESMaiAiiBvMAA45PCPi44lsQ4mMlCEZx5WPhY6GbuBFG3SiiiIhIcKNMUBFUEtyoQSVqgkSCEhNFYkYdQzSYQU0cF1XNtJ2+fR8zgwnOD003Vafqr//06XPqXuYwK1iLnzD/vy7kMMH5mMSd3Qy+AH/j/or9cbyH7zGBPdiMNTi5Ta6jcAc+xj7sz5j7cHSbmFvwDD7Ab1n4Kw319sPRj5bXsRvHN9QC1mMvhir2P7PIlzAiRG4SAnfhtJpca9P/I17E0/gybaNCfBVb0r8P23SewH44+tFyUfofaajFUrH6XqjxzWsT81gmfq5iX5X2HVhYsh8j3uYkbq/JdzmWCOEtzRPYL0evWgpsw3far2wjmeCKdgNqcE7GbKjYi5Vxd03MivR91iF3S/MEzgRHGe20FFiT/msKw0BlwJU4KJZ3t7gh719U7KfkfUdNTGE7Dyf2wFXFTHO001JgY96vKgyDJed8DItl+nsDyYNiI10gDpyLk3CkMm4872fW5Fhcel6utxc2kxzdaimwKe+X1jmXiuW5vrFkxnJccb2DRTXjbk3/dpxUsg9iXSn+ugauluZPeLoc3WopYyLjDsHKTPJqhwQFFuFGfIUfxKdSxgDezpxj4mB6CluziK/Td3UDR0vzBM4ERzdaytiFA3WO4SR7swNZFafjD1F0FYN4QLQmE6Kve1c0ph8l33BD7pbObcx0ObrVUmCPaLEOwalJ9mGXZGVsztiFnQYmhoTY/aLlaIeWzhM4XY4qmrQMiDbvm7KhwG78jGW9ViomnzjBu8Ftohd7DX/1wTebHE1alon+dEu74FEx+2dV7MtNtQxlDJhqPjfW+E+osV1o6jNYXOMvo6XzCuyVo18tsDr99xSGwcqAdbhZNIrbS/Zr8STeF8v3F7HxXpYFjuGuGsIN4jPammLOxvVin7lJff+2Ki+mhK7Ey/k8LtqPfjn61UIcRgc1nBPHZoJPKvYVeFYs3XFxCv0q+qJH/buFKOMh8UtgbwraiedxRrsCMt9kw/XtNDn61bJAvKg3GmoHD2eh53Ya+D/DvWJeLuk0cJ74wfzWbFd0BGFI9IejVUfdvwoH8DmOw6dm75Q8krBEbA9PiK1iDnM4TPAPJ4IzA2AKDXIAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left ( 39193\\right )$$"
      ],
      "text/plain": [
       "(39193,)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "W_b_wls_train = np.multiply(W_b_train, np.asmatrix(weights).transpose())\n",
    "tau_s_wls_train = np.multiply(tau_s_train, weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/yan/anaconda2/envs/dynamics/lib/python2.7/site-packages/ipykernel_launcher.py:1: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    }
   ],
   "source": [
    "xb_wls = np.linalg.lstsq(W_b_wls_train, tau_s_wls_train)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}1.0 L9xy & -8.2224259618987 \\cdot 10^{-6}\\\\1.0 L9xz & -2.08504490877446 \\cdot 10^{-6}\\\\1.0 L9yz & -5.04127915180116 \\cdot 10^{-6}\\\\1.0 L8yz & 0.000249480513952491\\\\1.0 L8xy & 2.40615011777425 \\cdot 10^{-5}\\\\1.0 L8xz & -0.000294144879958623\\\\1.0 L7xy & -0.000392150272010622\\\\1.0 L8xx - 1.0 L8yy + 1.0 L9yy & 0.000379280242023272\\\\1.0 L9zz & -4.60695358544757 \\cdot 10^{-7}\\\\1.0 L7xz & 3.21900579684124 \\cdot 10^{-5}\\\\1.0 L7yz & -5.40234340821989 \\cdot 10^{-5}\\\\1.0 l9x & 1.96411726272238 \\cdot 10^{-5}\\\\1.0 L8xx - 1.0 L8yy + 1.0 L9xx & 0.000369282022699822\\\\1.0 l9y & 9.88662665355887 \\cdot 10^{-6}\\\\1.0 l8y + 1.0 l9z & 0.00520711150126434\\\\1.0 l8x & -0.000686021410510316\\\\1.0 L6xz & -0.00469791867631522\\\\- 1.0 L8xx + 1.0 L8yy + 1.0 L8zz & -0.000103042996775051\\\\1.0 l7y + 1.0 l8z & -0.00387023881391342\\\\1.0 L6xy & -0.0109738322291764\\\\1.0 L6yz & -0.0011737291190241\\\\1.0 l7x & 0.00510965885926799\\\\1.0 l6x & -0.00297230078248823\\\\1.0 l6y - 1.0 l7z & 0.0165715983656561\\\\1.0 L7zz + 1.0 L8yy & -0.000538844711392346\\\\1.0 L3zz + 1.0 L4zz + 1.0 L6xx + 1.0 L7xx + 1.0 L8yy - 0.302 l3y + 0.01 m_{5} + 0.11005925 m_{6} + 0.11005925 m_{7} + 0.11005925 m_{8} + 0.11005925 m_{9} & 0.185007456577232\\\\- 0.35790981 l2x + 1.0 l3x - 0.1 m_{3} + 0.2645 m_{6} + 0.2645 m_{7} + 0.2645 m_{8} + 0.2645 m_{9} & 0.295465118656418\\\\1.0 l3y + 1.0 l6z + 0.151 m_{6} + 0.151 m_{7} + 0.151 m_{8} + 0.151 m_{9} & -0.224691504031772\\\\1.0 l5y & -0.640092884692574\\\\1.0 l2x + 1.0 l5x + 0.2794 m_{3} + 0.2794 m_{6} + 0.2794 m_{7} + 0.2794 m_{8} + 0.2794 m_{9} & 0.0496861345851086\\\\- 1.0 L3zz - 1.0 L4zz - 1.0 L6xx + 1.0 L6zz + 0.302 l3y - 0.01 m_{5} - 0.11005925 m_{6} - 0.11005925 m_{7} - 0.11005925 m_{8} - 0.11005925 m_{9} & -0.184686415730163\\\\1.0 L2xy + 1.0 L5xy & 0.0258939003685607\\\\1.0 L3xy + 1.0 L4xy + 0.3645 l3y & -0.102739195965554\\\\1.0 L3zz + 1.0 L4zz + 1.0 L6yy - 0.302 l3y + 0.01 m_{5} + 0.11005925 m_{6} + 0.11005925 m_{7} + 0.11005925 m_{8} + 0.11005925 m_{9} & 0.18779244780013\\\\1.0 Fv_{3} + 1.0 Fv_{5} & 0.0207526730495343\\\\1.0 L2yz + 1.0 L5yz & 0.00963386916121269\\\\1.0 K_{6} & 0.00881520178367528\\\\1.0 L2xz + 1.0 L5xz - 0.2794 l3z & 0.00498187240357966\\\\1.0 L3xz + 1.0 L4xz - 0.1 l5z & 0.0169887047248875\\\\1.0 L3yz + 1.0 L4yz & -0.00124935004925675\\\\1.0 Fv_{6} & 0.00909319600598446\\\\1.0 L1zz + 1.0 L2xx + 1.0 L3xx - 1.0 L3zz + 1.0 L4xx - 1.0 L4zz + 1.0 L5xx - 0.01 m_{5} - 0.13286025 m_{6} - 0.13286025 m_{7} - 0.13286025 m_{8} - 0.13286025 m_{9} & -0.0714211798050254\\\\1.0 L3zz + 1.0 L4zz + 1.0 L6xx + 1.0 L7yy - 0.302 l3y + 0.01 m_{5} + 0.11005925 m_{6} + 0.11005925 m_{7} + 0.11005925 m_{8} + 0.11005925 m_{9} & 0.182880372541963\\\\1.0 l4y & 0.243766624388673\\\\0.35790981 l2x + 1.0 l4x + 0.1 m_{3} + 0.1 m_{5} + 0.1 m_{6} + 0.1 m_{7} + 0.1 m_{8} + 0.1 m_{9} & -0.270569999630215\\\\1.0 Fv_{9} & 0.000109780799647846\\\\1.0 Fv_{7} & 0.00132732577142983\\\\- 1.0 L3xx + 1.0 L3yy + 1.0 L3zz - 1.0 L4xx + 1.0 L4yy + 1.0 L4zz + 0.02 m_{5} + 0.2657205 m_{6} + 0.2657205 m_{7} + 0.2657205 m_{8} + 0.2657205 m_{9} & 0.39199492137858\\\\1.0 Fv_{8} & -0.000682824552670663\\\\1.0 K_{8} & 0.0067357291622003\\\\1.0 L2zz + 1.0 L5zz + 0.07806436 m_{3} + 0.07806436 m_{6} + 0.07806436 m_{7} + 0.07806436 m_{8} + 0.07806436 m_{9} & 0.111490060095449\\\\1.0 K_{7} & -0.0139046163190738\\\\1.0 Fv_{1} & 0.0427653042092932\\\\1.0 K_{1} & 0.317957031143243\\\\1.0 Fv_{2} & 0.0788401772692013\\\\1.0 Fv_{4} & 0.107081418869084\\\\1.0 L1zz + 1.0 L2yy + 1.0 L3xx - 1.0 L3zz + 1.0 L4xx - 1.0 L4zz + 1.0 L5yy + 0.07806436 m_{3} - 0.01 m_{5} - 0.05479589 m_{6} - 0.05479589 m_{7} - 0.05479589 m_{8} - 0.05479589 m_{9} & -0.0789840258945499\\\\1.0 Fc_{3} + 1.0 Fc_{5} & -6.24820666085095 \\cdot 10^{-5}\\\\1.0 Fc_{6} & 0.0398738559702731\\\\1.0 l2y & 0.649485893058986\\\\1.0 Fc_{8} & 0.00384582586772801\\\\1.0 Fc_{9} & 0.00113531369137249\\\\1.0 Fc_{2} & 0.0310557011190414\\\\1.0 Fc_{1} & 0.0637620042262926\\\\1.0 Fc_{4} & 0.0546573728206601\\\\1.0 Fc_{7} & 0.0073272573126136\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                   1.0⋅L8xx -\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                   1.0⋅L8xx -\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                         1.0⋅\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                  -1.0⋅L8xx +\n",
       "⎢                                                                             \n",
       "⎢                                                                         1.0⋅\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                         1.0⋅\n",
       "⎢                                                                             \n",
       "⎢                                                                        1.0⋅L\n",
       "⎢                                                                             \n",
       "⎢             1.0⋅L3zz + 1.0⋅L4zz + 1.0⋅L6xx + 1.0⋅L7xx + 1.0⋅L8yy - 0.302⋅l3y\n",
       "⎢                                                                             \n",
       "⎢                                         -0.35790981⋅l2x + 1.0⋅l3x - 0.1⋅m₃ +\n",
       "⎢                                                                             \n",
       "⎢                                                   1.0⋅l3y + 1.0⋅l6z + 0.151⋅\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                           1.0⋅l2x + 1.0⋅l5x + 0.2794⋅m₃ + 0.\n",
       "⎢                                                                             \n",
       "⎢                  -1.0⋅L3zz - 1.0⋅L4zz - 1.0⋅L6xx + 1.0⋅L6zz + 0.302⋅l3y - 0.\n",
       "⎢                                                                             \n",
       "⎢                                                                        1.0⋅L\n",
       "⎢                                                                             \n",
       "⎢                                                                  1.0⋅L3xy + \n",
       "⎢                                                                             \n",
       "⎢                        1.0⋅L3zz + 1.0⋅L4zz + 1.0⋅L6yy - 0.302⋅l3y + 0.01⋅m₅ \n",
       "⎢                                                                             \n",
       "⎢                                                                         1.0⋅\n",
       "⎢                                                                             \n",
       "⎢                                                                        1.0⋅L\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                  1.0⋅L2xz + \n",
       "⎢                                                                             \n",
       "⎢                                                                   1.0⋅L3xz +\n",
