Automatic Optimal Biped Walking As a Mixed-Integer Quadratic Program

This chapter proposes an original Model Predictive Control approach to the walking control for humanoid robots, which allows to generate stable walking motions without the prior definition of footsteps positions and instants. Both the instant and amplitude of the changes in the supporting surface are part of the walking motion generation problem, and are described by a set of highly-constrained integer and real variables. Combined with the center of mass trajectory of the robot, this description leads to the formulation of a Mixed-Integer Quadratic Program in a Model Predictive Control framework aiming at reaching high-level objectives, such as velocity tracking and tip-over riskminimization. The contribution of this approach is illustrated by the simulation of two scenarii, demonstrating the validity of the steps and trajectories computed in push-recovery and walking velocity tracking cases.