Switching adaptive control of robot manipulators.

Abstract

A switching adaptive-PD controller for the trajectory tracking problem of robotic manipulators subjected to large and abrupt changes of the system parameters is developed. The manipulator arm and the payload are considered, in the most general form, to have a highly nonlinear dynamical model with unknown or partially known parameters. A switching controller is proposed to give the system the ability to deal with abrupt and large changes of parameters. The proposed control system is comprised of two different schemes called, in this thesis, the low-level and the high-level controllers. The high-level controller is an adaptive version of the computed torque control scheme and the low-level controller is a simple PD regulator with an on-line parameter estimator. The system switches from the adaptive to the PD controller for a limited period when abrupt and large changes in parameters are observed. An on-line parameter estimator identifies the new parameters of the manipulator during the course of low-level regulation. This identification eases smooth switching from PD to adaptive control in the next stage of the process. A least-squares parameter estimator modified by a type of moving window, also known as exponential bounded gain forgetting, is used for this purpose. The robot dynamic response is filtered to make the estimator independent of joint acceleration measurements For designing the adaptive part of the system, the Lyapunov stability criterion is utilized. Typically, the choice of the Lyapunov function to be used in the stable design of highly nonlinear systems is not easy and requires insight into the problem. A new methodology based on the direct exploitation of the generalized Krasovskii theorem is presented. This straightforward utilization of the theorem provides an easy means for the choice of the Lyapunov function for robot manipulators. A parameter-adaptive controller with a new adaptation law is developed based on a new Lyapunov function. The derived adaptive scheme is adopted for a computed torque control system. The boundedness of the vectors of the system states and parameter errors are proven. This guarantees the global stability of the high-level controller and the convergence of its tracking error. A priori knowledge of the system is used to avoid estimating all the parameters and to accelerate the performance of the control system. The stability and robustness of the switching mechanism are studied by using the Lyapunov method. In the case of the switch from adaptive to PD mode, the robustness is justified intuitively and theoretically. The more critical part of the switching mechanism is that of switching from PD mode to adaptive mode. This is due to the robustness limitations of the high level controller. The Lyapunov study of the switching mechanism resulted in a criterion for finding the states under which the upper bound of the parameter mismatch and the disturbance torque vector does not cause instability. The results of this criterion leads the monitoring function to the choice of the suitable states for switching back to the adaptive controller. Numerical simulations, using the proposed control scheme for a 3DOF articulated robot manipulator, are presented for testing the performance of the control system. The software and codes were developed using C-language and Matlab. In a typical test for the PD mode, the identification of a 100% change in parameters took 2.67 seconds. The results are reliable for the switching back action. In the adaptive mode, a complete identification with no a priori knowledge took 6.5 seconds. This may seem slow in some applications. The identification scheme with a priori knowledge takes 1.3 seconds. In the cases with the priority for tracking rather than identification, the tracking mode is more appropriate. A combination of the identification mode followed by the tracking mode is recommended for switching from the PD to the adaptive controller.