4. Closed-Chain Robotic Systems and Mechanisms

Control of closed-chain robots is a non-trivial problem because it is often associated with complicated dynamic and kinematics models exhibiting nonlinearities. Unlike robotic manipulators with a free end-effector, closed-chain robotic mechanisms include actuators which are usually placed on a fixed base. On the one side this enables to develop robotic and mechatronic systems with low moving inertia and fast motion control. On the other side this may incur underactuation problems. Comparing to open-chain robots, closed-chain robotic mechanisms have many advantages such as high stiffness, high accuracy, and high payload-to-weight ratio To solve the nonlinear control problem of closed-chain robotic systems the following approaches are proposed (i) nonlinear control based on global linearization methods, (ii) nonlinear control based on approximate linearization methods and (iii) nonlinear control based on Lyapunov methods. Besides to apply model-free control for such a type of robotic manipulators, online estimation algorithms of the unknown dynamics of the robot can be considered once again. The global asymptotic stability of the control based on the real-time estimation of the robot’s dynamics is proven. Moreover, as in the previously analysed multi-DOF manipulator models, to implement feedback control through the measurement of a limited number of the closed-chain robot’s state vector elements, nonlinear filtering methods of proven convergence are developed. In particular the chapter analyzes the following topics: (a) Model-based control of closed-chain kinematic mechanisms with the use of differential flatness theory, (b) Flatness-based adaptive fuzzy control of closed-chain kinematic mechanisms (c) Nonlinear optimal control for closed-chain kinematic mechanisms.