Robust Adaptive Control Of Robotic Manipulators

Abstract

Robustness issues arising in the adaptive control of robotic manipulators are analyzed. Modeling errors are specifically accounted for and addressed by the design and analysis of the robust adaptive manipulator system. First, instability examples for two typical adaptive manipulator controllers in the literature demonstrate how instability can occur. The detailed core stability analysis results of two robust adaptive controllers is then presented. In the most general case, local stability of the robust adaptive system is ensured in that all signals remain bounded and the tracking errors converge to a residual mean tracking error set whose size depends upon the strength/bound of the unmodeled dynamics/bounded disturbances. The size of the region for which the local stability holds is inversely proportional to the strength of the unmodeled dynamics and global stability without unmodeled dynamics is shown. A robustness analysis with respect to time-varying plant parameters consisting of both smooth but not necessarily slow variations and jump plant parameter changes is also given. The adaptive laws are then recapitulated by minimizing specific cost criterion. Next, a stability analysis is performed on a flexible link manipulator model. By treating the flexible link dynamics as unmodeled dynamics, local stability of the closed-loop adaptive system is shown where the inverse of the size of the residual mean tracking error set and the size of the local stability region is proportional to the flexural rigidity. Excitation conditions for parameter convergence with the adaptive laws are generated which specifically address and depend upon the severity of the modeling errors. Robust adaptive controller structures consisting of a discrete-time adaptive controller in hybrid with the continuous-time manipulator plant are presented and analyzed. The stability of the adaptive system with bounded disturbances/noise on the required measurements of the manipulator joint angle positions and rates is also obtained. Performance is demonstrated in simulation results of both a commercial PUMA manipulator and an experimental direct-drive manipulator. (Copies available exclusively from Micrographics Department, Doheny Library, USC, Los Angeles, CA 90089-0182.)