Line Coverage with Multiple Robots: Algorithms and Experiments

TL;DR

This work formulates the line coverage problem for multiple resource-constrained robots on graphs with required and non-required edges, incorporating asymmetric costs and resource demands. It introduces a fast constructive MEM heuristic and extends it to multi-depot (MD-MEM) and nonholonomic (MD-MEM-Turns) variants, embedding turns and smooth paths directly into the routing process. Through extensive simulations on large road networks and real UAV experiments, MEM achieves solutions within a small percentage of ILP optima while offering orders-of-magnitude faster runtimes and scalability to thousands of edges. The results demonstrate the practical viability of deploying autonomous aerial and ground robots for continuous line coverage tasks, including area coverage translations, with potential for online and distributed implementations.

Abstract

The line coverage problem involves finding efficient routes for the coverage of linear features by one or more resource-constrained robots. Linear features model environments like road networks, power lines, and oil and gas pipelines. Two modes of travel are defined for robots: servicing and deadheading. A robot services a feature if it performs task-specific actions, such as taking images, as it traverses the feature; otherwise, it is deadheading. Traversing the environment incurs costs (e.g., travel time) and demands on resources (e.g., battery life). Servicing and deadheading can have different cost and demand functions, which can be direction-dependent. The environment is modeled as a graph, and an integer linear program is provided. As the problem is NP-hard, we design a fast and efficient heuristic algorithm, Merge-Embed-Merge (MEM). Exploiting the constructive property of the MEM algorithm, algorithms for line coverage of large graphs with multiple depots are developed. Furthermore, turning costs and nonholonomic constraints are efficiently incorporated into the algorithm. The algorithms are benchmarked on road networks and demonstrated in experiments with aerial robots.

Figures (21)

• Figure 1: Line coverage of the UNC Charlotte road network using a team of resource-constrained UAVs. (a) The input road network is 13 km in length and spans an area of 1.5 km$^{2}$. The road network is modeled as a graph comprising 842 vertices and 865 required edges representing the road segments. As the UAVs can fly from one vertex to another, we add a non-required edge between each pair of vertices, resulting in 353,196 non-required edges in the graph. (b) Eight routes for a team of UAVs are computed using the multi-depot Merge-Embed-Merge (MEM) algorithm developed in this paper. The algorithm computes depot locations, shown by black squares, from where the UAVs start and end their routes. The solid lines represent servicing, while the dashed lines represent deadheading. The UAVs can fly faster while deadheading, thereby optimizing total flight time. (c) An orthomosaic of the road network generated from the images taken by the UAVs flown autonomously along the computed routes.
• Figure 2: Three types of features and the corresponding coverage problems: (a) Point coverage is the coverage of zero-dimensional point features and is commonly solved using node routing algorithms. (b) Line coverage is the coverage of one-dimensional line features and belongs to the broad class of arc routing problems. (c) Area coverage is the coverage of two-dimensional regions, often solved using computational geometry techniques.
• Figure 3: Representation of a route $R_p$ as a sequence of arcs corresponding to required edges: The required arcs are shown as solid blue lines, and deadheadings are shown as dashed green lines. The route internally includes deadheadings given by shortest paths to and from the depot $v_0$ (black square). The route may have deadheadings between two non-adjacent required arcs.
• Figure 4: The figure shows four of the eight permutations to merge two routes $R_p$ and $R_q$. The remaining four permutations consist of the shown permutations in the reverse directions. The tail and the head vertices for $R_p$ are $t_p$ and $h_p$, respectively. Similarly, $t_q$ and $h_q$ are defined for $R_q$. The first merged route is $v_0\rightarrow t_p \xrightarrow{R_p} h_p\rightarrow t_q\xrightarrow{R_q} h_q\rightarrow v_0$ and its reverse direction route is $v_0\rightarrow h_q\xrightarrow{\overline R_q} t_q\rightarrow h_p\xrightarrow{\overline R_p} t_p\rightarrow v_0$. The savings for merging two routes come from potentially reduced deadheading to and from the depot.
• Figure 5: MD-MEM::Initialize()