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The line coverage problem is the task of servicing a given set of one-dimensional features in an environment. Its applications include the inspection of road networks, power lines, and oil and gas lines. The line coverage problem is a generalization of the standard arc routing problems, and is NP-hard in general. We address the single robot line coverage problem where the service and deadhead costs are distinct and asymmetric. We model the problem as an optimization problem that minimizes the total cost of travel on a given graph. We present approximation algorithms to obtain bounded solutions efficiently, using the minimum cost flow problem. We build the main algorithm in stages by considering three simpler subproblems. The subproblems are based on the structure of the required graph, i.e., the graph induced by the features that require servicing. We first present an optimal algorithm for the case of Eulerian graphs with only required edges. Next we consider general graphs, not necessarily Eulerian, with only required edges and present a 2-approximation algorithm. Finally, we consider the general case with both required and non-required edges. The approximation algorithm is dependent on the Asymmetric Traveling Salesperson Problem (ATSP), and is bounded by alpha(C) + 2, where alpha(C) is the approximation factor of the ATSP algorithm with C connected components. Our upper bound is also an improvement over the existing results for the asymmetric rural postman problem. 

The line coverage problem is the coverage of linear environment features (e.g., road networks, power lines), modeled as 1D segments, by one or more robots while respecting resource constraints (e.g., battery capacity, flight time) for each of the robots. The robots incur direction dependent costs and resource demands as they traverse the edges. We treat the line coverage problem as an optimization problem, with the total cost of the tours as the objective, by formulating it as a mixed integer linear program (MILP). The line coverage problem is NP-hard and hence we develop a heuristic algorithm, Merge- Embed-Merge (MEM). We compare it against the optimal MILP approach and a baseline heuristic algorithm, Extended Path Scanning. We show the MEM algorithm is fast and suitable for real-time applications. To tackle large-scale problems, our approach performs graph simplification and graph partitioning, followed by robot tour generation for each of the partitioned subgraphs. We demonstrate our approach on a large graph with 4,658 edges and 4,504 vertices that represents an urban region of about 16 sq. km. We compare the performance of the algorithms on several small road networks and experimentally demonstrate the approach using UAVs on the UNC Charlotte campus road network.