Experimental and Analytical Prescribed-Time Trajectory Tracking Control of 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. A key feature of this control strategy is that this terminal convergence time is explicitly prescribed by the control designer, and is thus independent of the initial conditions of the tracking errors. In order to achieve this beneficial property of the proposed controller, a scaling of the state by a function of time that grows unbounded towards 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, non-vanishing 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 initial conditions of the tracking errors and a sinusoidal disturbance being applied in each joint.