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A Graph Search Algorithm for Indoor Pursuit / Evasion
, 2008
"... Using concepts from both robotics and graph theory, we formulate the problem of indoor pursuit / evasion in terms of searching a graph for a mobile evader. We present an offline, greedy, iterative algorithm which performs guaranteed search, i.e. no matter how the evader moves, it will eventually be ..."
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Cited by 9 (2 self)
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Using concepts from both robotics and graph theory, we formulate the problem of indoor pursuit / evasion in terms of searching a graph for a mobile evader. We present an offline, greedy, iterative algorithm which performs guaranteed search, i.e. no matter how the evader moves, it will eventually be captured; in fact our algorithm can be applied to either an adversarial (actively trying to avoid capture) or randomly moving evader. Furthermore the algorithm produces an internal search (the searchers move only along the edges of the graph, “teleporting” is not used) and can accommodate “extended” (across nodes) visibility and finite or infinite evader speed. We present search experiments for several indoor environments, some of them quite complicated, in all of which the algorithm succeeds in clearing the graph (i.e. capturing the evader).
Efficient, Guaranteed Search with MultiAgent Teams
"... Abstract — Here we present an anytime algorithm for clearing an environment using multiple searchers. Prior methods in the literature treat multiagent search as either a worstcase problem (i.e., clear an environment of an adversarial evader with potentially infinite speed), or an averagecase prob ..."
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Cited by 8 (2 self)
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Abstract — Here we present an anytime algorithm for clearing an environment using multiple searchers. Prior methods in the literature treat multiagent search as either a worstcase problem (i.e., clear an environment of an adversarial evader with potentially infinite speed), or an averagecase problem (i.e., minimize average capture time given a model of the target’s motion). We introduce an algorithm that combines finitehorizon planning with spanning tree traversal methods to generate plans that clear the environment of a worstcase adversarial target and have good averagecase performance considering a target motion model. Our algorithm is scalable to large teams of searchers and yields theoretically bounded averagecase performance. We have tested our proposed algorithm through a large number of experiments in simulation and with a team of robot and human searchers in an office building. Our combined search algorithm both clears the environment and reduces average capture times by up to 75 % when compared to a purely worstcase approach. I.
PursuitEvasion in 2.5d based on TeamVisibility
"... Abstract — In this paper we present an approach for a pursuitevasion problem that considers a 2.5d environment represented by a height map. Such a representation is particularly suitable for largescale outdoor pursuitevasion, captures some aspects of 3d visibility and can include target heights. ..."
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Cited by 7 (1 self)
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Abstract — In this paper we present an approach for a pursuitevasion problem that considers a 2.5d environment represented by a height map. Such a representation is particularly suitable for largescale outdoor pursuitevasion, captures some aspects of 3d visibility and can include target heights. In our approach we construct a graph representation of the environment by sampling points and computing detection sets, an extended notion of visibility. Moreover, the constructed graph captures overlaps of detection sets allowing for a coordinated teambased clearing of the environment with robots that move to the sampled points. Once a graph is constructed we compute strategies on it utilizing previous work on graphsearching. This is converted into robot paths that are planned on the height map by classifying the terrain appropriately. In experiments we investigate the performance of our approach and provide examples including a sample map with multiple loops and elevation plateaus and two realistic maps, one of a village and one of a mountain range. To the best of our knowledge the presented approach is the first viable solution to 2.5d pursuitevasion with height maps. I.
Searching the nodes of a graph: theory and algorithms
, 2009
"... One or more searchers must capture an invisible evader hiding in the nodes of a graph. We study this version of the graph search problem under additional restrictions, such as monotonicity and connectedness. We emphasize that we study node search, i.e., the capture of a nodelocated evader; this pro ..."
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Cited by 7 (2 self)
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One or more searchers must capture an invisible evader hiding in the nodes of a graph. We study this version of the graph search problem under additional restrictions, such as monotonicity and connectedness. We emphasize that we study node search, i.e., the capture of a nodelocated evader; this problem has so far received much less attention than edge search, i.e., the capture of an edgelocated evader. We show that in general graphs the problem of node search is easier than that of edge search, Namely, every edge clearing search is also node clearing, but the converse does not hold in general (however node search is NPcomplete, just like edge search). Then we concentrate on the internal monotone connected (IMC) node search of trees and show that it is essentially equivalent to IMC edge search; hence Barriere’s tree search algorithm [2], originally designed for edge search, can also be used for node search. We return to IMC node search on general graphs and present (several variants of) a new algorithm: GSST (Guaranteed Search by Spanning Tree). GSST clears a graph G by performing all its clearing moves along a spanning tree T of G. Because spanning trees can be generated and cleared very quickly, GSST can test a large number of spanning trees and find one which clears G with a small (though not necessarily minimal) number of searchers. We prove the existence of probabilistically complete variants of GSST (i.e., these variants are guaranteed to find a minimal IMC node clearing schedule if run for sufficiently long time). Our experiments also indicate that GSST can efficiently nodeclear large graphs given only a small running time. An implementation of GSST (running on Windows and Linux computers) is also provided and made publicly available. 1
Improving the Efficiency of Clearing with MultiAgent Teams
"... We present an anytime algorithm for coordinating multiple autonomous searchers to find a potentially adversarial target on a graphical representation of a physical environment. This problem is closely related to the mathematical problem of searching for an adversary on a graph. Prior methods in the ..."