       "⎢                                                                             \n",
       "⎢                                                                        1.0⋅L\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢        1.0⋅L1zz + 1.0⋅L2xx + 1.0⋅L3xx - 1.0⋅L3zz + 1.0⋅L4xx - 1.0⋅L4zz + 1.0\n",
       "⎢                                                                             \n",
       "⎢                  1.0⋅L3zz + 1.0⋅L4zz + 1.0⋅L6xx + 1.0⋅L7yy - 0.302⋅l3y + 0.0\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                           0.35790981⋅l2x + 1.0⋅l4x + 0.1⋅m₃ \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢               -1.0⋅L3xx + 1.0⋅L3yy + 1.0⋅L3zz - 1.0⋅L4xx + 1.0⋅L4yy + 1.0⋅L4\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                1.0⋅L2zz + 1.0⋅L5zz + 0.07806436⋅m₃ + 0.07806\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢1.0⋅L1zz + 1.0⋅L2yy + 1.0⋅L3xx - 1.0⋅L3zz + 1.0⋅L4xx - 1.0⋅L4zz + 1.0⋅L5yy + \n",
       "⎢                                                                             \n",
       "⎢                                                                         1.0⋅\n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎣                                                                             \n",
       "\n",
       " 1.0⋅L9xy                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L9xz                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L9yz                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L8yz                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L8xy                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L8xz                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L7xy                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L8yy + 1.0⋅L9yy                                                          \n",
       "                                                                              \n",
       " 1.0⋅L9zz                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L7xz                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L7yz                                                                     \n",
       "                                                                              \n",
       " 1.0⋅l9x                                                                      \n",
       "                                                                              \n",
       " 1.0⋅L8yy + 1.0⋅L9xx                                                          \n",
       "                                                                              \n",
       " 1.0⋅l9y                                                                      \n",
       "                                                                              \n",
       "l8y + 1.0⋅l9z                                                                 \n",
       "                                                                              \n",
       " 1.0⋅l8x                                                                      \n",
       "                                                                              \n",
       " 1.0⋅L6xz                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L8yy + 1.0⋅L8zz                                                          \n",
       "                                                                              \n",
       "l7y + 1.0⋅l8z                                                                 \n",
       "                                                                              \n",
       " 1.0⋅L6xy                                                                     \n",
       "                                                                              \n",
       " 1.0⋅L6yz                                                                     \n",
       "                                                                              \n",
       " 1.0⋅l7x                                                                      \n",
       "                                                                              \n",
       " 1.0⋅l6x                                                                      \n",
       "                                                                              \n",
       "l6y - 1.0⋅l7z                                                                 \n",
       "                                                                              \n",
       "7zz + 1.0⋅L8yy                                                                \n",
       "                                                                              \n",
       " + 0.01⋅m₅ + 0.11005925⋅m₆ + 0.11005925⋅m₇ + 0.11005925⋅m₈ + 0.11005925⋅m₉    \n",
       "                                                                              \n",
       " 0.2645⋅m₆ + 0.2645⋅m₇ + 0.2645⋅m₈ + 0.2645⋅m₉                                \n",
       "                                                                              \n",
       "m₆ + 0.151⋅m₇ + 0.151⋅m₈ + 0.151⋅m₉                                           \n",
       "                                                                              \n",
       " 1.0⋅l5y                                                                      \n",
       "                                                                              \n",
       "2794⋅m₆ + 0.2794⋅m₇ + 0.2794⋅m₈ + 0.2794⋅m₉                                   \n",
       "                                                                              \n",
       "01⋅m₅ - 0.11005925⋅m₆ - 0.11005925⋅m₇ - 0.11005925⋅m₈ - 0.11005925⋅m₉         \n",
       "                                                                              \n",
       "2xy + 1.0⋅L5xy                                                                \n",
       "                                                                              \n",
       "1.0⋅L4xy + 0.3645⋅l3y                                                         \n",
       "                                                                              \n",
       "+ 0.11005925⋅m₆ + 0.11005925⋅m₇ + 0.11005925⋅m₈ + 0.11005925⋅m₉               \n",
       "                                                                              \n",
       "Fv₃ + 1.0⋅Fv₅                                                                 \n",
       "                                                                              \n",
       "2yz + 1.0⋅L5yz                                                                \n",
       "                                                                              \n",
       "  1.0⋅K₆                                                                      \n",
       "                                                                              \n",
       "1.0⋅L5xz - 0.2794⋅l3z                                                         \n",
       "                                                                              \n",
       " 1.0⋅L4xz - 0.1⋅l5z                                                           \n",
       "                                                                              \n",
       "3yz + 1.0⋅L4yz                                                                \n",
       "                                                                              \n",
       " 1.0⋅Fv₆                                                                      \n",
       "                                                                              \n",
       "⋅L5xx - 0.01⋅m₅ - 0.13286025⋅m₆ - 0.13286025⋅m₇ - 0.13286025⋅m₈ - 0.13286025⋅m\n",
       "                                                                              \n",
       "1⋅m₅ + 0.11005925⋅m₆ + 0.11005925⋅m₇ + 0.11005925⋅m₈ + 0.11005925⋅m₉          \n",
       "                                                                              \n",
       " 1.0⋅l4y                                                                      \n",
       "                                                                              \n",
       "+ 0.1⋅m₅ + 0.1⋅m₆ + 0.1⋅m₇ + 0.1⋅m₈ + 0.1⋅m₉                                  \n",
       "                                                                              \n",
       " 1.0⋅Fv₉                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fv₇                                                                      \n",
       "                                                                              \n",
