Stability of inverse Jacobian control for robot manipulator

Task-space control of robot manipulators can be classified into two fundamental approaches, namely transpose Jacobian control and inverse Jacobian control. Much progress has been achieved in respect to understanding the transpose Jacobian regulation problem. Yet, the stability of the inverse Jacobian regulation problem has not been proven rigorously, taking the nonlinear dynamics and kinematics into consideration. In this paper, two inverse Jacobian regulators with gravity compensations are presented and the stability problems are formulated and solved. The results in this paper provide an answer to the open problem on why the inverse Jacobian setpoint control system can be stabilized even though the inverse Jacobian matrix is structurally very different from transpose Jacobian matrix. The theoretical results are verified experimentally by implementing the inverse Jacobian regulators on an industrial robot, PUMA560.