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Visibility-Based Pursuit-Evasion in a Polygonal Region by a Searcher
- Proceedings of the International Colloquium on Automata, Languages and Programming (ICALP
, 2001
"... We consider the most basic visibility-based pursuit-evasion problem defined as follows: Given a polygonal region, a searcher with 360 # vision, and an unpredictable intruder that is arbitrarily faster than the searcher, plan the motion of the searcher so as to see the intruder. In this paper, we ..."
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Cited by 48 (1 self)
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We consider the most basic visibility-based pursuit-evasion problem defined as follows: Given a polygonal region, a searcher with 360 # vision, and an unpredictable intruder that is arbitrarily faster than the searcher, plan the motion of the searcher so as to see the intruder. In this paper, we present simple necessary and su#cient conditions for a polygon to be searchable, which settles a decade-old open problem raised in [15]. We also show that every searchable polygon is also searchable by a searcher with two flashlights (that is, ray visions). This implies, combined with the previous work, that there is an O(n 2 )-time algorithm for constructing a search path for an n-sided polygon. 1 Introduction The visibility-based pursuit-evasion problem is that of planning the motion of one or more searchers in a polygonal environment to eventually see an intruder that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. This problem can mode...
Randomized pursuit-evasion in graphs
- Proceedings of the International Colloquium on Automata, Languages and Programming (ICALP
, 2002
"... We analyze a randomized pursuit-evasion game on graphs. This game is played by two players, a hunter and a rabbit. Let G be any connected, undirected graph with n nodes. The game is played in rounds and in each round both the hunter and the rabbit are located at a node of the graph. Between rounds b ..."
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Cited by 37 (0 self)
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We analyze a randomized pursuit-evasion game on graphs. This game is played by two players, a hunter and a rabbit. Let G be any connected, undirected graph with n nodes. The game is played in rounds and in each round both the hunter and the rabbit are located at a node of the graph. Between rounds both the hunter and the rabbit can stay at the current node or move to another node. The hunter is assumed to be restricted to the graph G: in every round, the hunter can move using at most one edge. For the rabbit we investigate two models: in one model the rabbit is restricted to the same graph as the hunter, and in the other model the rabbit is unrestricted, i.e., it can jump to an arbitrary node in every round. We say that the rabbit is caught as soon as hunter and rabbit are located at the same node in a round. The goal of the hunter is to catch the rabbit in as few rounds as possible, whereas the rabbit aims to maximize the number of rounds until it is caught. Given a randomized hunter strategy for G, the escape length for that strategy is the worst case expected number of rounds it takes the hunter to catch the rabbit, where the worst case is with regards to all (possibly randomized) rabbit strategies. Our main result is a hunter strategy for general graphs with an escape length of only O(n log(diam(G))) against restricted as well as unrestricted rabbits. This bound is close to optimal since Ω(n) is a trivial lower bound on the escape length in both models. Furthermore, we prove that our upper bound is optimal up to constant factors against unrestricted rabbits. 1
Sweeping simple polygons with a chain of guards
- In Proceedings of the 11th ACM-SIAM Symposium on Discrete Algorithms (SODA
, 2000
"... Abstract We consider the problem of locating a continuously-moving target using a group of guardsmoving inside a simple polygon. Our guards always form a simple polygonal chain within the polygon such that consecutive guards along the chain are mutually visible. We developalgorithms that sweep such ..."
