Stochastic and Robust MPC for Bipedal Locomotion: A Comparative Study on Robustness and Performance
This work addresses robustness and performance trade-offs in humanoid robot walking for the robotics community, presenting a novel application of SMPC in this domain.
The authors tackled the problem of uncertainty in bipedal locomotion control by proposing linear stochastic MPC (SMPC) as an alternative to robust MPC, showing that SMPC allows user-defined constraint violation probabilities and achieves near-perfect satisfaction with less performance sacrifice than RMPC.
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 Robust MPC (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 stochastic MPC (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 against RMPC in terms of robustness (constraint satisfaction) and performance (optimality). Our results highlight the benefits of SMPC and its interest for the robotics community as a powerful mathematical tool for dealing with uncertainties.