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23
PursuitEvasion on Trees by Robot Teams
, 2010
"... We present GraphClear, a novel pursuitevasion problem on graphs which models the detection of intruders in complex indoor environments by robot teams. The environment is represented by a graph, and a robot team can execute sweep and block actions on vertices and edges respectively. A sweep action ..."
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Cited by 25 (4 self)
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We present GraphClear, a novel pursuitevasion problem on graphs which models the detection of intruders in complex indoor environments by robot teams. The environment is represented by a graph, and a robot team can execute sweep and block actions on vertices and edges respectively. A sweep action detects intruders in a vertex and represents the capability of the robot team to detect intruders in the region associated to the vertex. Similarly, a block action prevents intruders from crossing an edge and represents the capability to detect intruders as they move between regions. Both actions may require multiple robots to be executed. A strategy is a sequence of block and sweep actions detecting all intruders. When solving instances of GraphClear the goal is to determine optimal strategies, i.e. strategies using the least number of robots. We prove that for the general case of graphs the problem of computing optimal strategies is NPhard. Next, for the special case of trees we provide a polynomial time algorithm. The algorithm ensures that throughout the execution of the strategy all cleared vertices form a connected subtree, and we show it produces optimal strategies.
Complexity result for the pursuitevasion game of maintaining visibility of a moving evader
 In Robotics and Automation, 2008. ICRA 2008. IEEE International Conference on, 2008. BIBLIOGRAPHY 114
"... Abstract — In this paper we consider the problem of maintaining visibility of a moving evader by a mobile robot, the pursuer, in an environment with obstacles. We simultaneously consider bounded speed for both players and a variable distance separating them. Unlike our previous efforts [11], we giv ..."
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Cited by 12 (4 self)
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Abstract — In this paper we consider the problem of maintaining visibility of a moving evader by a mobile robot, the pursuer, in an environment with obstacles. We simultaneously consider bounded speed for both players and a variable distance separating them. Unlike our previous efforts [11], we give special attention to the combinatorial problem that arises when searching for a solution through visiting several locations. We approach evader tracking by decomposing the environment into convex regions. We define two graphs: one is called the mutual visibility graph (MVG) and the other the accessibility graph (AG). The MVG provides a sufficient condition to maintain visibility of the evader while the AG defines possible regions to which either the pursuer or the evader may go to. The problem is framed as a non cooperative game. We establish the existence of a solution, based on a k −Min approach, for the following givens: the environment, the initial state of the evader and the pursuer, including their maximal speeds. We show that the problem of finding a solution to this game is NPcomplete. I.
Strategy Generation in MultiAgent ImperfectInformation Pursuit Games
, 2010
"... We describe a formalism and algorithms for gametree search in partiallyobservable Euclidean space, and implementation and tests in a scenario where a multiagent team, called tracking agents, pursues a target agent that wants to evade the tracking agents. Our contributions include— A formalism tha ..."
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Cited by 5 (2 self)
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We describe a formalism and algorithms for gametree search in partiallyobservable Euclidean space, and implementation and tests in a scenario where a multiagent team, called tracking agents, pursues a target agent that wants to evade the tracking agents. Our contributions include— A formalism that combines geometric elements (agents ’ locations and trajectories and observable regions, and obstacles that restrict mobility and observability) with gametheoretic elements (information sets, utility functions, and strategies). A recursive formula for informationset minimax values based on our formalism, and a implementation of the formula in a gametree search algorithm. A heuristic evaluation function for use at the leaf nodes of the gametree search. It works by doing a quick lookahead search of its own, in a relaxed version of the problem. Experimental results in 500 randomly generated trials. With the strategies generated by our heuristic, the tracking agents were more than twice as likely to know the target agent’s location at the end of the game than with the strategies generated by heuristics that compute estimates of the target’s possible locations.
Hierarchical Visibility for Guaranteed Search in LargeScale Outdoor Terrain
 AUTONOMOUS AGENTS AND MULTIAGENT SYSTEMS
"... ..."
A Homicidal Differential Drive Robot
 In Proc. IEEE Int. Conf. Robot. Autom
, 2012
"... Abstract—In this paper, we consider the problem of capturing an omnidirectional evader using a Differential Drive Robot in an obstacle free environment. At the beginning of the game the evader is at a distance L> l from the pursuer. The pursuer goal is to get closer from the evader than the capt ..."
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Cited by 3 (2 self)
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Abstract—In this paper, we consider the problem of capturing an omnidirectional evader using a Differential Drive Robot in an obstacle free environment. At the beginning of the game the evader is at a distance L> l from the pursuer. The pursuer goal is to get closer from the evader than the capture distance l. The goal of the evader is to keep the pursuer at all time farther from it than this capture distance. In this paper, we found closedform representations of the motion primitives and timeoptimal strategies for each player. These strategies are in Nash Equilibrium, meaning that any unilateral deviation of each player from these strategies does not provide to such player benefit toward the goal of winning the game. We also present the condition defining the winner of the game and we construct a solution over the entire reduced space. I.
