Three-Rigid-Body Model Based NMPC for Bounding of a Quadruped with Two Spinal Joints

While real-world quadrupedal animals exploit significant spine motions to realize high-speed running, current high-speed quadrupedal robots seldom incorporate spinal structures. One main reason for this gap is the complicated robot dynamics brought by spinal structures, which causes difficulties in designing high-speed locomotion controllers like Model Predictive Control (MPC). In this paper, we propose the planar Three-Rigid-Body model for a planar quadruped with two actuated spinal joints. Based on this simplified model, we derive a Nonlinear MPC for the robot’s bounding control. The Three-Rigid-Body model catches the main dynamical effects of the spinal motions, meanwhile being simple enough to facilitate the NMPC’s real-time execution. We employ Whole-Body Control (WBC) as a bottom-layer controller for the NMPC to complement modeling errors. The whole control scheme is verified in simulation. The 13 kg robot, with maximum joint torque and speed of 21 Nm and 20 rad/s, reaches the highest speed of 4.3 m/s with a Froude number of 5.24. The controllers’ computation time implies real-time execution on the real robot.