       "zz + 0.02⋅m₅ + 0.2657205⋅m₆ + 0.2657205⋅m₇ + 0.2657205⋅m₈ + 0.2657205⋅m₉      \n",
       "                                                                              \n",
       " 1.0⋅Fv₈                                                                      \n",
       "                                                                              \n",
       "  1.0⋅K₈                                                                      \n",
       "                                                                              \n",
       "436⋅m₆ + 0.07806436⋅m₇ + 0.07806436⋅m₈ + 0.07806436⋅m₉                        \n",
       "                                                                              \n",
       "  1.0⋅K₇                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fv₁                                                                      \n",
       "                                                                              \n",
       "  1.0⋅K₁                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fv₂                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fv₄                                                                      \n",
       "                                                                              \n",
       "0.07806436⋅m₃ - 0.01⋅m₅ - 0.05479589⋅m₆ - 0.05479589⋅m₇ - 0.05479589⋅m₈ - 0.05\n",
       "                                                                              \n",
       "Fc₃ + 1.0⋅Fc₅                                                                 \n",
       "                                                                              \n",
       " 1.0⋅Fc₆                                                                      \n",
       "                                                                              \n",
       " 1.0⋅l2y                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fc₈                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fc₉                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fc₂                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fc₁                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fc₄                                                                      \n",
       "                                                                              \n",
       " 1.0⋅Fc₇                                                                      \n",
       "\n",
       "            -8.2224259618987e-6 ⎤\n",
       "                                ⎥\n",
       "           -2.08504490877446e-6 ⎥\n",
       "                                ⎥\n",
       "           -5.04127915180116e-6 ⎥\n",
       "                                ⎥\n",
       "           0.000249480513952491 ⎥\n",
       "                                ⎥\n",
       "            2.40615011777425e-5 ⎥\n",
       "                                ⎥\n",
       "           -0.000294144879958623⎥\n",
       "                                ⎥\n",
       "           -0.000392150272010622⎥\n",
       "                                ⎥\n",
       "           0.000379280242023272 ⎥\n",
       "                                ⎥\n",
       "           -4.60695358544757e-7 ⎥\n",
       "                                ⎥\n",
       "            3.21900579684124e-5 ⎥\n",
       "                                ⎥\n",
       "           -5.40234340821989e-5 ⎥\n",
       "                                ⎥\n",
       "            1.96411726272238e-5 ⎥\n",
       "                                ⎥\n",
       "           0.000369282022699822 ⎥\n",
       "                                ⎥\n",
       "            9.88662665355887e-6 ⎥\n",
       "                                ⎥\n",
       "            0.00520711150126434 ⎥\n",
       "                                ⎥\n",
       "           -0.000686021410510316⎥\n",
       "                                ⎥\n",
       "           -0.00469791867631522 ⎥\n",
       "                                ⎥\n",
       "           -0.000103042996775051⎥\n",
       "                                ⎥\n",
       "           -0.00387023881391342 ⎥\n",
       "                                ⎥\n",
       "            -0.0109738322291764 ⎥\n",
       "                                ⎥\n",
       "            -0.0011737291190241 ⎥\n",
       "                                ⎥\n",
       "            0.00510965885926799 ⎥\n",
       "                                ⎥\n",
       "           -0.00297230078248823 ⎥\n",
       "                                ⎥\n",
       "            0.0165715983656561  ⎥\n",
       "                                ⎥\n",
       "           -0.000538844711392346⎥\n",
       "                                ⎥\n",
       "             0.185007456577232  ⎥\n",
       "                                ⎥\n",
       "             0.295465118656418  ⎥\n",
       "                                ⎥\n",
       "            -0.224691504031772  ⎥\n",
       "                                ⎥\n",
       "            -0.640092884692574  ⎥\n",
       "                                ⎥\n",
       "            0.0496861345851086  ⎥\n",
       "                                ⎥\n",
       "            -0.184686415730163  ⎥\n",
       "                                ⎥\n",
       "            0.0258939003685607  ⎥\n",
       "                                ⎥\n",
       "            -0.102739195965554  ⎥\n",
       "                                ⎥\n",
       "             0.18779244780013   ⎥\n",
       "                                ⎥\n",
       "            0.0207526730495343  ⎥\n",
       "                                ⎥\n",
       "            0.00963386916121269 ⎥\n",
       "                                ⎥\n",
       "            0.00881520178367528 ⎥\n",
       "                                ⎥\n",
       "            0.00498187240357966 ⎥\n",
       "                                ⎥\n",
       "            0.0169887047248875  ⎥\n",
       "                                ⎥\n",
       "           -0.00124935004925675 ⎥\n",
       "                                ⎥\n",
       "            0.00909319600598446 ⎥\n",
       "                                ⎥\n",
       "₉           -0.0714211798050254 ⎥\n",
       "                                ⎥\n",
       "             0.182880372541963  ⎥\n",
       "                                ⎥\n",
       "             0.243766624388673  ⎥\n",
       "                                ⎥\n",
       "            -0.270569999630215  ⎥\n",
       "                                ⎥\n",
       "           0.000109780799647846 ⎥\n",
       "                                ⎥\n",
       "            0.00132732577142983 ⎥\n",
       "                                ⎥\n",
       "             0.39199492137858   ⎥\n",
       "                                ⎥\n",
       "           -0.000682824552670663⎥\n",
       "                                ⎥\n",
       "            0.0067357291622003  ⎥\n",
       "                                ⎥\n",
       "             0.111490060095449  ⎥\n",
       "                                ⎥\n",
       "            -0.0139046163190738 ⎥\n",
       "                                ⎥\n",
       "            0.0427653042092932  ⎥\n",
       "                                ⎥\n",
       "             0.317957031143243  ⎥\n",
       "                                ⎥\n",
       "            0.0788401772692013  ⎥\n",
       "                                ⎥\n",
       "             0.107081418869084  ⎥\n",
       "                                ⎥\n",
       "479589⋅m₉   -0.0789840258945499 ⎥\n",
       "                                ⎥\n",
       "           -6.24820666085095e-5 ⎥\n",
       "                                ⎥\n",
       "            0.0398738559702731  ⎥\n",
       "                                ⎥\n",
       "             0.649485893058986  ⎥\n",
       "                                ⎥\n",
       "            0.00384582586772801 ⎥\n",
       "                                ⎥\n",
       "            0.00113531369137249 ⎥\n",
       "                                ⎥\n",
       "            0.0310557011190414  ⎥\n",
       "                                ⎥\n",
       "            0.0637620042262926  ⎥\n",
       "                                ⎥\n",
       "            0.0546573728206601  ⎥\n",
       "                                ⎥\n",
       "            0.0073272573126136  ⎦"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#np.set_printoptions(precision=2)\n",
