A saturated PD plus scheme for asymptotic tracking of robot manipulators

This paper studies the asymptotic tracking of robot manipulators subject to actuator saturation. A saturated proportional-derivative (SPD) plus (SPD+) scheme is developed based on the commonly used linear proportional-derivative (PD) plus computed feedforward of robot dynamics (PD+). The closed-loop system formed by the proposed SPD+ controller and the robot system is shown to be semiglobal asymptotically stable with Lyapunov´s direct method. The fact that the proposed controller can be a priori bounded is a significant added advantage. The practical implication is that the actuators can be appropriately sized without an ad hoc saturation scheme to remove the possibility of actuator failure due to excessive torque input levels. Benefiting from a new saturation function, a much improved performance is obtained over the commonly used hyperbolic tangent function. Simulations performed on a two-degree-of-freedom (DOF) robot are presented to illustrate the effectiveness and improved performance of the proposed approach.