Min-Time Escape of a Dubins Car from a Polygon

TL;DR

This paper develops a method to compute the minimum-time escape paths for a turn-constrained vehicle, modeled as a Dubins car, from polygonal regions using optimal control techniques.

Contribution

It extends the method of characteristics to polygonal regions, enabling the calculation of optimal escape trajectories for a Dubins car.

Findings

Derived time-optimal strategies for reaching infinite lines.

Extended approach to complex polygonal regions.

Identified minimum-time escape trajectories.

Abstract

A turn constrained vehicle is initially located inside a polygon region and desires to escape in minimum time. First, the method of characteristics is used to describe the time-optimal strategies for reaching a line of infinite length. Next, the approach is extended to polygons constructed of a series of line segments. Using this construction technique, the min-time path to reach each edge is obtained; the resulting minimum of the set of optimal trajectories is then selected for escaping the polygon.