Abstract
In this paper, we consider a position control of a rigid ball which is held between two parallel plates. The kinematic constraint of the system is rolling constraint which is a nonholonomic constraint. Thus, the system becomes drift-less nonlinear system. As Brockett showed, the equilibrium of such systems can not be stabilized with any continuous static state feedbacks even though the system is controllable in the sense of nonlinear. We applied a control strategy which is transforming this system into time-state control form by coordinate transformation and input transformation. By the simulation, we will show that we can stabilize both ball and the plate at the goal point.
