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We present a closed-loop approach to solve the semi-autonomous nonholonomic vehicle-parking assistant problem. The method allows for a priori unknown and potentially high vehicle speeds and dynamic environment variations. The computationally low-cost, memory-efficient algorithm respects constraints on the steering angle and its first two derivatives, allowing for comfortable, safe, and smooth steering motions. A parking situation is captured by an arrangement of precalculated vector fields of feasible nonholonomic paths, by which the vehicle is controlled toward a desired goal configuration inside a parking bay. Using standard onboard environment perception sensors, the system adapts to changes in the environment and avoids collisions whenever possible, without aborting a parking procedure.