Position control of a rigid ball between two parallel plates

Summary form only given. In this paper, we consider a position control of a rigid ball which is held between two parallel plates. The purpose of our study is to stabilize the ball to the center of the upper and lower plates by translational and rotational motion of the upper plate. The kinematic constraint of the system is rolling constraint and thus, this system appears to be a nonholonomic system. As Brockett showed, the equilibrium of such systems can not be stabilized with any continuous static state feedback even though the system is controllable in the sense of nonlinear control theory. We applied a control strategy which transforms this system into time-state control form by coordinate transformation and input transformation. By the computer simulation and the experiment, we show that this control strategy is useful for stabilizing this system.