3. Rigid-Link Manipulators: Model-Free Control

The chapter analyzes model-free nonlinear control approaches for multi-DOF rigid-link robots, based on Lyapunov methods. There, one comes against problems of minimization of Lyapunov functions so as to ensure the asymptotic stability of the control loop. Model-free control takes often the form of indirect adaptive control. In such a case the design of the controller is not based on prior knowledge of the robot’s dynamics. With the use of adaptive algorithms and elaborated estimation methods it is possible to identify in real-time the unknown dynamics of the robots and subsequently to use this information in the control loop, thus arriving at indirect adaptive control schemes. Finally, the development of nonlinear state-estimation methods for robotic manipulators allows the implementation of feedback control through measuring of only a small number of the robot’s state variables. Global stability is proven for the control loop that comprises both the nonlinear controller of the robot’s dynamics and nonlinear observers that estimate the robot’s state vector from indirect measurements. In particular, the chapter develops the following topics: (a) Model-free adaptive control of rigid-link manipulators using full-state feedback, (ii) Model-free adaptive control of rigid-link manipulators using output feedback, (iii) Model-free adaptive control of the underactuated rotary (Furuta’s) pendulum.