Adaptive motion/force control of multiple manipulators with jointflexibility based on virtual decomposition

In this paper, a virtual decomposition-based adaptive motion/force control scheme is presented to deal with the control problem of coordinated multiple manipulators with flexible joints holding a common object in contact with the environment. The control scheme is essentially a generalized Newton-Euler approach in which the original system is virtually decomposed into several subsystems, including the held object, the rigid links, and the flexible joints, so that the control problem of the original system can be greatly simplified. An interesting result is that the dynamic coupling between every two physically connected subsystems is completely represented by the so-called virtual power flow (VPF) at the cutting point between them. The VPF takes a very simple form and is very easy to handle. Control design of the constraint/internal forces can be performed with respect to the held object. Asymptotic stability of the overall system is ensured in the sense of Lyapunov. Computer simulations of two manipulators transporting an object in the plane are given to show the validity of the proposed scheme