Adaptive step duration in biped walking: A robust approach to nonlinear constraints

When a biped robot is walking in a crowd, being able to adapt the duration of steps is a key element to avoid collisions. Model Predictive Control (MPC) schemes for biped walking usually assume a fixed step duration since adapting it leads to a nonlinear problem, in general. Nonlinear solvers do not guarantee the satisfaction of nonlinear constraints at every iterate and this can be problematic for the real-time operation of robots. We propose a method to make sure that all iterates satisfy the nonlinear constraints by borrowing concepts from robust control: we make the problem robust to nonlinearities within some bounds. These bounds are linear with respect to the variables of the problem and can be adapted online.