Distributed force/position tracking of multiple robot manipulators interacting with uncertain compliant environment

The paper addresses distributed coordinated force/position tracking problem of networked robot manipulators in the presence of dynamic uncertainties. The end-effectors of the manipulators are in contact with flat compliant environments with uncertain stiffness and distance. The control objective is for the robotic followers to track a desired force/position trajectory formed by the convex hull of all the leaders under a directed graph. By exploiting the containment control theory developed for distributed position tracking in free space, we propose a distributed adaptive force control scheme with an adaptive force observer to achieve the asymptotic force tracking in constrained space, which also maintains a cascade closed-loop structure separating the system into kinematic module and dynamic module. A decentralized stiffness updating law is also proposed to deal with the environment uncertainties. The convergence for force and position tracking errors is proved with Lyapunov stability theory and input-output stability analysis. Finally, simulations are performed to show the effectiveness of the theoretical approach.