PD-Based Trajectory Tracking Control for Robot Manipulators

In this paper, it is proved that a trajectory tracking system of a manipulator is globally stable if the system is controlled under the decentralized PD control law plus a sliding term with a constant coefficient, and the norm of the coefficient matrix of its differential term is no less than that of the centripetal and Coriolis’ force term corresponding to the desired angular velocity, i.e., ∥K_d∥ ≥ ∥C(q, q˙_d)∥. Condition ∥K_d∥ ≥ ∥C(q, q˙_d)∥ implies that K_d increases only with q˙_d instead of q˙. A type of globally asymptotically stable adaptive sliding mode PD-based control scheme is proposed, and the proof of stability of the system is also given. It is easy to implement in real-time compared with other adaptive control laws as no estimation of gravitational and frictional forces is necessary.