The Single Robot Line Coverage Problem: Theory, Algorithms, and Experiments

TL;DR

This paper models the single robot line coverage problem as an optimization task, proposing algorithms with guarantees that efficiently generate near-optimal solutions for inspecting linear infrastructure using aerial and ground robots.

Contribution

It introduces a novel integer linear programming formulation and approximation algorithms with proven guarantees, improving solution quality for the asymmetric rural postman problem.

Findings

Algorithms run within 3 seconds on large road networks.

Solutions are within 10% of the optimal.

Demonstrated effectiveness with commercial UAVs.

Abstract

Line coverage is the task of servicing a given set of one-dimensional features in an environment. It is important for the inspection of linear infrastructure such as road networks, power lines, and oil and gas pipelines. This paper addresses the single robot line coverage problem for aerial and ground robots by modeling it as an optimization problem on a graph. The problem belongs to the broad class of arc routing problems and is closely related to the rural postman problem (RPP) on asymmetric graphs. The paper presents an integer linear programming formulation with proofs of correctness. Using the minimum cost flow problem, we develop approximation algorithms with guarantees on the solution quality. These guarantees also improve the existing results for the asymmetric RPP. The main algorithm partitions the problem into three cases based on the structure of the required graph, i.e., the graph induced by the features that require servicing. We evaluate our algorithms on road networks from the 50 most populous cities in the world, consisting of up to 730 road segments. The algorithms, augmented with improvement heuristics, run within 3s and generate solutions that are within 10% of the optimum. We experimentally demonstrate our algorithms with commercial UAVs.