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.

翻译：线覆盖是服务于环境中一组指定一维特征的任务，对于道路网络、电力线路及油气管道等线性基础设施的巡检至关重要。本文通过将问题建模为图上的优化问题，研究面向空中和地面机器人的单机器人线覆盖问题。该问题属于弧路径问题的广泛范畴，与非对称图上的乡村邮递员问题（RPP）密切相关。本文提出了一种整数线性规划公式并给出正确性证明。利用最小费用流问题，我们开发了具有解质量保证的近似算法，这些保证也改进了非对称RPP的现有结果。主要算法根据需求图（即需要服务的特征所导出的图）的结构将问题划分为三种情形。我们在全球人口最多的50个城市（包含多达730条道路段）的道路网络上评估了算法。经改进启发式增强后的算法在3秒内运行完毕，生成的解与最优解的偏差在10%以内。我们通过商用无人机实验验证了算法的有效性。