Dynamic Locomotion of a Quadruped Robot with Active Spine via Model Predictive Control

As an active spine introduces more degree of freedoms (DOFs) as well as time-varying inertia, locomotion control of spined quadruped robots is challenging. Direct optimization on the full dynamics model causes prohibitive calculation time and is difficult to apply to embedded platforms. Model predictive control (MPC)-based on SRB dynamics is a prevalent approach for ordinary quadruped robots, regarding the whole robot as a single rigid body (SRB). However, the approach ignores the changes of the center of mass (CoM) and inertia, which seriously affects the robot's stability and could not be used in spined quadruped robots directly. To resolve the above issue, this paper presents an MPC approach that considers the movements of the spine in the SRB model. Since the mass of the robot is concentrated on its body, the whole robot is modelled as an unactuated SRB with fully-actuated internal spine joints. MPC finds the optimal ground reaction forces (GRFs) based on the SRB dynamics, in which the missing spine part is complemented by the pre-defined spine joints' states and corresponding inertia sequence. According to the GRFs, the full dynamic model calculates the precise joint torques. In addition, a quadruped robot with a 3-DOF active spine, Yat-sen Lion, is developed. With the presented approach, experimental results illustrate that Yat-sen Lion freely achieves bending, arching, and turning behaviors while trotting at speeds of 3.8 m/s in simulations and 0.5 m/s in real-world experiments.