Trajectory Free Linear Model Predictive Control for Stable Walking in the Presence of Strong Perturbations

Abstract

Abstract-A humanoid walking robot is a highly nonlinear dynamical system that relies strongly on contact forces between its feet and the ground in order to realize stable motions, but these contact forces are unfortunately severely limited. Model Predictive Control, also known as Receding Horizon Control, is a general control scheme specifically designed to deal with such contrained dynamical systems, with the potential ability to react efficiently to a wide range of situations. Apart from the question of computation time which needs to be taken care of carefully (these schemes can be highly computation intensive), the initial question of which optimal control problems should be considered to be solved online in order to lead to the desired walking movements is still unanswered. A key idea for answering to this problem can be found in the ZMP Preview Control scheme. After presenting here this scheme with a point of view slightly different from the original one, we focus on the problem of compensating strong perturbations of the dynamics of the robot and propose a new Linear Model Predictive Control scheme which is an improvement of the original ZMP Preview Control scheme.

Online generation of cyclic leg trajectories synchronized with sensor measurement

“…More generally, the use of nonlinear oscillators as periodic trajectory generators for dynamically stable biped walking has not yet been studied. A way to address the problem might be to connect to the very promising works of Kajita [36] and Wieber [37], who use a predictive control approach to compute on line the parameters which maintains the Center of Pressure in a given area.…”

Omni-directional closed-loop walk for NAO

“…H. DIEDAM et al [17] proposed an algorithm based on the previous paper of P.B. WIEBER [14] that looks promising for such tasks.…”

Synthesis of complex humanoid whole-body behavior: A focus on sequencing and tasks transitions

“…A polygonal approximation of the cone, lying in the real Coulomb cone, may be used to linearize equation (14). Given C f i the representation of this linearized cone, the inequality becomes…”

“…The direct control of z may be unstable, so an approach which takes into account the prediction of the future position must be implemented. As described in [14], the initial configuration of the CoM is denoted C 0 = [c,ċ,c] T and the prediction of the ZMP along a time horizon H is denoted…”