Motion-planning for autonomous vehicles involves a two-level planning hierarchy: a high-level task-planning algorithm and a lower-level trajectory generation algorithm. The task planner operates on a discrete structure, such as a graph, whereas the trajectory generator operates on a dynamical system with a continuous state space. The problem of ensuring “compatibility” between these two planners has been approached in the literature by constructing discrete abstractions of continuous systems. However, such abstractions do not always exist, especially for nonholonomic vehicle dynamical models. We propose abstractions for such models based on geometric analysis of the vehicle's motion. The proposed motion-planning approach ensures that the task planner operates independently of the trajectory generation algorithm while maintaining a guarantee of “compatibility”, and also provides significant reductions in overall execution time.