Robust Locomotion Exploiting Multiple Balance Strategies: An Observer-Based Cascaded Model Predictive Control Approach

Robust locomotion is a challenging task for humanoid robots, especially when considering dynamic disturbances. This article proposes a disturbance observer-based cascaded model predictive control (MPC) approach for bipedal locomotion, with the capability of exploiting ankle, stepping, hip and height variation strategies. Specifically, based on the variable-height inverted pendulum model, a nonlinear MPC that is run at a low frequency is built for 3-D locomotion (i.e., with height variation) while accounting for the footstep modulation as well. Differing from previous works, the nonlinear MPC is formulated as a convex optimization problem by semidefinite relaxation. Subsequently, assuming a flywheel at the pelvis center, a linear MPC that is run at a high frequency is proposed to regulate angular momentum (e.g., through rotating the upper body), which is solved by convex quadratic programming. To run the cascaded MPC in a closed-loop manner, a high order sliding mode observer is designed to estimate system states and dynamic disturbances simultaneously. Simulation and hardware experiments demonstrate the walking robustness in real-world scenarios, including 3-D walking with varying speeds, walking across non-coplanar terrains and push recovery.