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Cited by 6 (3 self)
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We present an anytime algorithm for coordinating multiple autonomous searchers to find a potentially adversarial target on a graphical representation of a physical environment. This problem is closely related to the mathematical problem of searching for an adversary on a graph. Prior methods in the literature treat multiagent search as either a worstcase problem (i.e., clear an environment of an adversarial evader with potentially infinite speed), or an averagecase problem (i.e., minimize average capture time given a model of the target’s motion). Both of these problems have been shown to be NPhard, and optimal solutions typically scale exponentially in the number of searchers. We propose treating search as a resource allocation problem, which leads to a scalable anytime algorithm for generating schedules that clear the environment of a worstcase adversarial target and have good averagecase performance considering a nonadversarial motion model. Our algorithm yields theoretically bounded averagecase performance and allows for online and decentralized operation, making it applicable to realworld search tasks. We validate our proposed algorithm through a large number of experiments in simulation and with a team of robot and human searchers in an office building.
Solving PursuitEvasion Problems on Height Maps
"... Abstract — In this paper we present an approach for a pursuitevasion problem that considers a 2.5d environment represented by a height map. Such a representation is particularly suitable for largescale outdoor pursuitevasion. By allowing height information we not only capture some aspects of 3d v ..."
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Abstract — In this paper we present an approach for a pursuitevasion problem that considers a 2.5d environment represented by a height map. Such a representation is particularly suitable for largescale outdoor pursuitevasion. By allowing height information we not only capture some aspects of 3d visibility but can also consider target heights. In our approach we construct a graph representation of the environment by sampling points and their detection sets which extend the usual notion of visibility. Once a graph is constructed we compute strategies on this graph using a modification of previous work on graphsearching. This strategy is converted into robot paths that are planned on the height map by classifying the terrain appropriately. In experiments we investigate the performance of our approach and provide examples including a map of a small village with surrounding hills and a sample map with multiple loops and elevation plateaus. Experiments are carried out with varying sensing ranges as well as target and sensor heights. To the best of our knowledge the presented approach is the first viable solution to 2.5d pursuitevasion with height maps. I.
Solving Pursuitevasion Problems with GraphClear: an Overview
"... Abstract—This paper presents an overview of the numerous results we recently published for the problem of multirobot pursuit evasion. We review the GraphClear formalism we introduced, we summarize the variants we studied, and the main results we derived. Finally, we outline directions for future r ..."
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Abstract—This paper presents an overview of the numerous results we recently published for the problem of multirobot pursuit evasion. We review the GraphClear formalism we introduced, we summarize the variants we studied, and the main results we derived. Finally, we outline directions for future research both in GraphClear and for pursuitevasion and search problems in general. I.
Editorial Manager(tm) for Journal of Autonomous Agents and MultiAgent Systems Manuscript Draft Manuscript Number: Title: Hierarchical Visibility for Guaranteed Search in LargeScale Outdoor Terrain Article Type: Manuscript
"... To search for moving targets in a large area is a challenging task that is relevant in several problem domains, such as capturing an invader in a camp, guarding security facilities, and searching for victims in largescale search and rescue scenarios. The guaranteed search problem is to coordinate t ..."
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To search for moving targets in a large area is a challenging task that is relevant in several problem domains, such as capturing an invader in a camp, guarding security facilities, and searching for victims in largescale search and rescue scenarios. The guaranteed search problem is to coordinate the search of a team of agents in a way that all targets are guaranteed to be found. In this paper we present a selfcontained solution to this problem in threedimensional realworld domains represented by digital elevation models (DEMs). We introduce hierarchical sampling on DEMs for selecting strategical valuable locations from which larger parts of the map are visible. These locations are utilized to form a search graph from which search schedules are deduced, and agent paths that are directly executable in the terrain, are computed. Presented experimental results indicate that the proposed method leads to schedules requiring a significantly low number of agents for the search. The practical feasibility of our approach has been validated during a field experiment at the Gascola robot training site, where teams of humans equipped with IPads successfully searched for adversarial and omniscient evaders.