    "sympy.Matrix.hstack(sympy.Matrix(robot_model.base_param), sympy.Matrix(xb_wls))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "tau_p_wls_train = np.zeros(tau_f_train.shape)\n",
    "tau_ps_wls_train = W_b_train.dot(xb_wls)\n",
    "for i in range(dof):\n",
    "    tau_p_wls_train[:, i] = tau_ps_wls_train[i::dof]\n",
    "    \n",
    "tau_p_wls_with_cable_train = copy.deepcopy(tau_p_wls_train);\n",
    "# tau_p_wls_with_cable_train[:,1] = tau_p_wls_train[:,1] + 0.6697*tau_cable4_f_train\n",
    "# tau_p_wls_with_cable_train[:,2] = tau_p_wls_train[:,2] - 0.6697*tau_cable4_f_train\n",
    "# tau_p_wls_with_cable_train[:,3] = tau_p_wls_train[:,3] + tau_cable4_f_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_meas_pred_tau(t_cut_train[:plot_data_num], tau_f_with_cable_train[:plot_data_num, :],\n",
    "                   tau_p_wls_with_cable_train[:plot_data_num, :],\n",
    "                   robot_model.coordinates_joint_type, \n",
    "                   robot_model.coordinates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.11687483, 0.19484476, 0.18483873, 0.27381924, 0.50862795,\n",
       "       0.28723848, 0.29564408])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(tau_f_with_cable_train[:plot_data_num, :] - tau_p_wls_with_cable_train[:plot_data_num, :], axis=0)\\\n",
    "    / np.linalg.norm(tau_f_with_cable_train[:plot_data_num, :], axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "weight = np.max(tau_f_test, axis=0) - np.min(tau_f_test, axis=0)\n",
    "weight\n",
    "weight[1] /= 1\n",
    "weight[2] /= 1\n",
    "weight[3] /= 1\n",
    "weight\n",
    "# repeat the weight to generate a large vecoter for all the data\n",
    "weights = 1.0/np.tile(weight, W_b_test.shape[0]/weight.shape[0])\n",
    "\n",
    "W_b_wls_test = np.multiply(W_b_test, np.asmatrix(weights).transpose())\n",
    "tau_s_wls_test = np.multiply(tau_s_test, weights)\n",
    "\n",
    "tau_p_wls_test = np.zeros(tau_f_test.shape)\n",
    "tau_ps_wls_test = W_b_test.dot(xb_wls)\n",
    "for i in range(dof):\n",
    "    tau_p_wls_test[:, i] = tau_ps_wls_test[i::dof]\n",
    "\n",
    "# add cable torque back\n",
    "# qm4_f_test = 0.6697*q_f_test[:,1] - 0.6697*q_f_test[:,2] + q_f_test[:,3]\n",
    "# tau_cable4_f_test = p[0]*qm4_f_test**7 + p[1]*qm4_f_test**6 + p[2]*qm4_f_test**5\\\n",
    "# + p[3]*qm4_f_test**4 + p[4]*qm4_f_test**3 + p[5]*qm4_f_test**2\\\n",
    "# + p[6]*qm4_f_test + p[7]\n",
    "# tau_f_with_cable_test = copy.deepcopy(tau_f_test);\n",
    "# tau_f_with_cable_test[:,1] = tau_f_test[:,1] + 0.6697*tau_cable4_f_test\n",
    "# tau_f_with_cable_test[:,2] = tau_f_test[:,2] - 0.6697*tau_cable4_f_test\n",
    "# tau_f_with_cable_test[:,3] = tau_f_test[:,3] + tau_cable4_f_test\n",
    "tau_p_wls_with_cable_test = copy.deepcopy(tau_p_wls_test);\n",
    "# tau_p_wls_with_cable_test[:,1] = tau_p_wls_test[:,1] + 0.6697*tau_cable4_f_test\n",
    "# tau_p_wls_with_cable_test[:,2] = tau_p_wls_test[:,2] - 0.6697*tau_cable4_f_test\n",
    "# tau_p_wls_with_cable_test[:,3] = tau_p_wls_test[:,3] + tau_cable4_f_test\n",
    "\n",
    "plot_meas_pred_tau(t_cut_test[:plot_data_num], tau_f_with_cable_test[:plot_data_num, :],\n",
    "                   tau_p_wls_with_cable_test[:plot_data_num, :],\n",
    "                   robot_model.coordinates_joint_type,\n",
    "                   robot_model.coordinates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.12949085, 0.15529172, 0.34341645, 0.32181876, 0.60237056,\n",
       "       0.36330126, 0.36876098])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(tau_f_with_cable_test[:plot_data_num, :] - tau_p_wls_with_cable_test[:plot_data_num, :], axis=0)\\\n",
    "/ np.linalg.norm(tau_f_test[:plot_data_num, :], axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convex optimization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate regressor matrix for barycentric parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "from identification import SDPOpt\n",
    "\n",
    "bary_param_num = len(robot_model.bary_param)\n",
    "H_func = robot_model.H_func\n",
    "W_train, tau_s_train = gen_regressor(bary_param_num, H_func,\n",
    "                                     q_f_train, dq_f_train, ddq_f_train, tau_f_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "weight = np.max(tau_f_train, axis=0) - np.min(tau_f_train, axis=0)\n",
    "# repeat the weight to generate a large vecoter for all the data\n",
    "weights = 1.0/np.tile(weight, W_train.shape[0]/weight.shape[0])\n",
    "W_w_train = np.multiply(W_train, np.asmatrix(weights).transpose())\n",
    "tau_w_s_train = np.multiply(tau_s_train, weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.70936727, 0.83087494, 1.26860941, 0.29147275, 0.09333127,\n",
       "       0.09894924, 0.00623326])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weight"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| min mass | max mass | min $r_x$ | max $r_x$ | min $r_y$ | max $r_y$ | min $r_z$ | max $r_z$ | max $F_c$ | max $F_v$ | max $F_o$ |\n",
    "|----------|----------|-----------|-----------|-----------|-----------|-----------|-----------|-----------|--------------|-----------|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "sdp_constraints = [(2, 20, -0.1, 0.1, -0.1, 0.1, -0.1, 0.3, 0.2, 0.2, 0.2, 0, 10), #1\n",
    "                  (1, 15, -0.1, 0.15, -0.05, 0.05, -0.05, 0.05, 0.2, 0.2, 0.3, 0, 0), #2\n",
    "                  (0.5, 5, -0.0, 0.3, -0.03, 0.03, -0.03, 0.03, 0.2, 0.2, 0.2, 0, 0), # 3\n",
    "                  (1, 10, -0.1, 0.1, -0.05, 0.05, -0.1, 0.1, 0.2, 0.2, 0.3, 0, 0), # 3'\n",
    "                  (0.05, 2, 0.05, 0.2, -0.02, 0.02, 0.02, 0.1, 0.2, 0.2, 0.2, 0, 0), # 3''\n",
    "                  (0.05, 2, -0.03, 0.03, -0.00, 0.12, -0.15, 0.0, 0.2, 0.2, 0.2, 0, 10), # 4\n",
    "                  (0.05, 1, -0.02, 0.02, -0.1, 0.00, -0.1, 0.00, 0.2, 0.2, 0.2, 0, 10), # 5\n",
    "                  (0.05, 0.5, -0.02, 0.02, 0, 0.1, -0.1, 0.00, 0.2, 0.2, 0.2, 0, 10), # 6\n",
    "                  (0.02, 0.5, -0.01, 0.01, -0.01, 0.01, -0.00, 0.1, 0.2, 0.2, 0.2, 0, 0),]#7]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$10$$"
      ],
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(sdp_constraints)\n",
    "robot_model.frame_num"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Regressor shape: (39193, 112)\n",
      "Regressand shape: (39193,)\n",
      "Creating variables...\n",
      "Creating optimization objective...\n",
      "Creating constraints...\n",
      "Solving problem...\n",
      "----------------------------------------------------------------------------\n",
      "\tSCS v1.2.6 - Splitting Conic Solver\n",
      "\t(c) Brendan O'Donoghue, Stanford University, 2012-2016\n",
      "----------------------------------------------------------------------------\n",
      "Lin-sys: sparse-indirect, nnz in A = 1719201, CG tol ~ 1/iter^(2.00)\n",
      "eps = 1.00e-03, alpha = 1.50, max_iters = 10000, normalize = 1, scale = 1.00\n",
      "Variables n = 113, constraints m = 39402\n",
      "Cones:\tlinear vars: 117\n",
      "\tsoc vars: 39195, soc blks: 1\n",
      "\tsd vars: 90, sd blks: 9\n",
      "Setup time: 5.99e-02s\n",
      "----------------------------------------------------------------------------\n",
      " Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n",
      "----------------------------------------------------------------------------\n",
      "     0|      inf       inf      -nan      -inf      -inf       inf  1.31e-01 \n",
      "   100| 1.06e+00  2.59e-02  5.45e-03 -1.90e-01 -1.98e-01  3.62e-14  7.22e+00 \n",
      "   200| 4.43e-01  2.68e-02  2.09e-01  1.97e-01 -6.64e-02  3.62e-14  1.13e+01 \n",
      "   300| 3.40e-01  6.25e-03  1.14e-04  4.89e-02  4.87e-02  3.62e-14  1.50e+01 \n",
      "   400| 3.28e-01  4.27e-03  7.22e-04  1.44e-01  1.43e-01  3.62e-14  1.90e+01 \n",
      "   500| 3.06e-01  5.66e-03  5.81e-04  2.28e-01  2.27e-01  3.62e-14  2.38e+01 \n",
      "   600| 3.05e-01  3.60e-03  1.75e-03  3.05e-01  3.08e-01  3.62e-14  2.87e+01 \n",
      "   700| 3.04e-01  1.48e-03  1.81e-03  3.84e-01  3.87e-01  3.62e-14  3.28e+01 \n",
      "   800| 3.01e-01  1.87e-03  1.42e-03  4.63e-01  4.65e-01  3.62e-14  3.72e+01 \n",
      "   900| 2.97e-01  2.04e-03  1.76e-03  5.39e-01  5.43e-01  3.62e-14  4.21e+01 \n",
      "  1000| 2.94e-01  3.22e-03  6.12e-03  6.09e-01  6.22e-01  3.62e-14  4.79e+01 \n",
      "  1100| 2.93e-01  2.31e-03  4.91e-03  6.84e-01  6.96e-01  3.62e-14  5.31e+01 \n",
      "  1200| 2.92e-01  1.50e-03  6.08e-04  7.63e-01  7.65e-01  3.62e-14  5.81e+01 \n",
      "  1300| 2.89e-01  2.85e-03  1.05e-03  8.38e-01  8.35e-01  3.62e-14  6.30e+01 \n",
