the Homicidal Chauffeur: mathematically, where should you run?

Have you ever wondered how long you would last if a car driver decided they really wanted to run you over? Try our game at demonstrations...
In Star Wars, Rey decides to run directly away from Kylo's Tie fighter - but is that the best choice against a faster, but less maneuverable opponent? The classic “homicidal chauffeur problem” solves this mathematically.
Code developed by PhD student Javier Garcia and Prof. Aaron T. Becker at the University of Houston.
The math for the reachable set of the car is at demonstrations...
For more on Dubins Car, see • Coding a Dubins Car Op...
For the Reeds-Shepp Car, see • Coding a Reeds-Shepp C...
Sources
@Gaming Sound FX “Splat - Gaming Sound Effect (HD)” • Splat - Sound Effect (HD)
@Raytheon “How missile defense works” • Video
@Tyler Piledriver “Ralph tags Mr. Burns” • Ralph tags Mr. Burns
@Star Wars “Star Wars: The Rise of Skywalker - Teaser” • Star Wars: The Rise of...
@Gaming Sound FX “Splat - Gaming Sound Effect (HD)” • Splat - Sound Effect (HD)
@Raytheon “How missile defense works” • Video

[@azophi]

Underrated video
(but I'd like a version where you could be a car and run over people)
ah wait... that's just GTA.

[@hakankosebas2085]

this looks like Decimate Drive game, love it, how to implement this? and I wonder does it capable of avoiding obstacles or just works on plain fields

[@dominikkrupke3948]

Funny problem and nice 'splat' sound :D I wonder what happens if you insert obstacles. Since Dubins paths become rather nasty with obstacles, I guess this problem gets even nastier (at least from a theoretical point of view).

[@AaronBecker]

🤔Two friends of mine, S Bhattacharya, S Hutchinson examined an approximation of pursuit evasion: A cell decomposition approach to visibility-based pursuit evasion among obstacles journals.sagepub.com/doi/abs/10.1177/0278364911415885. I don't know optimal solutions.

[@zaphod77]

The chauffeur should always win by being able to increase it's distance far enough that it can turn around and draw a bead. since by definition, the car is faster, it can always increase the distance between the two if it desires. How far away it must get is dependent on it's turning radius, but it's a finite distance.
The pedestrian is screwed if it's in front, and can't reach a circle. But if it can, it should aim for a circle, and then go towards the car when it gets there to maximize the amount of time it takes for it to get far away enough to swing back. once it has swung back around all you can do is flee directly away, because anything else lowers the distance more.
Note that this is a very idealized approximation. real empty lots are finite, and a real chauffeur can't track at arbitrary distances. And a real chauffeur can't turn the wheel instantly.

Have you watched the video?

[@AaronBecker]

I think Rey should have swerved sideways... just saying.