Robust Bipedal Locomotion via Stein Variational Gradient Descent Solution Framework for Model Predictive Control

This paper proposes a Stein Variational Gradient Descent (SVGD) solution framework for Model Predictive Control (MPC) to enhance robustness in bipedal locomotion. While conventional simplified rigid-body dynamics (SRBD) based MPC with deterministic solvers such as the active-set method performs reliably during straight-line walking, its performance degrades significantly in agile maneuvers, where modeling simplifications become more pronounced. Simulations on the 43-DoF QingLoong humanoid demonstrate that SVGD-MPC exhibits improved robustness in dynamic locomotion tasks, including high-angular-velocity turning and circular walking. However, conventional MPC fails to maintain stability. Rather than relying on a single nominal solution, SVGD-MPC maintains an ensemble of candidate control trajectories that evolve jointly within the MPC optimization process. This ensemble-based formulation reduces sensitivity to modeling inaccuracies and allows the controller to retain feasible control candidates when the assumptions underlying the SRBD model are violated. The method sacrifices marginal tracking precision to maintain viability under model inadequacy. Moreover, our framework establishes a paradigm for robust locomotion control where the traditional optimization method fails to work.