  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.
