An Approximation Algorithm for a Shortest Dubins Path Problem

TL;DR

This paper introduces a new approximation algorithm for the shortest Dubins path problem, significantly improving the solution quality guarantee for vehicle routing with motion constraints.

Contribution

The paper presents a novel approximation algorithm that reduces the solution guarantee from 3.04 to 2.04 for the shortest Dubins path problem.

Findings

Improved approximation guarantee from 3.04 to 2.04.

Algorithm tested on hundreds of instances with up to 30 points.

Demonstrated effectiveness of the approach in practical scenarios.

Abstract

The problem of finding the shortest path for a vehicle visiting a given sequence of target points subject to the motion constraints of the vehicle is an important problem that arises in several monitoring and surveillance applications involving unmanned aerial vehicles. There is currently no algorithm that can find an optimal solution to this problem. Therefore, heuristics that can find approximate solutions with guarantees on the quality of the solutions are useful. The best approximation algorithm currently available for the case when the distance between any two adjacent target points in the sequence is at least equal to twice the minimum radius of the vehicle has a guarantee of 3.04. This article provides a new approximation algorithm which improves this guarantee to 2.04. The developed algorithm is also implemented for hundreds of typical instances involving at most 30 points to corroborate the performance of the proposed approach.