Why control the vertical force difference rather than vertical forces directly?

[Saeed-Mansouri]

Hi Dr. Caron,

The foot damping control introduced by Kajita is implemented in the LIPM controller for CoP/torque control. Why didn't you use such a strategy to control the vertical contact force instead of the foot force different control?

[stephane-caron]

We indeed control the difference between vertical foot forces rather than the vertical forces themselves, because the latter are sensitive to modeling errors. Imagine for instance that the robot model underestimates the total robot mass, resulting in a desired vertical force lower than what it should be. Even at rest, the robot will measure a larger force than the desired one: the foot will go up (admittance control) to instantaneously reduce the measured force, which works in the short term but will result in the robot crouching forever. This point is discussed for instance in Section IV of the following paper on feedback control of the VHIP model.

The underlying idea behind the difference here is to control forces via translations in the nullspace of the contact Jacobian. See Multi-Contact Stabilization of a Humanoid Robot for Realizing Dynamic Contact Transitions on Non-coplanar Surfaces (Morisawa et al., 2019), equations (2)–(5) and (20)–(21), for insights into this more general approach.

[Saeed-Mansouri]

I have implemented Multi-Contact Stabilization of a Humanoid Robot for Realizing Dynamic Contact Transitions on Non-coplanar Surfaces to improve Stabilizer::updateFootForceDifferenceControl(). Section 4.2 of An inverse dynamics-based multi-contact locomotion control framework without joint torque feedback was helpful to understand this strategy better. Based on these two papers, I have found that the damping control term should be modified as below for walking on the horizontal plane.

Left:  vfz_L = - A * ( (1-p) * (fz_qp_L - fz_m_L) - p * (fz_qp_R - fz_m_R) )
Right:  vfz_R = - A * ( - (1-p) * (fz_qp_L - fz_m_L) + p * (fz_qp_R - fz_m_R) )

in which p is the leftFootRatio_. Considering these equations, the foot force errors should be distributed based on the p.