      "  1400| 2.91e-01  1.19e-03  4.99e-04  9.08e-01  9.09e-01  3.62e-14  6.75e+01 \n",
      "  1500| 2.90e-01  1.59e-03  2.42e-03  9.76e-01  9.83e-01  3.62e-14  7.26e+01 \n",
      "  1600| 2.88e-01  1.80e-03  2.57e-03  1.05e+00  1.06e+00  3.63e-14  7.70e+01 \n",
      "  1700| 2.89e-01  9.80e-04  1.61e-03  1.12e+00  1.13e+00  3.63e-14  8.16e+01 \n",
      "  1800| 2.88e-01  1.41e-03  1.03e-03  1.20e+00  1.20e+00  3.63e-14  8.74e+01 \n",
      "  1900| 2.88e-01  1.22e-03  9.51e-04  1.27e+00  1.27e+00  3.63e-14  9.20e+01 \n",
      "  2000| 2.89e-01  6.13e-04  1.46e-03  1.34e+00  1.34e+00  3.63e-14  9.69e+01 \n",
      "  2100| 2.88e-01  1.34e-03  1.71e-03  1.41e+00  1.42e+00  3.63e-14  1.03e+02 \n",
      "  2200| 2.88e-01  9.94e-04  1.70e-03  1.48e+00  1.49e+00  1.09e-13  1.08e+02 \n",
      "  2300| 2.89e-01  7.04e-04  1.62e-03  1.55e+00  1.56e+00  3.63e-14  1.15e+02 \n",
      "  2400| 2.88e-01  1.09e-03  1.41e-03  1.63e+00  1.63e+00  3.63e-14  1.21e+02 \n",
      "  2500| 2.88e-01  1.43e-03  3.68e-03  1.69e+00  1.70e+00  1.09e-13  1.30e+02 \n",
      "  2600| 2.87e-01  1.75e-03  4.78e-03  1.75e+00  1.78e+00  3.63e-14  1.38e+02 \n",
      "  2700| 2.87e-01  1.49e-03  3.75e-03  1.83e+00  1.85e+00  3.63e-14  1.47e+02 \n",
      "  2800| 2.87e-01  1.13e-03  1.38e-03  1.91e+00  1.92e+00  3.64e-14  1.57e+02 \n",
      "  2900| 2.87e-01  1.42e-03  1.73e-04  1.99e+00  1.99e+00  3.64e-14  1.65e+02 \n",
      "  3000| 2.86e-01  1.60e-03  4.54e-04  2.06e+00  2.06e+00  3.64e-14  1.73e+02 \n",
      "  3100| 2.87e-01  1.20e-03  5.98e-04  2.13e+00  2.13e+00  3.64e-14  1.81e+02 \n",
      "  3200| 2.87e-01  1.11e-03  2.10e-03  2.19e+00  2.20e+00  3.64e-14  1.91e+02 \n",
      "  3300| 2.87e-01  1.34e-03  2.85e-03  2.26e+00  2.28e+00  3.64e-14  1.99e+02 \n",
      "  3400| 2.87e-01  1.29e-03  2.73e-03  2.33e+00  2.35e+00  1.09e-13  2.07e+02 \n",
      "  3500| 2.87e-01  1.30e-03  2.34e-03  2.41e+00  2.42e+00  3.64e-14  2.16e+02 \n",
      "  3600| 2.87e-01  1.22e-03  1.72e-03  2.48e+00  2.49e+00  3.65e-14  2.25e+02 \n",
      "  3700| 2.87e-01  1.24e-03  1.20e-03  2.55e+00  2.56e+00  3.65e-14  2.32e+02 \n",
      "  3800| 2.87e-01  1.29e-03  1.15e-03  2.63e+00  2.63e+00  3.65e-14  2.40e+02 \n",
      "  3900| 2.87e-01  1.25e-03  1.38e-03  2.70e+00  2.70e+00  1.10e-13  2.47e+02 \n",
      "  4000| 2.87e-01  1.27e-03  1.69e-03  2.77e+00  2.78e+00  3.65e-14  2.54e+02 \n",
      "  4100| 2.87e-01  1.18e-03  2.02e-03  2.84e+00  2.85e+00  3.65e-14  2.62e+02 \n",
      "  4200| 2.87e-01  1.26e-03  2.18e-03  2.91e+00  2.92e+00  1.10e-13  2.68e+02 \n",
      "  4300| 2.87e-01  1.22e-03  2.18e-03  2.98e+00  2.99e+00  3.66e-14  2.75e+02 \n",
      "  4400| 2.87e-01  5.55e-04  1.96e-03  3.05e+00  3.06e+00  3.66e-14  2.83e+02 \n",
      "  4500| 2.87e-01  6.24e-04  1.70e-03  3.12e+00  3.13e+00  3.66e-14  2.90e+02 \n",
      "  4600| 2.88e-01  4.76e-04  1.47e-03  3.19e+00  3.20e+00  3.66e-14  2.98e+02 \n",
      "  4700| 2.88e-01  6.13e-04  1.44e-03  3.27e+00  3.28e+00  3.66e-14  3.05e+02 \n",
      "  4800| 2.88e-01  4.86e-04  1.50e-03  3.34e+00  3.35e+00  3.67e-14  3.15e+02 \n",
      "  4900| 2.88e-01  5.35e-04  1.67e-03  3.41e+00  3.42e+00  3.67e-14  3.23e+02 \n",
      "  5000| 2.88e-01  5.56e-04  1.85e-03  3.48e+00  3.49e+00  3.67e-14  3.32e+02 \n",
      "  5100| 2.88e-01  4.96e-04  1.88e-03  3.55e+00  3.56e+00  3.67e-14  3.40e+02 \n",
      "  5200| 2.88e-01  6.15e-04  1.82e-03  3.62e+00  3.64e+00  3.67e-14  3.49e+02 \n",
      "  5300| 2.89e-01  4.34e-04  1.75e-03  3.69e+00  3.71e+00  3.68e-14  3.57e+02 \n",
      "  5400| 2.89e-01  5.75e-04  1.60e-03  3.77e+00  3.78e+00  3.68e-14  3.65e+02 \n",
      "  5500| 2.89e-01  5.14e-04  1.51e-03  3.84e+00  3.85e+00  1.10e-13  3.74e+02 \n",
      "  5600| 2.89e-01  4.88e-04  1.51e-03  3.91e+00  3.93e+00  3.68e-14  3.82e+02 \n",
      "  5700| 2.89e-01  5.60e-04  1.56e-03  3.99e+00  4.00e+00  3.69e-14  3.89e+02 \n",
      "  5800| 2.90e-01  4.20e-04  1.68e-03  4.06e+00  4.07e+00  3.69e-14  3.97e+02 \n",
      "  5900| 2.90e-01  5.94e-04  1.78e-03  4.13e+00  4.15e+00  3.69e-14  4.05e+02 \n",
      "  6000| 2.90e-01  4.81e-04  1.78e-03  4.20e+00  4.22e+00  3.69e-14  4.12e+02 \n",
      "  6100| 2.90e-01  5.38e-04  1.70e-03  4.28e+00  4.29e+00  3.70e-14  4.21e+02 \n",
      "  6200| 2.90e-01  5.35e-04  1.61e-03  4.35e+00  4.36e+00  3.70e-14  4.28e+02 \n",
      "  6300| 2.91e-01  4.61e-04  1.53e-03  4.42e+00  4.44e+00  3.70e-14  4.35e+02 \n",
      "  6400| 2.91e-01  5.96e-04  1.51e-03  4.50e+00  4.51e+00  3.70e-14  4.42e+02 \n",
      "  6500| 2.91e-01  4.37e-04  1.54e-03  4.57e+00  4.58e+00  3.71e-14  4.50e+02 \n",
      "  6600| 2.91e-01  5.63e-04  1.60e-03  4.64e+00  4.66e+00  3.71e-14  4.57e+02 \n",
      "  6700| 2.91e-01  5.07e-04  1.68e-03  4.71e+00  4.73e+00  3.71e-14  4.65e+02 \n",
      "  6800| 2.92e-01  5.20e-04  1.74e-03  4.79e+00  4.81e+00  3.71e-14  4.73e+02 \n",
      "  6900| 2.92e-01  5.83e-04  1.71e-03  4.86e+00  4.88e+00  3.72e-14  4.80e+02 \n",
      "  7000| 2.92e-01  4.42e-04  1.62e-03  4.94e+00  4.95e+00  1.12e-13  4.88e+02 \n",
      "  7100| 2.92e-01  5.91e-04  1.52e-03  5.01e+00  5.03e+00  3.72e-14  4.95e+02 \n",
      "  7200| 2.93e-01  4.79e-04  1.47e-03  5.09e+00  5.10e+00  3.73e-14  5.00e+02 \n",
      "  7300| 2.93e-01  5.50e-04  1.50e-03  5.16e+00  5.18e+00  3.73e-14  5.07e+02 \n",
      "  7400| 2.93e-01  5.40e-04  1.57e-03  5.23e+00  5.25e+00  3.73e-14  5.13e+02 \n",
      "  7500| 2.93e-01  4.79e-04  1.63e-03  5.31e+00  5.33e+00  3.74e-14  5.20e+02 \n",
      "  7600| 2.94e-01  6.08e-04  1.67e-03  5.38e+00  5.40e+00  3.74e-14  5.26e+02 \n",
      "  7700| 2.94e-01  4.72e-04  1.67e-03  5.46e+00  5.48e+00  3.74e-14  5.31e+02 \n",
      "  7800| 2.94e-01  5.81e-04  1.62e-03  5.53e+00  5.55e+00  1.12e-13  5.38e+02 \n",
      "  7900| 2.94e-01  5.05e-04  1.53e-03  5.61e+00  5.63e+00  3.75e-14  5.43e+02 \n",
      "  8000| 2.95e-01  5.21e-04  1.46e-03  5.68e+00  5.70e+00  3.75e-14  5.47e+02 \n",
      "  8100| 2.95e-01  5.81e-04  1.45e-03  5.76e+00  5.78e+00  3.76e-14  5.53e+02 \n",
      "  8200| 2.95e-01  4.60e-04  1.51e-03  5.83e+00  5.85e+00  1.13e-13  5.59e+02 \n",
      "  8300| 2.96e-01  6.00e-04  1.59e-03  5.91e+00  5.93e+00  3.76e-14  5.65e+02 \n",
      "  8400| 2.96e-01  4.98e-04  1.64e-03  5.98e+00  6.00e+00  3.77e-14  5.73e+02 \n",
      "  8500| 2.96e-01  5.77e-04  1.63e-03  6.06e+00  6.08e+00  3.77e-14  5.79e+02 \n",
      "  8600| 2.96e-01  5.54e-04  1.59e-03  6.13e+00  6.16e+00  3.77e-14  5.85e+02 \n",
      "  8700| 2.97e-01  4.88e-04  1.53e-03  6.21e+00  6.23e+00  3.78e-14  5.91e+02 \n",
      "  8800| 2.81e-01  6.00e-04  1.41e-03  6.29e+00  6.31e+00  3.78e-14  5.98e+02 \n",
      "  8900| 2.81e-01  4.74e-04  1.38e-03  6.36e+00  6.37e+00  1.14e-13  6.05e+02 \n",
      "  9000| 2.81e-01  5.86e-04  1.40e-03  6.42e+00  6.44e+00  3.79e-14  6.11e+02 \n",
      "  9100| 2.81e-01  5.11e-04  1.46e-03  6.49e+00  6.51e+00  3.79e-14  6.17e+02 \n",
      "  9200| 2.81e-01  5.40e-04  1.53e-03  6.56e+00  6.58e+00  1.14e-13  6.24e+02 \n",
      "  9300| 2.81e-01  5.97e-04  1.56e-03  6.62e+00  6.65e+00  3.80e-14  6.29e+02 \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  9400| 2.80e-01  4.99e-04  1.51e-03  6.69e+00  6.72e+00  3.80e-14  6.34e+02 \n",
      "  9500| 2.80e-01  5.98e-04  1.45e-03  6.76e+00  6.78e+00  3.81e-14  6.44e+02 \n",
      "  9600| 2.80e-01  4.83e-04  1.38e-03  6.83e+00  6.85e+00  3.81e-14  6.54e+02 \n",
      "  9700| 2.80e-01  5.67e-04  1.36e-03  6.90e+00  6.92e+00  1.14e-13  6.59e+02 \n",
      "  9800| 2.80e-01  5.48e-04  1.37e-03  6.97e+00  6.99e+00  3.82e-14  6.64e+02 \n",
      "  9900| 2.80e-01  4.96e-04  1.41e-03  7.03e+00  7.05e+00  3.82e-14  6.69e+02 \n",
      " 10000| 2.80e-01  5.97e-04  1.46e-03  7.10e+00  7.12e+00  3.83e-14  6.73e+02 \n",
      "----------------------------------------------------------------------------\n",
      "Status: Solved/Inaccurate\n",
      "Hit max_iters, solution may be inaccurate\n",
      "Timing: Solve time: 6.73e+02s\n",
      "\tLin-sys: avg # CG iterations: 24.53, avg solve time: 6.65e-02s\n",
      "\tCones: avg projection time: 1.53e-04s\n",
      "----------------------------------------------------------------------------\n",
      "Error metrics:\n",
      "dist(s, K) = 8.6101e-09, dist(y, K*) = 2.3019e-09, s'y/|s||y| = -1.3798e-11\n",
      "|Ax + s - b|_2 / (1 + |b|_2) = 2.8021e-01\n",
      "|A'y + c|_2 / (1 + |c|_2) = 5.9742e-04\n",
      "|c'x + b'y| / (1 + |c'x| + |b'y|) = 1.4589e-03\n",
      "----------------------------------------------------------------------------\n",
      "c'x = 7.0996, -b'y = 7.1218\n",
