# Parallel parking problem

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Parallel_parking_problem
> Markdown URL: https://mediated.wiki/source/Parallel_parking_problem.md
> Source: https://en.wikipedia.org/wiki/Parallel_parking_problem
> Source revision: 1339996600
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

{{Short description|Robotics and planning computational problem}}
thumb|upright|Animation of a car parallel parking, turning only its front wheels
The '''parallel parking problem''' is a [motion planning](/source/motion_planning) problem in [control theory](/source/control_theory) and [mechanics](/source/mechanics) to determine the path a car must take to [parallel park](/source/parallel_parking) into a parking space.  The front wheels of a car are permitted to turn, but the rear wheels must stay aligned.  When a car is initially adjacent to a parking space, to move into the space it would need to move in a direction perpendicular to the allowed path of motion of the rear wheels.  The admissible motions of the car in its configuration space are an example of a [nonholonomic system](/source/nonholonomic_system).

==See also==
* [Automatic parking](/source/Automatic_parking)
* [Bicycle and motorcycle dynamics](/source/Bicycle_and_motorcycle_dynamics)
* [Falling cat problem](/source/Falling_cat_problem)
* [Moving sofa problem](/source/Moving_sofa_problem)

==References==
* {{citation|url=https://philsci-archive.pitt.edu/794/1/falling-cats.pdf|title=Falling cats, parallel parking, and polarized light|last=Batterman|first=R|journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics|volume=34|issue=4|year=2003|pages=527–557|doi=10.1016/s1355-2198(03)00062-5|bibcode=2003SHPMP..34..527B }}.
* {{citation|title=Optimal paths for a car that goes both forwards and backwards|first1=J.A.|last1=Reeds|first2=L.A.|last2=Shepp|journal=Pacific Journal of Mathematics|year=1990|volume=145|issue=2|pages=367–393|doi=10.2140/pjm.1990.145.367|doi-access=free|url=https://projecteuclid.org/journals/pacific-journal-of-mathematics/volume-145/issue-2/Optimal-paths-for-a-car-that-goes-both-forwards-and/pjm/1102645450.pdf}}.

Category:Control theory

{{applied-math-stub}}

---
Adapted from the Wikipedia article [Parallel parking problem](https://en.wikipedia.org/wiki/Parallel_parking_problem) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Parallel_parking_problem?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.