Rigid-Link Manipulators: Model-Based Control

Abstract

The chapter analyzes the model-based nonlinear control approaches for multi-DOF rigid-link robots, that is (i) control based on global linearization methods, and (ii) control based on approximate linearization methods. As far as approach (i) is concerned, that is methods relying on global linearization, these are techniques for the transformation of the nonlinear dynamics of the robotic system to equivalent linear state-space descriptions for which one can design state feedback controllers and can also solve the associated state estimation (filtering) problem. One can classify here methods mainly elaborating on the theory of differentially flat systems. Differentially flat systems form the widest class of systems to which global linearization-based nonlinear control can be applied. As far as approach (ii) is concerned. solutions are sought to the problem of nonlinear control of robots with the use of local linear models (defined around local equilibria). For such local linear models, feedback controllers of proven global stability can be developed. One can select the parameters of such local controllers in a manner that ensures the robustness of the control loop to both external perturbations and to model’s parametric uncertainty. In particular the chapter develops the following topics: (a) Kinematics and dynamics of multi-DOF robotic manipulators. (b) Model-based control of rigid-link manipulators using global linearization methods, (c) Model-based control of rigid-link manipulators using approximate linearization methods, (d) Model-based control using global linearization methods for rigid-link manipulators subject to time-delays.