A Newton method with always feasible iterates for Nonlinear Model Predictive Control of walking in a multi-contact situation

In this paper, we present a Nonlinear Model Predictive Control scheme, which is able to generate walking motions in multi-contact situations. Walking up and down stairs with an additional hand support is a typical example, which we address in simulation. Computing such a nonlinear control scheme is usually done with a Newton method, a potentially time-consuming procedure involving iterative linearizations. We propose here a Newton method which is specifically designed to provide at each iteration a feasible solution, always satisfying the (nonlinear) dynamic balance constraints. This results in a significant reduction in computation time, by minimizing the number of necessary iterations to reach a feasible solution.