Simple boundary control of two one-link flexible arms for grasping

This paper is concerned with a grasping task by means of two one-link flexible arms. To accomplish this task, we propose simple boundary control based on the dynamic model, which consists of partial differential equations (PDEs) and ordinary differential equations (ODEs) subject to the geometric constraints. Since the data, which is needed in the implementation of the controller, can be obtained by the strain gauge and the rotary encoder, it is easy to implement the controller. Furthermore, the controller is derived based on the original infinite dimensional model, and the stability of the closed-loop system is given by using the semigroup theory and the LaSalle's invariance principle which is extended to the infinite dimensional systems. Thus we can avoid the drawbacks resulting from the finite dimensional approximation.