Stability analysis of a joint space control law for a two-manipulator system

The control problem for a truly cooperative manipulator system cannot be regarded as a simple extension of single manipulator control since additional complexity arises from the need for ensuring coordinated motion of the system. Recently, we have proposed a control strategy based on two stages, namely, kinematic inversion of a set of cooperative task variables and a joint space control law with kinetostatic filtering of cooperative task space errors; this strategy avoids some of the drawbacks of other approaches. In this paper, the stability analysis for the joint space control law is provided and asymptotic stability of a set of equilibrium points is demonstrated. The case of imperfect compensation of the gravity terms has been analyzed. The addition of a force loop to achieve internal force regulation is also discussed.