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The problem of motion planning for affine control systems consists ofdesigning control inputs that drive a system from a well-defined initial tofinal states in a desired amount of time. For control systems with drift,however, understanding which final states are reachable in a given time, orreciprocally the amount of time needed to reach a final state, is often themost difficult part of the problem. We address this issue in this paper andintroduce a new method to solve motion planning problems for affine controlsystems, where the motion desired can have indefinite boundary conditions andthe time required to perform the motion is free. The method extends on ourearlier work on motion planning for systems without drift. A canonical exampleof parallel parking of a unicycle with constant linear velocity is provided inthis paper to demonstrate our algorithm.

Geometric Motion Planning for Affine Control Systems with Indefinite Boundary Conditions and Free Terminal Time