High-order Control Barrier Function-based Impedance Control for Constrained Robotic Systems with Input Saturation: A Time-varying Functions Reconstruction Method

The impedance control of the constrained robotic systems with input saturation is investigated in this article. The High-order Control Barrier Function (HoCBF) is applied to address the state and/or output constraints for robotic systems, where the HoCBF-based controller can be obtained by a quadratic program (QP). Input saturation poses significant challenges to the solvability of the QP-based control framework and constraint satisfaction. To surmount these issues, we introduce a time-varying functions-based HoCBF (TFHoCBF), which is reconstructed by introducing time-varying functions to a typical HoCBF. To inherit the properties of the zeroing CBFs (ZCBF), the time-varying functions are treated as standard ZCBFs by introducing the auxiliary system to make sure the funcitons are non-negative. To enable robotic systems to comply with external contact forces when interacting with the environment, we design the TFHoCBF-based impedance control strategy. In this design, the impedance control is applied as the nominal control, while the designed barrier conditions are set as the QP constraints. To validate the efficacy of this proposed control method, we conduct simulations experiments using a two-link manipulator system.