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MRL.m
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MRL.m
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classdef MRL
methods
%% Forward Kinematics
function t = kinematics_forward_head(~, q, neckOffsetZ, cameraOffsetZ)
t = Transform();
t = t.translateZ(neckOffsetZ)...
.mDH(0, 0, q(19), 0)...
.mDH(-pi/2, 0, q(20), 0)...
.mDH(pi/2, 0, 0, cameraOffsetZ);
end
function t = kinematics_forward_rarm(~, q, lALZ, hoX)
t = Transform();
t = t.rotateX(-pi/2).rotateZ(pi/2)...
.mDH(0, 0, q(1), 0)...
.mDH(pi/2, 0, q(3), 0)...
.mDH(pi/2, lALZ, q(5), 0)...
.translateX(hoX);
end
function t = kinematics_forward_larm(~, q, lALZ, hoX)
t = Transform();
t = t.rotateX(-pi/2).rotateZ(pi/2)...
.mDH(0, 0, q(2), 0)...
.mDH(pi/2, 0, q(4), 0)...
.mDH(pi/2, lALZ, q(6), 0)...
.translateX(hoX);
end
function t = kinematics_forward_rleg(~ , q, hipOffsetY, hipOffsetZ, dThigh, dTibia, aThigh, aTibia, footHeight)
t = Transform();
t = t.translateY(-hipOffsetY).translateZ(-hipOffsetZ)...
.mDH(0, 0,(pi/2)+q(7), 0)...
.mDH(pi/2, 0, (pi/2)+q(9) ,0)...
.mDH(pi/2, 0, aThigh+q(11), 0)...
.mDH(0, -dThigh, -aThigh-aTibia+q(13), 0)...
.mDH(0, -dTibia, aTibia+q(15) ,0)...
.mDH(-pi/2, 0, q(17), 0)...
.rotateZ(pi).rotateY(-pi/2).translateZ(-footHeight);
end
function t = kinematics_forward_lleg(~ , hipOffsetY, hipOffsetZ, q, dThigh, dTibia, footHeight)
t = Transform();
t = t.translateY(hipOffsetY).translateZ(-hipOffsetZ)...
.mDH(0, 0, (pi/2)+q(8), 0)...
.mDH(pi/2, 0, (pi/2)+q(10), 0)...
.mDH(pi/2, 0, 0+q(12), 0)...
.mDH(0, -dThigh, 0+q(14), 0)...
.mDH(0, -dTibia, 0+q(16), 0)...
.mDH(-pi/2, 0, q(18), 0)...
.rotateZ(pi).rotateY(-pi/2).translateZ(-footHeight);
end
%% Inverse Kinematics
function [t1 t2 t3 t4] = kinematics_inverse_head(~, x, y, z, neckOffsetZ, cameraOffsetZ)
t1 = atan2(y,x);
t2 = atan2(-y,-x);
t3 = acos((z-neckOffsetZ)/cameraOffsetZ);
t4 = -acos((z-neckOffsetZ)/cameraOffsetZ);
end
function t = kinematics_inverse_larm(~, transLArm, lALZ, hoX)
t = zeros(1,5);
Calpha = (hoX^2+lALZ^2-transLArm(1,4)^2-transLArm(2,4)^2-transLArm(3,4)^2)/(2*hoX*lALZ);
t(4) = pi-acos(Calpha); %teta6 Geometry
t(5) = -acos(Calpha); %teta6 Geometry
% (transLArm(3,4)<0)&(transLArm(1,4)<0)
% if transLArm(3,4)>0
% t(4) = pi-acos(Calpha);
% end
t(3) = asin(transLArm(2,4)/(lALZ+(hoX*cos(t(4))))); %teta4 Algebra
a = -hoX*sin(t(4));
b = (-lALZ*cos(t(3)))-(hoX*cos(t(4))*cos(t(3)));
c = transLArm(1,4);
t(1) = 2*atan((b+sqrt(a^2+b^2-c^2))/(a+c));
t(2) = 2*atan((b-sqrt(a^2+b^2-c^2))/(a+c));
end
function t = kinematics_inverse_rarm(~, transRArm, lALZ, hoX)
t = zeros(1,5);
Calpha = (hoX^2+lALZ^2-transRArm(1,4)^2-transRArm(2,4)^2-transRArm(3,4)^2)/(2*hoX*lALZ);
t(4) = pi-acos(Calpha); %teta6 Geometry
t(5) = -acos(Calpha); %teta6 Geometry
% (transLArm(3,4)<0)&(transLArm(1,4)<0)
% if transLArm(3,4)>0
% t(4) = pi-acos(Calpha);
% end
