Dynamic Walking with Footstep Adaptation on the MIT Humanoid via Linear Model Predictive Control

This paper proposes a model predictive control (MPC) framework for realizing dynamic walking gaits on the MIT Humanoid. In addition to adapting footstep location and timing online, the proposed method can reason about varying height, contact wrench, torso rotation, kinematic limit and negotiating uneven terrains. Specifically, a linear MPC (LMPC) optimizes for the desired footstep location by linearizing the single rigid body dynamics with respect to the current footstep location. A low-level task-space controller tracks the predicted state and control trajectories from the LMPC to leverage the full-body dynamics. Finally, an adaptive gait frequency scheme is employed to modify the step frequency and enhance the robustness of the walking controller. Both LMPC and task-space control can be efficiently solved as quadratic programs (QP), and thus amenable for real-time applications. Simulation studies where the MIT Humanoid traverses a wave field and recovers from impulsive disturbances validated the proposed approach.