Whole-body Compliance Control for Quadruped Manipulator with Actuation Saturation of Joint Torque and Ground Friction

In normal operations, when quadruped manipulators with impedance control experience external disturbances, they may become unstable and lose balance due to actuation saturation, affecting their stability, safety, and compliance with the environment. To address this issue, we propose a whole-body compliance controller to prevent unstable behaviors like slip, oscillation, and overshoot, which arise from actuation saturation. The controller includes an admittance scheme with a set-valued operator as the internal feedback, to constrain joint torques within actuators' limits and ground reaction forces within friction cones to ensure stability against disturbances. Then, it formulates a hierarchical optimization problem using the Hierarchical Quadratic Programming (HQP) to impose the output of the admittance scheme while ensuring physical consistency to maintain compliance behaviors. Unlike traditional compliance control with one-dimensional torque limitations, our approach considers both joints torque limits of manipulator joints and friction cones of quadruped ground reaction as actuation saturation. This ensures overall compliance and stability for the quadruped manipulators, even under significant external forces, regardless of where they are exerted on the robot. We demonstrate through experiments involving variable stiffness environments and external forces during normal operations how effective our approach is in enhancing the safety of quadruped manipulators.