Turn on a Dime

A revised car-like vehicle model with forwards and backwards motion, an upper bound on the derivative of curvature and a pause for steering at cusp points is presented. This model has improved performance near cusp points and is shown to converge toward the optimal "Reeds and Shepp" paths under two conditions: 1) when the upper bound of the curvature derivative bound tends to infinity and 2) when the pause at the cusp is sufficient for the vehicle to completely re-orientate its steering before departing the cusp point. This motion model was applied to the general problem of turning a vehicle around between two parallel lines. This required the development of a specialised path planner and a method to search for near-time optimal solutions