Sensitivity of Legged Balance Control to Uncertainties and Sampling Period

Abstract

We propose to quantify the effect of sensor and actuator uncertainties on the control of the center of mass and center of pressure in legged robots, since this is central for maintaining their balance with a limited support polygon. Our approach is based on robust control theory, considering uncertainties that can take any value between specified bounds. This provides a principled approach to deciding optimal feedback gains. Surprisingly, our main observation is that the sampling period can be as long as 200 ms with literally no impact on maximum tracking error and, as a result, on the guarantee that balance can be maintained safely. Our findings are validated in simulations and experiments with the torquecontrolled humanoid robot Toro developed at DLR. The proposed mathematical derivations and results apply nevertheless equally to biped and quadruped robots.

Recent Progress in Legged Robots Locomotion Control

“…Sensor-based control could be an alternative, largely unexplored so far [94]. Robust control could be another alternative, not much explored either [95][96][97][98]. A recent conclusion from robust control analysis of legged balance is that perfectly stable feedback can be obtained at surprisingly low frequency, as demonstrated with both humanoid [97] and quadruped robots [59].…”

Effect of Planning Period on MPC-based Navigation for a Biped Robot in a Crowd

“…Thanks to the safe linear approximation of (C), feasible iterates are always generated. Note that the convergence condition (16) does not guarantee optimality. The main interest of this work is not to guarantee optimality of the motion with the Newton method, but to plan a motion that treat collision avoidance as close as possible to a nonlinear problem.…”

“…The objective of this paper is to measure if re-planning the walking motion more often than once at every footstep can lead to an improvement in collision avoidance when navigating in a crowd. As an element of comparison, it has been shown in [16] that when considering only the balance of a biped robot, reacting more often than every 0.2[s] to potential perturbations leads to no practical improvement in the maximal tracking error.…”

Torque Controlled Locomotion of a Biped Robot with Link Flexibility

“…At each step, big CoP y oscillations appear and are quickly stabilized. We think these oscillations may be produced by our bad estimation of the hip damping coefficients or a too high cutting frequency in the filter (13). Nevertheless, the whole robot motion is smooth and fluid as illustrated in the video 1 .…”

“…The remaining (much smaller) model error, as well as all internal and external disturbances, produce tracking errors that grow with the robot dynamics. We use state feedback to stabilize the behavior of the Center of Mass (CoM) of the robot and, based on a reachability analysis of the resulting closed-loop system [13], we deploy a tube-based MPC [14] scheme that guarantees robust feasibility when disturbances are bounded.…”