A Control Method for Palm Circle Task on Contact Juggling of a Ball by a 3-DOF Manipulator

This paper proposes a control method to achieve the palm circle task for a ball-beam system in a planar space, where the beam is actuated by a 3-DOF manipulator. The palm circle means the situation where the spatial position of the ball is stationary at a point while the beam is moving cyclically. The manipulator dynamics is firstly linearized with respect to the beam's orientation and the contact force on the object. This technique makes the linearized system simplified while the direct linearization for the control objective variables of the palm circle task results in too complex. Then, the tracking controller for the control objective variables can be easily designed with the simplified linearized system based on LQR servo control. The proposed controller is verified in numerical simulation examples. Some conclusions and further research are finally mentioned.