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In this contribution, we develope a flatness-based control strategy suitable for parking assistance and autonomous maneuvering in static environments. It is derived from quasistatic trajectory tracking control in a straight-forward manner and preserves the invariance property (with respect to the choice of the initial frame) of the plant for the closed loop system. In addition, it solves the nearest-point projection of the car onto the curve implicitly. The results are illustrated by simulation and experiment.