A Palm Circle Task Controller of Contact Juggling for Ball-and-Plate System with 6-DOF Manipulator

In this paper, we develop a control method of 3-dimensional nonprehensile manipulation for a ball-and-plate system with a 6-DOF manipulator. In the first part of the method, the position and orientation of the plate is controlled to track a desired trajectory by a joint-space controller which consists of a PD controller, the gravity compensator, and a desired wrench (a couple of force and moment) for the plate. This joint-space controller is imposed to compensate the nonlinearity of the manipulator dynamics. In the second part, a LQR based controller is derived, where the acceleration of the desired trajectory in the first part is employed as the control input for the ball-and-plate system with assuming that the desired plate wrench is only applied for the plate dynamics. Here, the total DOFs of the motion are controlled to realize the palm circle task of the contact juggling, where the spatial pall position is stationary and the contact point on the beam is moving cyclic. The proposed controller is verified in a numerical simulation example. Some conclusions and further research are finally mentioned.