An Improved Hierarchical Optimization Framework for Walking Control of Underactuated Humanoid Robots Using Model Predictive Control and Whole Body Planner and Controller

This paper addresses the fundamental challenge of achieving stable and efficient walking in a lightweight, underactuated humanoid robot that lacks an ankle roll degree of freedom. To tackle this relevant critical problem, we present a hierarchical optimization framework that combines model predictive control (MPC) with a tailored whole body planner and controller (WBPC). At the high level, we employ a matrix exponential (ME)-based discretization of the MPC, ensuring numerical stability across a wide range of step sizes (5 to 100 ms), thereby reducing computational complexity without sacrificing control quality. At the low level, the WBPC is specifically designed to handle the unique kinematic constraints imposed by the missing ankle roll DOF, generating feasible joint trajectories for the swing foot phase. Meanwhile, a whole body control (WBC) strategy refines ground reaction forces and joint trajectories under full-body dynamics and contact wrench cone (CWC) constraints, guaranteeing physically realizable interactions with the environment. Finally, a position–velocity–torque (PVT) controller integrates feedforward torque commands with the desired trajectories for robust execution. Validated through walking experiments on the MuJoCo simulation platform using our custom-designed lightweight robot X02, this approach not only improves the numerical stability of MPC solutions, but also provides a scientifically sound and effective method for underactuated humanoid locomotion control.