The roles of shape and motion in dynamic manipulation: the butterfly example

We study the juggler skill called the "butterfly". Starting with a ball resting on the palm of his/her open hand, a skilled juggler can accelerate and shape his/her hand so that the ball rolls up the fingers, over the top, and back down to the back of the hand. This paper describes a robotic implementation of the butterfly. The combined hand shape and motion set the rolling motion of the ball, and we find that the shape and motion parameters enter the dynamic equations in a similar way. We define parametrized spaces of hand shape and motion, and using a simulation based on the rolling equations, we identify shape and motion solutions that roll the ball from one side of the hand to the other. We describe an implementation of the butterfly on our planar dynamic manipulation testbed FLATLAND. This example is our first step toward exploring the roles of shape and motion in dynamic manipulation.