Coverage Path Planning For Minimizing Expected Time to Search For an Object With Continuous Sensing

TL;DR

This paper introduces new algorithms and heuristics for coverage path planning that minimize expected search time, extending classic problems with theoretical guarantees and practical simulations.

Contribution

It presents the quota lawn mowing problem with approximation algorithms and develops the first provable approximation for expected detection time in geometric search.

Findings

Constant-factor approximations for quota lawn mowing.

First approximation algorithm with error bounds for expected detection time.

Effective heuristics validated through simulations.

Abstract

In this paper, we present several results of both theoretical as well as practical interests. First, we propose the quota lawn mowing problem, an extension of the classic lawn mowing problem in computational geometry, as follows: given a quota of coverage, compute the shortest lawn mowing route to achieve said quota. We give constant-factor approximations for the quota lawn mowing problem. Second, we investigate the expected detection time minimization problem in geometric coverage path planning with local, continuous sensory information. We provide the first approximation algorithm with provable error bounds with pseudopolynomial running time. Our ideas also extend to another search mechanism, namely visibility-based search, which is related to the watchman route problem. We complement our theoretical analysis with some simple but effective heuristics for finding an object in minimum expected time, on which we provide simulation results.