Feedback control of robot Arm with discrete nonlinear model

Abstract

Abstract This article looks at the problem of controlling a robot arm from a discrete time perspective. We develop the theories and obtain results that feedback linearizes the discrete nonlinear system representing a PUMA 560 robot arm. The effect of sampling on the performance of the arm has been studied and shown through experiments. The results presented here, where the nonlinear robot model has been linearized and controlled completely in discrete time, are new to the robotics literature. We shown certain restrictions necessary on the sampling time of the system. The results obtained have been experimentally verified at the Center for Robotics and Automation at Washington University. Because a number of researchers have addressed the problem of loss of feedback linearizability under sampling, it was important to develop theories and obtain results in discrete time that take into consideration the effects due to sampling. This problem has been addressed here. Analysis of the control law under the assumptions of bounded input is performed and a recursive sensitivity function is derived. The results we obtain in discrete time show the dependency of the performance of the arm on the sampling time. It has been seen that with a higher sampling frequency the performance of the arm substantially improves and it is expected that close to 1000 Hz sampling rate, the peak performance of the PUMA 560 robot arm, will be reached.