Abstract
In this article, we consider the problem of using multiple robots (searchers) to capture intruders in an environment. Assume that a robot can access the position of an intruder in real time, that is, an intruder is visible by a robot. We simplify the environment so that robots and worst-case intruders move along a weighted graph, which is a topological map of the environment. In such settings, a worst-case intruder is characterized by unbounded speed, complete awareness of searcher location and intent, and full knowledge of the search environment. The weight of an edge or a vertex in a weighted graph is a cost describing the clearing requirement of the edge or the vertex. This article provides non-monotone search algorithms to capture every visible intruder. Our algorithms are easy to implement, thus are suitable for practical robot applications. Based on the non-monotone search algorithms, we derive the minimum number of robots required to clear a weighted tree graph. Considering a general weighted graph, we derive bounds for the number of robots required. Finally, we present switching algorithms to improve the time efficiency of capturing intruders while not increasing the number of robots. We verify the effectiveness of our approach using MATLAB simulations.
Highlights
Monitoring and securing of an environment is an important task in sensor networks
This article considers a simplified environment where robots and worst-case intruders move along a weighted graph, which is a topological map of the environment
We further show that the upper bound for the minimum number of robots required to clear a weighted graph can be calculated by solving the weighted feedback vertex set problem (WFVP)
Summary
Monitoring and securing of an environment is an important task in sensor networks. Sensor network becomes feasible due to the development of small sensor nodes, such as the Berkeley MOTES.[1]. This article presents the minimum number of robots (searchers) required to capture worst-case intruders on the topological map of the workspace. Kolling and Carpin[16] provided an upper bound for the minimum number of searchers by presenting a monotone search strategy to clear a weighted graph. Since this article considers a visible intruder, the number of searchers required to clear a weighted graph can reduce considerably compared to the case where an intruder is not visible. Based on the non-monotone searching algorithms, we derive the minimum number of searchers required to clear a weighted tree graph. Considering some special graphs, the WFVP can be solved in polynomial time or in linear time This implies that the upper bound for the minimum number of robots required to clear a weighted graph can be calculated in polynomial time or in linear time.
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