Stochastic and Robust MPC for Bipedal Locomotion: A Comparative Study on Robustness and Performance

Linear Model Predictive Control (MPC) has been successfully used for\ngenerating feasible walking motions for humanoid robots. However, the effect of\nuncertainties on constraints satisfaction has only been studied using Robust\nMPC (RMPC) approaches, which account for the worst-case realization of bounded\ndisturbances at each time instant. In this letter, we propose for the first\ntime to use linear stochastic MPC (SMPC) to account for uncertainties in\nbipedal walking. We show that SMPC offers more flexibility to the user (or a\nhigh level decision maker) by tolerating small (user-defined) probabilities of\nconstraint violation. Therefore, SMPC can be tuned to achieve a constraint\nsatisfaction probability that is arbitrarily close to 100\\%, but without\nsacrificing performance as much as tube-based RMPC. We compare SMPC against\nRMPC in terms of robustness (constraint satisfaction) and performance\n(optimality). Our results highlight the benefits of SMPC and its interest for\nthe robotics community as a powerful mathematical tool for dealing with\nuncertainties.\n