Stable positioning control of redundant multi-link manipulator with collision phenomena

A methodology is proposed for analyzing the stability of a nonlinear redundant multi-link manipulator system that is interacting with a flexible wall with collision phenomena. The stability and response of the system are examined by parameter studies of numerical simulation. A Hertz-type model with energy dissipation parameter is used to express the impact or contact force between the manipulator and the object. Using this general model, it is proved theoretically by the Lyapunov direct method that this nonlinear system can be controlled with a linear feedback law without any assumption of the manipulator´s robustness and that the collision has a stabilization effect. A methodology for determining a control law for this kind of system is also proposed. The simulations show that a simple decoupled local feedback is preferable to the coupled feedback, if the stability must be guaranteed