      "============================================================================\n",
      "CPU times: user 1h 22min 24s, sys: 45.5 s, total: 1h 23min 9s\n",
      "Wall time: 11min 13s\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "sdp_opt_std = SDPOpt(W_w_train, tau_w_s_train, robot_model,\n",
    "                     sdp_constraints)\n",
    "# sdp_opt_std = SDPOpt(W, tau_s, robot_model, sdp_constraints)\n",
    "%time sdp_opt_std.solve(10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare measured torque and predicted torque on training set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate predicted torque"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "tau_p_sdp_train = np.zeros(tau_f_train.shape)\n",
    "tau_ps_sdp_train = W_train.dot(sdp_opt_std.x_result)\n",
    "for i in range(dof):\n",
    "    tau_p_sdp_train[:, i] = tau_ps_sdp_train[i::dof]\n",
    "\n",
    "# disable polynomial cable torque\n",
    "# add cable torque back\n",
    "# qm4_f_train = 0.6697*q_f_train[:,1] - 0.6697*q_f_train[:,2] + q_f_train[:,3]\n",
    "# tau_cable4_f_train = p[0]*qm4_f_train**7 + p[1]*qm4_f_train**6 + p[2]*qm4_f_train**5\\\n",
    "# + p[3]*qm4_f_train**4 + p[4]*qm4_f_train**3 + p[5]*qm4_f_train**2\\\n",
    "# + p[6]*qm4_f_train + p[7]\n",
    "# tau_f_with_cable_train = copy.deepcopy(tau_f_train);\n",
    "# tau_f_with_cable_train[:,1] = tau_f_train[:,1] + 0.6697*tau_cable4_f_train\n",
    "# tau_f_with_cable_train[:,2] = tau_f_train[:,2] - 0.6697*tau_cable4_f_train\n",
    "# tau_f_with_cable_train[:,3] = tau_f_train[:,3] + tau_cable4_f_train\n",
    "tau_p_sdp_with_cable_train = copy.deepcopy(tau_p_sdp_train);\n",
    "# tau_p_sdp_with_cable_train[:,1] = tau_p_sdp_train[:,1] + 0.6697*tau_cable4_f_train\n",
    "# tau_p_sdp_with_cable_train[:,2] = tau_p_sdp_train[:,2] - 0.6697*tau_cable4_f_train\n",
    "# tau_p_sdp_with_cable_train[:,3] = tau_p_sdp_train[:,3] + tau_cable4_f_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.13099819, 0.21834573, 0.23266792, 0.31401481, 0.49678029,\n",
       "       0.29614103, 0.29587482])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(tau_f_with_cable_train[:plot_data_num, :] - tau_p_sdp_with_cable_train[:plot_data_num, :], axis=0)\\\n",
    "    / np.linalg.norm(tau_f_with_cable_train[:plot_data_num, :], axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot measured torque and predicted torque"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_data_num = int(1.0 / base_freq * trajectory_sampling_rate)\n",
    "plot_meas_pred_tau(t_cut_train[:plot_data_num] - t_cut_train[0],\n",
    "                   tau_f_with_cable_train[:plot_data_num, :],\n",
    "                   tau_p_sdp_with_cable_train[:plot_data_num, :],\n",
    "                   robot_model.coordinates_joint_type,\n",
    "                   robot_model.coordinates)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare measured torque and predicted torque on test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "bary_param_num = len(robot_model.bary_param)\n",
    "H_func = robot_model.H_func\n",
    "W_test, tau_s_test = gen_regressor(bary_param_num, H_func,\n",
    "                                   q_f_test, dq_f_test, ddq_f_test, tau_f_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "tau_p_sdp_test = np.zeros(tau_f_test.shape)\n",
    "tau_ps_sdp_test = W_test.dot(sdp_opt_std.x_result)\n",
    "for i in range(dof):\n",
    "    tau_p_sdp_test[:, i] = tau_ps_sdp_test[i::dof]\n",
    "    \n",
    "# add cable torque back\n",
    "# qm4_f_test = 0.6697*q_f_test[:,1] - 0.6697*q_f_test[:,2] + q_f_test[:,3]\n",
    "# tau_cable4_f_test = p[0]*qm4_f_test**7 + p[1]*qm4_f_test**6 + p[2]*qm4_f_test**5\\\n",
    "# + p[3]*qm4_f_test**4 + p[4]*qm4_f_test**3 + p[5]*qm4_f_test**2\\\n",
    "# + p[6]*qm4_f_test + p[7]\n",
    "tau_f_with_cable_test = copy.deepcopy(tau_f_test);\n",
    "# tau_f_with_cable_test[:,1] = tau_f_test[:,1] + 0.6697*tau_cable4_f_test\n",
    "# tau_f_with_cable_test[:,2] = tau_f_test[:,2] - 0.6697*tau_cable4_f_test\n",
    "# tau_f_with_cable_test[:,3] = tau_f_test[:,3] + tau_cable4_f_test\n",
    "tau_p_sdp_with_cable_test = copy.deepcopy(tau_p_sdp_test);\n",
    "# tau_p_sdp_with_cable_test[:,1] = tau_p_sdp_test[:,1] + 0.6697*tau_cable4_f_test\n",
    "# tau_p_sdp_with_cable_test[:,2] = tau_p_sdp_test[:,2] - 0.6697*tau_cable4_f_test\n",
    "# tau_p_sdp_with_cable_test[:,3] = tau_p_sdp_test[:,3] + tau_cable4_f_test\n",
    "\n",
    "plot_data_num = int(1 / base_freq * trajectory_sampling_rate)\n",
    "plot_meas_pred_tau(t_cut_test[:plot_data_num] - t_cut_test[0],\n",
    "                   tau_f_with_cable_test[:plot_data_num, :],\n",
    "                   tau_p_sdp_with_cable_test[:plot_data_num, :],\n",
    "                   robot_model.coordinates_joint_type,\n",
    "                   robot_model.coordinates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_plot_data_folder = 'data/' + model_name +'/test_plot_data_folder/'\n",
    "test_plot_data = (t_cut_test[:plot_data_num] - t_cut_test[0],\n",
    "                   tau_f_test[:plot_data_num, :],\n",
    "                   tau_p_sdp_test[:plot_data_num, :],\n",
    "                   robot_model.coordinates_joint_type,\n",
    "                   robot_model.coordinates)\n",
    "save_data(test_plot_data_folder, test_trajectory_name, test_plot_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.11503431, 0.18592568, 0.3995263 , 0.36182945, 0.6934144 ,\n",
       "       0.31096307, 0.36986051])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(tau_f_test[:plot_data_num, :] - tau_p_sdp_test[:plot_data_num, :], axis=0)\\\n",
    "/ np.linalg.norm(tau_f_test[:plot_data_num, :], axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compare results based on our modeling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "# reload(identification)\n",
    "# reload(identification.plot_meas_2pred_tau)\n",
    "from identification.data_processing import plot_meas_2pred_tau\n",
    "\n",
    "# from identification import plot_meas_2pred_tau\n",
    "(t_cut_test_mtm, tau_f_test_mtm, tau_p_sdp_test_mtm, joint_type_mtm, coordinates_mtm)= \\\n",
    "    load_data('data/' + 'mtm' +'/test_plot_data_folder/', test_trajectory_name)\n",
    "\n",
    "plot_meas_2pred_tau(t_cut_test[:plot_data_num] - t_cut_test[0],\n",
    "                    tau_f_test[:plot_data_num, :],\n",
    "                    tau_p_sdp_test[:plot_data_num, :],\n",
    "                    tau_p_sdp_test_mtm,\n",
    "                    robot_model.coordinates_joint_type,\n",
    "                    robot_model.coordinates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{array}{cccccccccccccccc}link & L_{xx} & L_{xy} & L_{xz} & L_{yy} & L_{yz} & L_{zz} & l_{x} & l_{y} & l_{z} & m & F_{c} & F_{v} & F_{o} & I_{m} & K\\\\1 & 9.8416674 & 0.0 & 0.0 & 9.8416674 & 0.0 & 2.2 \\cdot 10^{-6} & 0.0 & 0.0 & 0.8319763 & 7.8803346 & 0.0527431 & 0.0602643 & 0 & 0 & 0.3079577\\\\2 & 0.0183364 & 0.000621 & 0.0022639 & 0.0300482 & 0.005132 & 0.0150189 & -0.3627954 & -0.0293436 & 0.2009085 & 11.010124 & 0.0327126 & 0.0832541 & 0 & 0 & 0\\\\3 & 0.0083767 & 0.0026589 & 0.0025635 & 0.0188209 & -0.0008857 & 0.0116383 & 0.0886302 & -0.0214145 & -0.0213247 & 0.7108245 & 0.0009918 & 0.001004 & 0 & 0 & 0\\\\4 & 0.0244545 & -0.0007867 & 0.0192811 & 0.0443905 & 0.0005613 & 0.0198973 & -0.4100324 & -0.0159784 & 0.3983218 & 8.437437 & 0.0594039 & 0.1044564 & 0 & 0 & 0\\\\5 & 0.0166861 & -0.000361 & -0.0065029 & 0.0207145 & 0.0039511 & 0.0088901 & 0.0999954 & 0.0400222 & 0.0400003 & 2.0000074 & 0.0009918 & 0.001004 & 0 & 0 & 0\\\\6 & 0.0133038 & -0.0005617 & -0.0035948 & 0.0136383 & -0.0013557 & -0.0007048 & -0.0027141 & 0.0031421 & -0.0134108 & 0.0887525 & 0.0419278 & 0.0075698 & 0 & 0 & 0.0012259\\\\7 & -6.0 \\cdot 10^{-5} & -0.0004667 & 0.0002862 & -0.0011427 & -0.0001625 & -0.000814 & 0.005529 & -4.17 \\cdot 10^{-5} & -0.0128695 & 0.2374334 & 0.0080257 & 0.0011775 & 0 & 0 & -0.001853\\\\8 & 0.0007037 & 0.0001247 & -0.0002952 & 0.000198 & 0.000301 & 0.0003354 & -0.0006545 & 0.004434 & -0.0019808 & 0.0499827 & 0.0029644 & 0.0008942 & 0 & 0 & 0.0007937\\\\9 & -9.96 \\cdot 10^{-5} & -8.9 \\cdot 10^{-6} & -1.1 \\cdot 10^{-6} & -8.72 \\cdot 10^{-5} & -4.7 \\cdot 10^{-6} & -4.0 \\cdot 10^{-7} & 2.1 \\cdot 10^{-5} & 9.4 \\cdot 10^{-6} & 0.0008054 & 0.0199821 & 0.0011279 & 0.0001109 & 0 & 0 & 0\\end{array}\\right]$$"
      ],
      "text/plain": [
       "⎡link     Lₓₓ        L_xy        L_xz        L_yy        L_yz        L_zz     \n",
       "⎢                                                                             \n",
