The rigid body dynamics of Shoot-the-moon game and model-based controller design

Abstract

A wooden game board named Shoot-the-Moon has interesting dynamics properties despite its simple structure of one steel ball rolling on two cylindrical rods. In this paper, we derive the equations of motion for Shoot-the-moon using an Eular-Lagrangian approach and explore its underactuated, nonlinear, nonholonomic dynamics. Two positon controllers are designed, one for a local linearization and another with nonlinear feedforward. Simulations of both controllers are performed, showing that the ball converges to the setpoint from its vicinity for the linearized controller, and that a continuous signal can be tracked with the feedforward controller. Simulation also demonstrates the effect of the nonholonomic constraint relating the ball's linear and angular position.