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

Abstract

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

Publication
Robotics and Automation Letters (under review)
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