Decentralized sliding force/position PD control of cooperative robots in operational space under Jacobian uncertainty

Abstract

Cooperative robots have attracted the attention because they allow carrying out of tasks which cannot be done with a single robot. Though cooperative robot dynamics are quite complex to handle, regularly it is necessary to implement a nonlinear dynamics-based controller which guarantees fast tracking. A method for very fast constrained object maneuvering for non redundant rigid cooperative robot manipulators is proposed in this paper. The novelty of our approach lies in the fact that very fast decentralized Cartesian cooperative tracking is obtained without using the model of the robot nor exact knowledge of inverse Jacobian. The model-free sliding PD force controller, driven by second order position/force commuting sliding surfaces, is presented, such that approximate compensation of nonlinear dynamics of each robot arises, and the residual error dynamics is finally cancelled by a chattering-free Cartesian sliding mode to guarantee convergence of position and force tracking errors. Notice that inverse kinematics are avoided by synthesized Cartesian, rather than joint, error sliding surfaces, thus the commuting manifold does not depend on the Jacobian, therefore, the system is robust against Jacobian uncertainty, A simulation study of two cooperative robots manipulating a constrained object shows the expected performance.