Dual-MPC Footstep Planning for Robust Quadruped Locomotion

In this paper, we propose a footstep planning strategy based on model predictive control (MPC) that enables robust regulation of body orientation against undesired body rotations by optimizing footstep placement. Model-based locomotion approaches typically adopt heuristic methods or planning based on the linear inverted pendulum model. These methods account for linear velocity in footstep planning, while excluding angular velocity, which leads to angular momentum being handled exclusively via ground reaction force (GRF). Footstep planning based on MPC that takes angular velocity into account recasts the angular momentum control problem as a dual-input approach that coordinates GRFs and footstep placement, instead of optimizing GRFs alone, thereby improving tracking performance. A mutual-feedback loop couples the footstep planner and the GRF MPC, with each using the other's solution to iteratively update footsteps and GRFs. The use of optimal solutions reduces body oscillation and enables extended stance and swing phases. The method is validated on a quadruped robot, demonstrating robust locomotion with reduced oscillations, longer stance and swing phases across various terrains.