Dynamics and Control of the Shoot-the-Moon Tabletop Game

Abstract

The classic tabletop game Shoot-the-Moon has interesting dynamics despite its simple structure, consisting of a steel ball rolling on two cylindrical rods. In this paper, we derive the equations of motion for Shoot-the-Moon using a Lagrangian approach and examine the underactuated, nonlinear, and nonholonomic dynamics. Two ball position controllers are designed, one using a local linearization and another using the nonlinear dynamics. Simulations of both controllers are performed, showing that the ball converges to the setpoint position for the linearized controller and continuous signals can be tracked by the nonlinear controller. Finally, the experimental results are presented for the nonlinear controller applied to a physical implementation of Shoot-the-Moon. The effect of the nonholonomic constraint relating the ball’s linear and angular position is demonstrated. This system has rich dynamics that can provide a challenging problem for control design and serve as a new educational example.