Locomotion Control of Biped Robot with Foot Described on SE(3)*

The unique challenge of the humanoid biped robot is the locomotion control of humanoid feet which is not a simple point-contact model. A new dynamics control based on model predictive control and whole-body control of a humanoid biped robot is proposed to achieve stable locomotion of the body and feet. To control the position and orientation of feet with no singularity, the locomotion of the foot is described on S E(3) using exponential mapping. Firstly, the velocity screw is used as the swing and supporting foot constraint in the model predictive control to achieve the trajectory optimization of feet. Then, the task of the supporting foot which should be no relative motion with the ground uses the velocity screw as the description. To achieve the following orientation between the body and swing feet, the acceleration task of the swing foot utilizes the rigid model. Finally, the proposed method for a humanoid biped robot is verified and effectively controls the orientation of robot feet to achieve stability walking in the simulation.