Smooth robust tracking controllers for uncertain robot manipulators

Abstract

In this paper two smooth robust tracking controllers for uncertain robot manipulators are presented. Ihe proposed controllers yield smooth acceleration response. A deteiministic approach is adopted in developing the controllers. Lyapunov direct method is used and a nonlinear Lyapunov function is employed to prove the stability of the system. Ihe first controller is shown to render the closed-loop system practically stable, forcing the state tracking error to converge exponentially to a small neighborhood of the origin. On the other hand, the second controller is shown to render the closed-loop system asymptotically stable, forcing the state tracking error to converge to the origin. n2e eflcacy of the proposed controllers is verified by application to a planar two-link manipulator.

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“…Furthermore, it can be easily shown from (3-18) that as t --f -, y , + 0 . Hence, it can he concluded that r asymptotically converges to zero as t + - [Vidyaagar, 19781 The convergence of r can he described as the following: r i exponentially converges to y1 with a rate of 17 = '~n ' n '~~, , ,~~, (Cai and Abdalla, 1993), meanwhile, yI converges linearly to zero As shown by Spong and Vidyasagar (1989), if r + 0, then e and e will converge to zero as t --f m , Therefore, global asymptotic stability of the closed-loop system for trajectory tracking control is achieved.…”