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
Approximation Algorithms for the Single Robot Line Coverage Problem
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.
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- NSF-PAR ID:
- 10176424
- Editor(s):
- LaValle, Steve M.; Lin, Ming; Ojala, Timo; Shell, Dylan; Yu, Jingjin
- Date Published:
- Journal Name:
- Algorithmic Foundations of Robotics XIV (WAFR 2020)
- Page Range / eLocation ID:
- 534-550
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1007/978-3-030-66723-8_32
