Legged Robot Locomotion via Hybrid Zero Dynamics and Model Predictive Control

During the motion of a quadruped robot, it may enter the underactuated state, such as when the legs are in the swinging phase of a trot gait. This underactuated state can lead to instability in the robot. In this paper, we present a nonlinear model predictive controller (MPC) to track periodic gaits generated by hybrid zero dynamics (HZD) for stabilizing legged robot locomotion, thereby ensuring stable periodic motion of the robot, particularly when a quadruped robot is in the underactuated state. Nonlinear optimization problem is designed based on HZD, considering the hybrid full-order dynamical model of the quadrupedal robot, which generates periodic trot gaits for the robot offline. The periodic trot gaits gurantee that the quadruped robot's state does not diverge, even when the robot is underactuated. We use a nonlinear MPC controller to track the desired periodic gait online. The MPC controller ensures that the constraints are satisfied during the tracking process. The simulation results show the effectiveness of the proposed controller in achieving stable locomotion.