On the Optimal Control of a Rolling Ball Robot Actuated by Internal Point Masses

The controlled motion of a rolling ball actuated by internal point masses that move along arbitrarily shaped rails fixed within the ball is considered. Application of the variational Pontryagin's minimum principle yields the ball's controlled equations of motion, a solution of which obeys the ball's uncontrolled equations of motion, satisfies prescribed initial and final conditions, and minimizes a prescribed performance index.