Shadow Information Spaces: Combinatorial Filters for Tracking Targets
"... This paper introduces and solves a problem of maintaining the distribution of hidden targets that move outside the field of view while a sensor sweep is being performed, resulting in a generalization of the sensing aspect of visibilitybased pursuitevasion games. Our solution first applies informat ..."
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Cited by 2 (1 self)
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This paper introduces and solves a problem of maintaining the distribution of hidden targets that move outside the field of view while a sensor sweep is being performed, resulting in a generalization of the sensing aspect of visibilitybased pursuitevasion games. Our solution first applies information space concepts to significantly reduce the general complexity so that information is processed only when the shadow region (all points invisible to the sensors) changes combinatorially or targets pass in and out of the field of view. The cases of distinguishable, partially distinguishable, and completely indistinguishable targets are handled. Depending on whether the targets move nondeterministically or probabilistically, more specific classes of problems are formulated. For each case, efficient filtering algorithms are introduced, implemented, and demonstrated that provide critical information for tasks such as counting, herding, pursuitevasion, and situational awareness.
Comparison of constrained geometric approximation strategies for planar information states
 In Proceedings of the IEEE International Conference on Robotics and Automation
, 2012
"... AbstractThis paper describes and analyzes a new technique for reasoning about uncertainty called constrained geometric approximation (CGA). We build upon recent work that has developed methods to explicitly represent a robot's knowledge as an element, called an information state, in an approp ..."
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AbstractThis paper describes and analyzes a new technique for reasoning about uncertainty called constrained geometric approximation (CGA). We build upon recent work that has developed methods to explicitly represent a robot's knowledge as an element, called an information state, in an appropriately defined information space. The intuition of our new approach is to constrain the Istate to remain in a structured subset of the Ispace, and to enforce that constraint using appropriate overapproximation methods. The result is a collection of algorithms that enable mobile robots with extreme limitations in both sensing and computation to maintain simple but provably meaningful representations of the incomplete information available to them. We present a simulated implementation of this technique for a sensorbased navigation task, along with experimental results for this task showing that CGA, compared to a highfidelity representation of the unapproximated Istate, achieves a similar success rate at a small fraction of the computational cost.
Lion and Man with Visibility in Monotone Polygons
, 2013
"... In the original version of the lion and man game, a lion tries to capture a man who is trying to escape in a circular arena. The players have equal speeds. They can observe each other at all times. We study a new variant of the game in which the lion has only lineofsight visibility. That is it can ..."
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Cited by 1 (0 self)
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In the original version of the lion and man game, a lion tries to capture a man who is trying to escape in a circular arena. The players have equal speeds. They can observe each other at all times. We study a new variant of the game in which the lion has only lineofsight visibility. That is it can observe the man’s position only if the line segment connecting them does not intersect the boundary. We show that despite this limitation, the lion can capture the man in any monotone polygon in finite time. 1
Generating Strategies for MultiAgent PursuitEvasion Games in Partially Observable Euclidean Space
"... Abstract. We introduce a heuristic search technique for multiagent pursuitevasion games in partially observable Euclidean space where a team of tracker agents attempt to minimize their uncertainty about an evasive target agent. Agents ’ movement and observation capabilities are restricted by polyg ..."
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Abstract. We introduce a heuristic search technique for multiagent pursuitevasion games in partially observable Euclidean space where a team of tracker agents attempt to minimize their uncertainty about an evasive target agent. Agents ’ movement and observation capabilities are restricted by polygonal obstacles, while each agents ’ knowledge of the other agents is limited to direct observation or periodic updates from team members. Our polynomialtime algorithm is able to generate strategies for games in continuous twodimensional Euclidean space, an improvement over past algorithms that were only applicable to simple gridworld domains. We show experimentally that our algorithm is tolerant of interruptions in communication between agents, continuing to generate good strategies despite long periods of time where agents are unable to communicate directly. Experimental results also show that our technique generates effective strategies quickly, with decision times of less than a second for reasonably sized domains with six or more agents.
1TimeOptimal Motion Strategies for Capturing an Omnidirectional Evader using a Differential Drive Robot
"... Abstract—In this paper, we consider the problem of capturing an omnidirectional evader using a Differential Drive Robot (DDR) in an obstaclefree environment. At the beginning of this game the evader is at a distance L> l (the capture distance) from the pursuer. The goal of the evader is to keep ..."
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Abstract—In this paper, we consider the problem of capturing an omnidirectional evader using a Differential Drive Robot (DDR) in an obstaclefree environment. At the beginning of this game the evader is at a distance L> l (the capture distance) from the pursuer. The goal of the evader is to keep the pursuer farther than this capture distance as long as possible. The goal of the pursuer is to capture the evader as soon as possible. In this work, we make the following contributions: We present closedform representations of the motion primitives and timeoptimal strategies for each player; these strategies are in Nash Equilibrium, meaning that any unilateral deviation of each player from these strategies does not provide to such player benefit towards the goal of winning the game. We propose a partition of the playing space into mutually disjoint regions where the strategies of the players are well established. This partition is represented as a graph which exhibits properties that guarantee global optimality. We also analyze the decision problem of the game and we present the conditions defining the winner.