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

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. Note to Practitioners—Major challenges of controlling user-led MRM systems include optimizing MRM system performance as well as layering interaction task between the robot and human. Traditional differential game, such as zero-sum game, nonzero-sum game and cooperative game only consider the same layer in the interaction progress that is not suitable for user-led MRM with leader and follower. Besides, the existed hierarchical game deals with one leader and one follower or followers formulated as nonzero-sum game that ignores the fully cooperative relationship among followers. Therefore, this paper proposes Stackelberg-Pareto differential game-based approximate optimal control for user-led MRM to improve system performance with theoretical analysis and experimental verification.