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Automatic parking system has been widely equipped on manual driving vehicles for decades. Due to the limited environment sensing ability and not-accurate-enough positioning system, however, it usually requires a very large redundant space for a car to accomplish one successful parking maneuver. There would be two differences in the coming era of automatic driving: (1) sufficiently accurate perception and positioning systems can be expected to be available, and (2) the number of parking trials could be large when parking without passengers on the vehicle. Under such circumstances, it is quite important for the vehicle to know exactly whether the external and internal spaces are large enough for parking and how the minimum number of trials will be required. This paper presents closed-form solutions of minimum internal and external space required for automatic parallel parking and the corresponding trials if the parking is based on circular arcs. On the other hand, it is also very useful for the vehicle to know the required minimum space if only one trial is allowed, for which the solutions are presented both for circular arcs and continuous-curvature curves based parking, respectively. To the best of our knowledge, there is no so far systematic analysis and research on the issue addressed in this paper.

On Minimum Parking Space Required by Automatic Parallel Parking