User-Led Modular Robot Manipulator Systems Interaction Tasks-Oriented Hierarchical Approximate Optimal Control: A Stackelberg-Pareto Differential Game Perspective

Abstract

A Stackelberg-Pareto differential game-based approximate optimal interaction control approach is proposed for user-led modular robot manipulator (MRM) systems modeled by joint torque feedback (JTF) technique. The major objective of optimal control with physical human-robot interaction (pHRI) is evolved into approximating Stackelberg-Pareto equilibrium by adopting cooperative differential game in MRM and Stackelberg differential game between the human and robot. Learning from adaptive dynamic programming (ADP), the approximate optimal interaction control strategy with pHRI is developed by critic neural network (NN) for solving the coupled Hamilton-Jacobian (HJ) and HJ-Bellman (HJB) equations. The position tracking error under pHRI task is ultimately uniformly bounded (UUB) by the concept of Lyapunov theorem. Two distinction experiments demonstrate the superiority of proposed control approach.