Design and Experiment of a Prescribed-Time Trajectory Tracking Controller for a 7-DOF Robot Manipulator

Abstract

We present an analytical design and experimental verification of trajectory tracking control of a 7-DOF robot manipulator, which achieves convergence of all tracking errors to the origin within a finite terminal time, also referred to as the “settling time.” A key feature of this control strategy is that the settling time is explicitly assigned by the control designer to a value desired, or “prescribed” by the user and that the settling time is independent of the initial conditions and of the reference signal. In order to achieve this beneficial property with the controller, a scaling of the state by a function of time that grows unbounded toward the terminal time is employed. Through Lyapunov analysis, we first demonstrate that the proposed controller achieves regulation of all tracking errors within the prescribed time as well as the uniform boundedness of the joint torques, even in the presence of a matched, nonvanishing disturbance. Then, through both simulation and experiment, we demonstrate that the proposed controller is capable of converging to the desired trajectory within the prescribed time, despite large distance between the initial conditions and the reference trajectory, i.e., in spite of large initial tracking errors, and in spite of a sinusoidal disturbance being applied in each joint.