On the implementation of model predictive control for on-line walking pattern generation

This article addresses the real-time implementation issues of a model predictive control based walking pattern generation for a humanoid robot. We approximate the multibody dynamic model with a linear discrete time system, and at each step solve a quadratic program in order to keep the output within a predefined set of constraints. The focus is on creating an efficient framework for forming and solving the underlying optimization problem. For that purpose we develop: a) a reliable guess for the active constraints at optimality; b) a fast way of generating an initial feasible point with respect to the set of constraints for each preview interval; c) a variable discretization sampling time. A simple implementation of a standard primal active set algorithm which exploits a "hot start" is used to demonstrate the advantages of the first point, while the latter one is verified using an existing dual solver.