Weighted Task-Priority Based Angular Momentum Control for Cyclic Gait of a Humanoid Robot on Deformable Terrain

Legged locomotion on deformable terrain is a challenging problem due to the large number of degrees of freedom of the robot and the terrain's deformation. Full-body dynamics of a 22-DOF robot is simplified as a spherical inverted pendulum (SIP), and a contact model is included to consider the terrain deformation. The total task of locomotion on deformable terrain is broken into primary and secondary tasks. The primary control task is to track the center of mass (COM) motion of the SIP model, i.e., control of the linear momentum. The secondary control task is to minimize the centroidal angular momentum (CAM), as the simplified model neglects the angular momentum of the robot about the COM. However, the nonholonomic constraint of zero angular momentum generates a noncyclic gait. In this paper, we propose a weighted task-priority based controller to minimize the CAM and the upper body joints motion, which utilizes adaptive task-priority weights dependent on the upper body joint configuration. The model-based control of a 22-DOF humanoid robot on deformable terrain is implemented in MuJoCo. MuJoCo contact solver parameters are obtained by combining the sphere-plane collision model with the robot's inverse dynamics. Tracking error of the COM and gait cyclicity of the upper body joints are analyzed for dynamic balance. The simulation results demonstrate that the proposed method achieves better tracking accuracy than LIPM-based walking on deformable terrain.