Advanced Nonlinear Control of Robot Manipulators

Abstract

In the development of modern robot manipulators, it is required that the robot controller has the capability to overcome unmodeled dynamics, variable payloads, friction torques, torque disturbances, parameter variations, measurement noises which can be often presented in the practical environment. The objective of this chapter is to provide the reader with an overview on advanced nonlinear control techniques of a rigid robot manipulator. In nonlinear control field, a common strategy is called model based control, which can be derived from the mathematical model of the system. However, in case of robot manipulator, it is weakened by inaccuracies present in the robot model, where the performance of the control algorithm is not guaranteed. As mentioned above, these inaccuracies can be defined as parametric uncertainties, unmodeled dynamics, and unknown external disturbances. To overcome the uncertainties’ drawback, robust nonlinear control can be a solution. The goal of robust control is to maintain performance in terms of stability, tracking error, or other specifications despite inaccuracies present in the system. In this chapter we present two nonlinear model based control strategies: the feedback linearization control and a nonlinear model predictive control for rigid robot manipulator. We first consider the dynamic of the robot manipulator driven by the Euler-Lagrange equations. Based on this general representation, we are able to derive equations of the nonlinear controller for both strategies. Then, a robustness study is carried out through compensation of the system inaccuracies. Two methods are used; the first one is based on the theory of guaranteed stability of uncertain systems, while the second is figured out using the nonlinear control law. The computation of the nonlinear model based control assumes that all state variables are available. In case of robot manipulators, it implies the presence of additional sensors in each joint such as velocity measurements. They are often obtained by means of tachometers, which are perturbed by noise, or moreover, velocity measuring equipment is frequently omitted due to the savings in cost, volume, and weight. Model-based observers are considered very well adapted for state estimation and allow, in most cases, a stability proof and a methodology to tune the observer gains, which guarantee a stable closed loop system. 7