Motion planning research has been successful in developing planning algorithms which are effective for solving problems with complicated geometric and kinematic constraints. Various applications in robotics and in other fields demand additional physical realism. Some progress has been made for non-holonomic systems. However systems with significant drift, underactuation and discrete system changes remain challenging for existing planning techniques particularly as the dimensionality of the state space increases. In this paper, we demonstrate a motion planning technique for the solution of problems with these challenging characteristics. Our approach uses sampling-based motion planning and subdivision methods. The problem that we solve is a game that was chosen to exemplify characteristics of dynamical systems that are difficult for planning. To our knowledge, this is first application of algorithmic motion planning to a problem of this type and complexity.
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