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

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 constrained 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.