Date of Award
Master of Science (MS)
Groff, Richard E
Dawson , Darren
The classic table-top game Shoot-the-Moon has interesting dynamics despite its simple structure, consisting of a steel ball rolling on two cylindrical rods. The two sloped rods are hinged at the lower ends and allowed to freely slide in a slot at the higher end. The ball can amazingly roll upward along the rods under carefully manipulation of the rods. There is also an interaction between ball rotation and translation that cause the ball to ``shoot'' (quickly accelerate).
In this thesis, the kinematics are developed for Shoot-the-Moon and then equations of motion are derived using both Lagrangian and Newtonian approaches. The modeling work yields an examine the underactuated, nonlinear, nonholonomic dynamic model for Shoot-the-Moon.
Two controllers are designed based on the dynamic model. The Linearized Position Regulator is developed using a local linearization at an equilibrium point of the dynamics. The Position Tracking Controller takes nonlinearities into account by inverting the significant nonlinear terms in the dynamics so that the system appears linear at the input and can be controlled using a PD controller. Simulations of both controllers are performed, showing that the ball converges to the setpoint for the linearized controller and continuous signals can be tracked by the nonlinear controller.
An experimental platform, an automated Shoot-the-Moon game controlled using the Position Tracking Controller, is built to facilitate understanding of the dynamics, explore the nonholonomic property of the system and demonstrate efficacy of the proposed controllers.
Experiment results are presented showing the effectiveness of the controller on the physical system. The results are compared with simulations under same conditions in order to highlight the fidelity of the dynamic model. The effect of the nonholonomic constraint relating the ball's linear and angular position is also demonstrated.
Shoot-the-Moon is a familiar system with rich dynamics. Moreover, it is one of the simplest system that shows nonholonomic properties and has substantial nonlinearity in dynamics. As such, it can provide an appealing challenge problem for control design techniques and serve as a new educational tool.
Xu, Peng, "Dynamics and Control of the Shoot-the-Moon Tabletop Game" (2011). All Theses. 1209.