       "⎢ 1    9.8416674     0.0         0.0      9.8416674      0.0        2.2e-6    \n",
       "⎢                                                                             \n",
       "⎢ 2    0.0183364   0.000621   0.0022639   0.0300482    0.005132   0.0150189   \n",
       "⎢                                                                             \n",
       "⎢ 3    0.0083767  0.0026589   0.0025635   0.0188209   -0.0008857  0.0116383   \n",
       "⎢                                                                             \n",
       "⎢ 4    0.0244545  -0.0007867  0.0192811   0.0443905   0.0005613   0.0198973   \n",
       "⎢                                                                             \n",
       "⎢ 5    0.0166861  -0.000361   -0.0065029  0.0207145   0.0039511   0.0088901   \n",
       "⎢                                                                             \n",
       "⎢ 6    0.0133038  -0.0005617  -0.0035948  0.0136383   -0.0013557  -0.0007048  \n",
       "⎢                                                                             \n",
       "⎢ 7     -6.0e-5   -0.0004667  0.0002862   -0.0011427  -0.0001625  -0.000814   \n",
       "⎢                                                                             \n",
       "⎢ 8    0.0007037  0.0001247   -0.0002952   0.000198    0.000301   0.0003354   \n",
       "⎢                                                                             \n",
       "⎣ 9    -9.96e-5    -8.9e-6     -1.1e-6     -8.72e-5    -4.7e-6     -4.0e-7    \n",
       "\n",
       "    lₓ         l_y         l_z          m         F_c        Fᵥ      Fₒ  I_m  \n",
       "                                                                              \n",
       "   0.0         0.0      0.8319763   7.8803346  0.0527431  0.0602643  0    0   \n",
       "                                                                              \n",
       "-0.3627954  -0.0293436  0.2009085   11.010124  0.0327126  0.0832541  0    0   \n",
       "                                                                              \n",
       "0.0886302   -0.0214145  -0.0213247  0.7108245  0.0009918  0.001004   0    0   \n",
       "                                                                              \n",
       "-0.4100324  -0.0159784  0.3983218   8.437437   0.0594039  0.1044564  0    0   \n",
       "                                                                              \n",
       "0.0999954   0.0400222   0.0400003   2.0000074  0.0009918  0.001004   0    0   \n",
       "                                                                              \n",
       "-0.0027141  0.0031421   -0.0134108  0.0887525  0.0419278  0.0075698  0    0   \n",
       "                                                                              \n",
       " 0.005529    -4.17e-5   -0.0128695  0.2374334  0.0080257  0.0011775  0    0   \n",
       "                                                                              \n",
       "-0.0006545   0.004434   -0.0019808  0.0499827  0.0029644  0.0008942  0    0   \n",
       "                                                                              \n",
       "  2.1e-5      9.4e-6    0.0008054   0.0199821  0.0011279  0.0001109  0    0   \n",
       "\n",
       "    K    ⎤\n",
       "         ⎥\n",
       "0.3079577⎥\n",
       "         ⎥\n",
       "    0    ⎥\n",
       "         ⎥\n",
       "    0    ⎥\n",
       "         ⎥\n",
       "    0    ⎥\n",
       "         ⎥\n",
       "    0    ⎥\n",
       "         ⎥\n",
       "0.0012259⎥\n",
       "         ⎥\n",
       "-0.001853⎥\n",
       "         ⎥\n",
       "0.0007937⎥\n",
       "         ⎥\n",
       "    0    ⎦"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from identification import params_array2table\n",
    "x_bary_round= np.around(sdp_opt_std.x_result, decimals=7)\n",
    "bary_param_table = params_array2table(x_bary_round, robot_model, 'bary')\n",
    "# sympy.Matrix.hstack(sympy.Matrix(robot_model.bary_param), sympy.Matrix(sdp_opt_std.x_result))\n",
    "bary_param_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "from identification import barycentric2standard_params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "x_std = barycentric2standard_params(sdp_opt_std.x_result, robot_model)\n",
    "s_round_std = np.round(np.array(x_std).astype(np.float), decimals=7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{array}{cccccccccccccccc}link & I_{xx} & I_{xy} & I_{xz} & I_{yy} & I_{yz} & I_{zz} & r_{x} & r_{y} & r_{z} & m & F_{c} & F_{v} & F_{o} & I_{m} & K\\\\1 & 9.7538305 & 0.0 & 0.0 & 9.7538305 & 0.0 & 2.2 \\cdot 10^{-6} & 0.0 & 0.0 & 0.1055763 & 7.8803346 & 0.0527431 & 0.0602643 & 0 & 0 & 0.3079577\\\\2 & 0.0145921 & 0.0015879 & -0.0043562 & 0.0144276 & 0.0045965 & 0.0029862 & -0.0329511 & -0.0026651 & 0.0182476 & 11.010124 & 0.0327126 & 0.0832541 & 0 & 0 & 0\\\\3 & 0.0070919 & -1.12 \\cdot 10^{-5} & -9.54 \\cdot 10^{-5} & 0.0071302 & -0.0002432 & -5.78 \\cdot 10^{-5} & 0.1246864 & -0.0301263 & -0.03 & 0.7108245 & 0.0009918 & 0.001004 & 0 & 0 & 0\\\\4 & 0.0056199 & -1.02 \\cdot 10^{-5} & -7.61 \\cdot 10^{-5} & 0.00566 & -0.000193 & -5.92 \\cdot 10^{-5} & -0.0485968 & -0.0018937 & 0.0472089 & 8.437437 & 0.0594039 & 0.1044564 & 0 & 0 & 0\\\\5 & 0.0150852 & 0.00164 & -0.0045029 & 0.014915 & 0.0047515 & 0.0030897 & 0.0499975 & 0.020011 & 0.0200001 & 2.0000074 & 0.0009918 & 0.001004 & 0 & 0 & 0\\\\6 & 0.0111662 & -0.0006578 & -0.0031847 & 0.0115289 & -0.0018304 & -0.000899 & -0.0305805 & 0.0354029 & -0.1511033 & 0.0887525 & 0.0419278 & 0.0075698 & 0 & 0 & 0.0012259\\\\7 & -0.0007575 & -0.0004676 & -1.35 \\cdot 10^{-5} & -0.001969 & -0.0001602 & -0.0009428 & 0.0232866 & -0.0001756 & -0.0542025 & 0.2374334 & 0.0080257 & 0.0011775 & 0 & 0 & -0.001853\\\\8 & 0.0002319 & 6.66 \\cdot 10^{-5} & -0.0002693 & 0.0001109 & 0.0001253 & -6.65 \\cdot 10^{-5} & -0.0130951 & 0.0887102 & -0.0396306 & 0.0499827 & 0.0029644 & 0.0008942 & 0 & 0 & 0.0007937\\\\9 & -0.0001321 & -8.8 \\cdot 10^{-6} & -2.0 \\cdot 10^{-7} & -0.0001197 & -4.3 \\cdot 10^{-6} & -5.0 \\cdot 10^{-7} & 0.0010501 & 0.0004727 & 0.0403049 & 0.0199821 & 0.0011279 & 0.0001109 & 0 & 0 & 0\\end{array}\\right]$$"
      ],
      "text/plain": [
       "⎡link     Iₓₓ         I_xy        I_xz        I_yy        I_yz        I_zz    \n",
       "⎢                                                                             \n",
       "⎢ 1    9.7538305      0.0         0.0      9.7538305      0.0        2.2e-6   \n",
       "⎢                                                                             \n",
       "⎢ 2    0.0145921   0.0015879   -0.0043562  0.0144276   0.0045965   0.0029862  \n",
       "⎢                                                                             \n",
       "⎢ 3    0.0070919    -1.12e-5    -9.54e-5   0.0071302   -0.0002432   -5.78e-5  \n",
       "⎢                                                                             \n",
       "⎢ 4    0.0056199    -1.02e-5    -7.61e-5    0.00566    -0.000193    -5.92e-5  \n",
       "⎢                                                                             \n",
       "⎢ 5    0.0150852    0.00164    -0.0045029   0.014915   0.0047515   0.0030897  \n",
       "⎢                                                                             \n",
       "⎢ 6    0.0111662   -0.0006578  -0.0031847  0.0115289   -0.0018304  -0.000899  \n",
       "⎢                                                                             \n",
       "⎢ 7    -0.0007575  -0.0004676   -1.35e-5   -0.001969   -0.0001602  -0.0009428 \n",
       "⎢                                                                             \n",
       "⎢ 8    0.0002319    6.66e-5    -0.0002693  0.0001109   0.0001253    -6.65e-5  \n",
       "⎢                                                                             \n",
       "⎣ 9    -0.0001321   -8.8e-6     -2.0e-7    -0.0001197   -4.3e-6     -5.0e-7   \n",
       "\n",
       "     rₓ         r_y         r_z          m         F_c        Fᵥ      Fₒ  I_m \n",
       "                                                                              \n",
       "    0.0         0.0      0.1055763   7.8803346  0.0527431  0.0602643  0    0  \n",
       "                                                                              \n",
       " -0.0329511  -0.0026651  0.0182476   11.010124  0.0327126  0.0832541  0    0  \n",
       "                                                                              \n",
       " 0.1246864   -0.0301263    -0.03     0.7108245  0.0009918  0.001004   0    0  \n",
