Compensation of sampled-data robot adaptive controllers for improved stability

This paper addresses the stability and performance of discretized adaptive control algorithms for robotic manipulator control, and the compensation of these algorithms for improved stability and tracking performance. The discretization of Slotine and Li´s (1987, 1988) direct adaptive control algorithm results in a sampled-data system for which stability has not been guaranteed. By formulating the entire sampled-data system in continuous-time, Lyapunov´s direct method is used to examine the stability bounds. A proposed nonlinear discrete-time compensating term is added to Slotine and Li´s adaptive algorithm, to stabilize the sampled-data system. For sufficiently high gain, globally stable performance and a known bound on the norm of the filtered error is proven. A multi-rate discrete-time controller implementation of the compensated adaptive controller is investigated. The stabilizing effect of the compensator is demonstrated through simulation of a 2 degree-of-freedom serial link manipulator