A feedback solution to ball-plate problem based on time-state control form

Presents a feedback control for the so-called ball-plate dextrous manipulation problem. The problem deals with a rigid sphere held between a pair of parallel plates, which are moved directly by external command (i.e., the translational velocity of the plates is assigned as control inputs). The control objective is to place the sphere at any desired position in any desired orientation. Since the position control problem and the orientation control problem can be solved separately and we have solved the former one in previous works, this paper concentrates on the orientation control problem. The problem is formulated as a stabilizing problem of this driftless system, which cannot be stabilized by any continuous state feedback. We have proposed a "time-state control" strategy as a practical feedback-based control for such systems, however, the orientation control problem cannot be solved by direct application of the time-state control strategy. We show that the obstruction is settled by iteratively executing the time-state control strategy. The authors also realized a dextrous manipulation system using a 5-DOF manipulator with an image processing system, and performed some laboratory experiments. The results are reported at the end of the paper.