       "                                                                              \n",
       " -0.0485968  -0.0018937  0.0472089   8.437437   0.0594039  0.1044564  0    0  \n",
       "                                                                              \n",
       " 0.0499975    0.020011   0.0200001   2.0000074  0.0009918  0.001004   0    0  \n",
       "                                                                              \n",
       " -0.0305805  0.0354029   -0.1511033  0.0887525  0.0419278  0.0075698  0    0  \n",
       "                                                                              \n",
       " 0.0232866   -0.0001756  -0.0542025  0.2374334  0.0080257  0.0011775  0    0  \n",
       "                                                                              \n",
       " -0.0130951  0.0887102   -0.0396306  0.0499827  0.0029644  0.0008942  0    0  \n",
       "                                                                              \n",
       " 0.0010501   0.0004727   0.0403049   0.0199821  0.0011279  0.0001109  0    0  \n",
       "\n",
       "     K    ⎤\n",
       "          ⎥\n",
       " 0.3079577⎥\n",
       "          ⎥\n",
       "     0    ⎥\n",
       "          ⎥\n",
       "     0    ⎥\n",
       "          ⎥\n",
       "     0    ⎥\n",
       "          ⎥\n",
       "     0    ⎥\n",
       "          ⎥\n",
       " 0.0012259⎥\n",
       "          ⎥\n",
       " -0.001853⎥\n",
       "          ⎥\n",
       " 0.0007937⎥\n",
       "          ⎥\n",
       "     0    ⎦"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "std_param_table = params_array2table(s_round_std, robot_model, 'std')\n",
    "#sympy.Matrix.hstack(sympy.Matrix(robot_model.std_param), sympy.Matrix(x_std))\n",
    "std_param_table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Write identified dynamic parameters into a JSON file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{array}{cccccccccccccccc}link & I_{xx} & I_{xy} & I_{xz} & I_{yy} & I_{yz} & I_{zz} & r_{x} & r_{y} & r_{z} & m & F_{c} & F_{v} & F_{o} & I_{m} & K\\\\1 & 9.7538305 & 0.0 & 0.0 & 9.7538305 & 0.0 & 2.2 \\cdot 10^{-6} & 0.0 & 0.0 & 0.1055763 & 7.8803346 & 0.0527431 & 0.0602643 & 0 & 0 & 0.3079577\\\\2 & 0.0144276 & -0.0045965 & 0.0015879 & 0.0029862 & 0.0043562 & 0.0145921 & 0.0026651 & 0.0182476 & 0.0329511 & 11.010124 & 0.0327126 & 0.0832541 & 0 & 0 & 0\\\\3 & 0.0070919 & 9.54 \\cdot 10^{-5} & 1.12 \\cdot 10^{-5} & -5.78 \\cdot 10^{-5} & -0.0002432 & 0.0071302 & -0.1246864 & -0.03 & -0.0301263 & 0.7108245 & 0.0009918 & 0.001004 & 0 & 0 & 0\\\\4 & 0.0056199 & 7.61 \\cdot 10^{-5} & 1.02 \\cdot 10^{-5} & -5.92 \\cdot 10^{-5} & -0.000193 & 0.00566 & 0.0485968 & 0.0472089 & -0.0018937 & 8.437437 & 0.0594039 & 0.1044564 & 0 & 0 & 0\\\\5 & 0.014915 & -0.0047515 & 0.00164 & 0.0030897 & 0.0045029 & 0.0150852 & -0.020011 & 0.0200001 & -0.0499975 & 2.0000074 & 0.0009918 & 0.001004 & 0 & 0 & 0\\\\6 & 0.0111662 & -0.0006578 & 0.0031847 & 0.0115289 & 0.0018304 & -0.000899 & 0.0305805 & -0.0354029 & -0.1511033 & 0.0887525 & 0.0419278 & 0.0075698 & 0 & 0 & 0.0012259\\\\7 & -0.0007575 & 1.35 \\cdot 10^{-5} & 0.0004676 & -0.0009428 & -0.0001602 & -0.001969 & -0.0232866 & -0.0542025 & -0.0001756 & 0.2374334 & 0.0080257 & 0.0011775 & 0 & 0 & -0.001853\\\\8 & 0.0001109 & -6.66 \\cdot 10^{-5} & 0.0001253 & 0.0002319 & 0.0002693 & -6.65 \\cdot 10^{-5} & 0.0887102 & 0.0130951 & -0.0396306 & 0.0499827 & 0.0029644 & 0.0008942 & 0 & 0 & 0.0007937\\\\9 & -5.0 \\cdot 10^{-7} & -2.0 \\cdot 10^{-7} & -4.3 \\cdot 10^{-6} & -0.0001321 & -8.8 \\cdot 10^{-6} & -0.0001197 & 0.0403049 & 0.0010501 & 0.0004727 & 0.0199821 & 0.0011279 & 0.0001109 & 0 & 0 & 0\\end{array}\\right]$$"
      ],
      "text/plain": [
       "⎡link     Iₓₓ         I_xy       I_xz        I_yy        I_yz        I_zz     \n",
       "⎢                                                                             \n",
       "⎢ 1    9.7538305      0.0         0.0     9.7538305      0.0        2.2e-6    \n",
       "⎢                                                                             \n",
       "⎢ 2    0.0144276   -0.0045965  0.0015879  0.0029862   0.0043562   0.0145921   \n",
       "⎢                                                                             \n",
       "⎢ 3    0.0070919    9.54e-5     1.12e-5    -5.78e-5   -0.0002432  0.0071302   \n",
       "⎢                                                                             \n",
       "⎢ 4    0.0056199    7.61e-5     1.02e-5    -5.92e-5   -0.000193    0.00566    \n",
       "⎢                                                                             \n",
       "⎢ 5     0.014915   -0.0047515   0.00164   0.0030897   0.0045029   0.0150852   \n",
       "⎢                                                                             \n",
       "⎢ 6    0.0111662   -0.0006578  0.0031847  0.0115289   0.0018304   -0.000899   \n",
       "⎢                                                                             \n",
       "⎢ 7    -0.0007575   1.35e-5    0.0004676  -0.0009428  -0.0001602  -0.001969   \n",
       "⎢                                                                             \n",
       "⎢ 8    0.0001109    -6.66e-5   0.0001253  0.0002319   0.0002693    -6.65e-5   \n",
       "⎢                                                                             \n",
       "⎣ 9     -5.0e-7     -2.0e-7     -4.3e-6   -0.0001321   -8.8e-6    -0.0001197  \n",
       "\n",
       "    rₓ         r_y         r_z          m         F_c        Fᵥ      Fₒ  I_m  \n",
       "                                                                              \n",
       "   0.0         0.0      0.1055763   7.8803346  0.0527431  0.0602643  0    0   \n",
       "                                                                              \n",
       "0.0026651   0.0182476   0.0329511   11.010124  0.0327126  0.0832541  0    0   \n",
       "                                                                              \n",
       "-0.1246864    -0.03     -0.0301263  0.7108245  0.0009918  0.001004   0    0   \n",
       "                                                                              \n",
       "0.0485968   0.0472089   -0.0018937  8.437437   0.0594039  0.1044564  0    0   \n",
       "                                                                              \n",
       "-0.020011   0.0200001   -0.0499975  2.0000074  0.0009918  0.001004   0    0   \n",
       "                                                                              \n",
       "0.0305805   -0.0354029  -0.1511033  0.0887525  0.0419278  0.0075698  0    0   \n",
       "                                                                              \n",
       "-0.0232866  -0.0542025  -0.0001756  0.2374334  0.0080257  0.0011775  0    0   \n",
       "                                                                              \n",
       "0.0887102   0.0130951   -0.0396306  0.0499827  0.0029644  0.0008942  0    0   \n",
       "                                                                              \n",
       "0.0403049   0.0010501   0.0004727   0.0199821  0.0011279  0.0001109  0    0   \n",
       "\n",
       "    K    ⎤\n",
       "         ⎥\n",
       "0.3079577⎥\n",
       "         ⎥\n",
       "    0    ⎥\n",
       "         ⎥\n",
       "    0    ⎥\n",
       "         ⎥\n",
       "    0    ⎥\n",
       "         ⎥\n",
       "    0    ⎥\n",
       "         ⎥\n",
       "0.0012259⎥\n",
       "         ⎥\n",
       "-0.001853⎥\n",
       "         ⎥\n",
       "0.0007937⎥\n",
       "         ⎥\n",
       "    0    ⎦"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Rs = [np.matrix(R.evalf(subs={q1: 0, q2: 0, q3: 0, q4: 0, q5: 0, q6: 0, q7: 0})).astype(np.float64)\n",
    "      for R in robot_model.R[1:]]\n",
    "x_std_base_frame = barycentric2standard_params(sdp_opt_std.x_result, robot_model, Rs)\n",
    "x_round_std_base_frame = np.round(np.array(x_std_base_frame).astype(np.float), decimals=7)\n",
    "std_param_base_frame_table = params_array2table(x_round_std_base_frame, robot_model, 'std')\n",
    "std_param_base_frame_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters have been written into [data/mtm_fontanelli/dynamic_params/params.json] successfully!\n"
     ]
    }
   ],
   "source": [
    "from identification import *\n",
    "param_folder = 'data/' + model_name +'/dynamic_params/'\n",
    "std_param_name = 'params'\n",
    "write_parameters2json(std_param_base_frame_table, param_folder, std_param_name)"
   ]
  }
 ],
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