t(3) = asin(transRArm(2,4)/(lALZ+(hoX*cos(t(4))))); %teta4 Algebra
a = -hoX*sin(t(4));
b = (-lALZ*cos(t(3)))-(hoX*cos(t(4))*cos(t(3)));
c = transRArm(1,4);
t(1) = 2*atan((b+sqrt(a^2+b^2-c^2))/(a+c));
t(2) = 2*atan((b-sqrt(a^2+b^2-c^2))/(a+c));
end
function qLeg = kinematics_inverse_leg(this, trLeg, isLeft)
hipOffsetX = 15; % robot_origin_to_left_hip_base_tra = [15 61 -240];
hipOffsetY = 60; % robot_origin_to_right_hip_base_tra = [15 -61 -240];
hipOffsetZ = 141.6; % 240;
thighLength = 160; % robot_right_thigh_to_right_lower_leg_tra = [-160 0 0];
tibiaLength = 160; % robot_right_lower_leg_to_right_ankle_tra = [-160 0 0];
footHeight = 52; % robot_right_foot_Endefector_tra = [-52.6 0 0];
kneeOffsetX = 0.0;
dThigh = sqrt(thighLength*thighLength+kneeOffsetX*kneeOffsetX);
aThigh = atan(kneeOffsetX/thighLength);
dTibia = sqrt(tibiaLength*tibiaLength+kneeOffsetX*kneeOffsetX);
aTibia = atan(kneeOffsetX/tibiaLength);
trInvLeg = trLeg.inverse();
xHipOffset = zeros(1,3);
xLeg = zeros(1,3);
if isLeft == true
xHipOffset(1) = 0.0;
xHipOffset(2) = hipOffsetY;
xHipOffset(3) = -hipOffsetZ;
else
xHipOffset(1) = 0.0;
xHipOffset(2) = -hipOffsetY;
xHipOffset(3) = -hipOffsetZ;
end
for i = 1:3
xLeg(i) = xHipOffset(i);
end
xLeg = trInvLeg.apply(xLeg);
xLeg(3) = xLeg(3)-footHeight;
dLeg = xLeg(1)*xLeg(1) + xLeg(2)*xLeg(2) + xLeg(3)*xLeg(3);
cKnee = 0.5*(dLeg-dTibia^2-dThigh^2)/(dTibia*dThigh);
if cKnee > 1
cKnee = 1;
elseif cKnee < -1
cKnee = -1;
end
kneePitch = acos(cKnee);
ankleRoll = atan2(xLeg(2), xLeg(3));
lLeg = sqrt(dLeg);
if lLeg < 1e-16
lLeg = 1e-16;
end
pitch0 = asin(dThigh*sin(kneePitch)/lLeg);
anklePitch = asin(-xLeg(1)/lLeg) - pitch0;
rHipT = trLeg;
rHipT = rHipT.rotateX(-ankleRoll).rotateY(-anklePitch-kneePitch);
R12 = rHipT.t(1,2);
R22 = rHipT.t(2,2);
R32 = rHipT.t(3,2);
R31 = rHipT.t(3,1);
R33 = rHipT.t(3,3);
hipYaw = atan2(-R12, R22);
hipRoll = asin(R32);
hipPitch = atan2(-R31, R33);
qLeg = zeros(1,6);
qLeg(1) = hipYaw;
qLeg(2) = -hipRoll;
qLeg(3) = hipPitch-aThigh;
qLeg(4) = kneePitch+aThigh+aTibia;
qLeg(5) = -anklePitch-aTibia;
qLeg(6) = -ankleRoll;
end
function t = kinematics_inverse_lleg(this,transLLeg)
t = this.kinematics_inverse_leg(transLLeg,true);
end
function t = kinematics_inverse_rleg(this,transRLeg)
t = this.kinematics_inverse_leg(transRLeg,false);
end
% function t = kinematics_inverse_leg(transLeg,isLeft)
%
% end
function t = kinematics_inverse_legs(this, pLLeg, pRLeg, pTorso, legSupport)
trLLeg = Transform();
trLLeg = trLLeg.transform6D(pLLeg);
trRLeg = Transform();
trRLeg = trRLeg.transform6D(pRLeg);
trTorso = Transform();
trTorso = trTorso.transform6D(pTorso);
trTorso_LLeg = multiple(trTorso.inverse(), trLLeg);
trTorso_RLeg = multiple(trTorso.inverse(), trRLeg);
qLLeg = this.kinematics_inverse_lleg(trTorso_LLeg);
qRLeg = this.kinematics_inverse_rleg(trTorso_RLeg);
qLLeg = [qLLeg qRLeg];
t = qLLeg;
end
end
end