5. Flexible-Link Robots

Control for flexible-link robots is a non-trivial problem that has elevated difficulty comparing to the control of rigid-link manipulators. This is because the dynamic model of the flexible-link robot contains the nonlinear rigid link motion coupled with the distributed effects of the links’ flexibility. This coupling depends on the inertia matrix of the flexible manipulator while the vibration characteristics are determined by structural properties of the links such as the damping and stiffness parameters. Moreover, in contrast to the dynamic model of rigid-link robots the dynamic model of flexible-link robots is an infinite dimensional one. As in the case of the rigid-link manipulators there is a certain number of mechanical degrees of freedom associated to the rotational motion of the robot’s joints and there is also an infinite number of degrees of freedom associated to the vibration modes in which the deformation of the flexible link is decomposed The controller of a flexible manipulator must achieve the same motion objectives as in the case of a rigid manipulator, i.e. tracking of specific joints position and velocity setpoints. Additionally, it must also stabilize and asymptotically eliminate the vibrations of the flexible-links that are naturally excited by the joints’ rotational motion. A first approach for the control of flexible-link robots is to consider the vibration modes as additional state variables and to develop stabilizing feedback controller for the extended state-space model of the flexible manipulator. To this end, one can use again (i) control based on global linearization methods, (ii) control based on approximate linearization methods, (iii) control based on Lyapunov methods. Another approach to the solution of the control problem of flexible manipulators is to treat the robot as a distributed parameter system and to apply control directly to the partial differential equations models that describe the motion of the flexible links. Again global asymptotic stability for this control approach can be demonstrated. On the other side, nonlinear filtering methods can be used for implementing state estimation-based feedback control through the measurement of a limited number of elements from the flexible robot’s state vector. In particular, the topics which are developed by the present chapter are as follows: (a) Inverse dynamics control of flexible-link robotic manipulators (b) sliding-mode control of flexible-link robotic manipulators.