Tracking Control of a Single Link Manipulator with Actuator Dynamics under Output Constraints

Abstract

In this paper, controller design for handling constraints on joint position and angular velocity of a single link manipulator with actuator dynamics is presented. Instead of using optimization approaches for constraint satisfaction, an analytical Barrier Lyapunov Function (BLF) based design has been presented to derive a control law. In this approach, barrier functions are used to construct a candidate Lyapunov function which inherently includes the constraints in its definition. Multiple controllers are designed using the same backstepping procedure with only modifications to the candidate Lyapunov function. The asymptotic stability of the closed loop system has been shown. Finally, a comparison on the performance of the designed controllers has been made through numerical simulations.