Advanced Nonlinear Control of Robot Manipulators

Abstract

This chapter has presented some methods of advanced nonlinear control for robot systems. However, to cover all issues related to nonlinear control in detail will demand more than a chapter. The study has focused on model based control where a model dynamic of the process is needed to carry out the control law. Two nonlinear control approaches have been detailed in this work. A feedback linearization control based on input-output linearization has been developed using differential-geometric methods for nonlinear systems. Then, a model based predictive control has been discussed for a nonlinear control design to robot manipulators. The predictive control law minimizes a cost function for the control trajectory over a future time horizon. The control solution has been analytically derived, with no need of an online optimization, which enables fast realtime implementation. Because of the uncertainties present in the system, a robustness strategy has been studied to enhance the tracking response of the system. Two methods have been investigated to deal with system uncertainties. One method is based on the theory of guaranteed stability of uncertain systems, which results to an observer taking information from the system tracking errors. The other one is an observer derived from the nonlinear model control law. It contains an integral action on system tracking errors. This type of control strategy is robust with respect to modeling errors, very effective in disturbance rejection, and gives no steady error caused by either parameters uncertainties or external disturbances. The development of these control strategies is related to the dynamic model of the process. In case of missing information about the system states, a version of control law based on state has been carried out with the quantities, angular positions and velocities, issued from a nonlinear state estimator. It has been shown that the tracking performance is achieved successfully when the uncertainties are well compensated. The issue of global stability of the closed loop system has been proved analytically via Lyapunov stability theory. The nonlinear control laws developed in this chapter are based on a dynamic model of the process. However, it is well known that mathematical representation of a dynamic model does not refer accurately to the reality. This is why it is very important to add to the control strategy a robustness analysis in order to compensate the uncertainties present in the dynamic model. As an alternative of this approach, intelligent control based on the process behavior can be considered as a solution for tracking motion of robot manipulators. Intelligent control achieves automation via the emulation of behavioral intelligence such as biological intelligence (e.g., the use of neural networks and genetics for control); the use of human’s knowledge to design a smart control methodology (fuzzy control). This research