Virtual decomposition based control for generalized high dimensional robotic systems with complicated structure

This paper presents a systematic adaptive control strategy which can accomplish a variety of control objectives (position control, internal force control, constraints, and optimizations) for the generalized high dimensional robotic systems (GHDRS) without restriction on target systems. Based on the concept of virtual decomposition by which a GHDRS is virtually decomposed into several objects and base-floating open chains, the motion control problem of the original system is converted into that of each object and that of each open chain, individually, while the internal force control as well as the constraint force control may be performed with respect to each object only. This feature makes it possible to implement the control algorithm of each subsystem in modularly structured hardware which can be integrated to form any specific robot controller dedicated to a specific application. In the sense of Lyapunov, it is the first time to declare that the dynamic coupling between every two physically connected subsystems can be completely represented by the so-called virtual power flows (VPF's) at the cutting points between them. Asymptotic stability of the complete system can be ensured by choosing the system Lyapunov function as the sum of all nonnegative accompanying functions assigned for the subsystems. Some possible applications based on the proposed approach are discussed. Finally, computer simulations of two PUMA 560 arms transporting a common object along a prespecified trajectory are carried out to verify the stability and robustness issues of the system.