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Cited by 36 (2 self)
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Abstract We consider the problem of locating a continuously-moving target using a group of guardsmoving inside a simple polygon. Our guards always form a simple polygonal chain within the polygon such that consecutive guards along the chain are mutually visible. We developalgorithms that sweep such a chain of guards through a polygon to locate the target. Our two main results are the following: 1. an algorithm to compute the minimum number r * of guards needed to sweep an n-vertexpolygon that runs in O(n3) time and uses O(n2) working space, and 2. a faster algorithm, using O(n log n) time and O(n) space, to compute an integer r suchthat max( r- 16, 2) < = r * < = r and P can be swept with a chain of r guards. We develop two other techniques to approximate r*. Using O(n2) time and space, we show howto sweep the polygon using at most r * + 2 guards. We also show that any polygon can be sweptby a number of guards equal to two more than the link radius of the polygon. As a key component of our exact algorithm, we introduce the notion of the link diagramof a polygon, which encodes the link distance between all pairs of points on the boundary of the polygon. We prove that the link diagram has size \Theta (n3) and can be constructed in \Theta (n3)time. We also show link diagram provides a data structure for optimal two-point link-distance queries, matching an earlier result of Arkin et al.As a key component of our O(n log n)-time approximation algorithm, we introduce the notionof the &quot;link width &quot; of a polygon, which may have independent interest, as it captures important
Cooperative Robotics for Multi-Target Observation
- Intelligent Automation and Soft Computing
, 1999
"... An important issue that arises in the automation of many security, surveillance, and reconnaissance tasks is that of observing (or monitoring) the movements of targets navigating in a bounded area of interest. A key research issue in these problems is that of sensor placement --- determining where s ..."
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Cited by 35 (2 self)
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An important issue that arises in the automation of many security, surveillance, and reconnaissance tasks is that of observing (or monitoring) the movements of targets navigating in a bounded area of interest. A key research issue in these problems is that of sensor placement --- determining where sensors should be located to maintain the targets in view. In complex applications involving limited-range sensors, the use of multiple sensors dynamically moving over time is required. In this article, we investigate the use of a cooperative team of autonomous sensor-based robots for the observation of multiple moving targets (a problem that we term CMOMMT). We focus primarily on developing the distributed control strategies that allow the robot team to attempt to maximize the collective time during which each target is being observed by at least one robot team member in the area of interest. Our initial efforts on this problem address the aspects of distributed control in robot teams with e...
Gap navigation trees: Minimal representation for visibility-based tasks
- In Proc. Workshop on the Algorithmic Foundations of Robotics
, 2004
"... Abstract. In this paper we present our advances in a data structure, the Gap Navigation Tree (GNT), useful for solving different visibility-based robotic tasks in unknown planar environments. We present its use for optimal robot navigation in simply-connected environments, locally optimal navigation ..."
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Cited by 30 (9 self)
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Abstract. In this paper we present our advances in a data structure, the Gap Navigation Tree (GNT), useful for solving different visibility-based robotic tasks in unknown planar environments. We present its use for optimal robot navigation in simply-connected environments, locally optimal navigation in multiply-connected environments, pursuit-evasion, and robot localization. The guiding philosophy of this work is to avoid traditional problems such as complete map building and exact localization by constructing a minimal representation based entirely on critical events in online sensor measurements made by the robot. The data structure is introduced from an information space perspective, in which the information used among the different visibility-based tasks is essentially the same, and it is up to the robot strategy to use it accordingly for the completion of the particular task. This is done through a simple sensor abstraction that reports the discontinuities in depth information of the environment from the robot’s perspective (gaps), and without any kind of geometric measurements. The GNT framework was successfully implemented on a real robot platform. 1
Cooperative Motion Control for Multi-Target Observation
- In Proceedings of the 1997 IEEE/RSJ International Conference on Intelligent Robots and Systems
, 1997
"... many security, surveillance, and reconnaissance tasks is that of monitoring (or observing) the movements of targets navigating in a bounded area of interest. A key research issue in these problems is that of sensor placement --- determining where sensors should be located to maintain the targets in ..."
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Cited by 30 (3 self)
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many security, surveillance, and reconnaissance tasks is that of monitoring (or observing) the movements of targets navigating in a bounded area of interest. A key research issue in these problems is that of sensor placement --- determining where sensors should be located to maintain the targets in view. In complex applications involving limited-range sensors, the use of multiple sensors dynamically moving over time is required. In this paper, we investigate the use of a cooperative team of autonomous sensor-based robots for the observation of multiple moving targets. We focus primarily on developing the distributed control strategies that allow the robot team to attempt to minimize the total time in which targets escape observation by some robot team member in the area of interest. This paper first formalizes the problem and discusses related work. We then present a distributed approximate approach to solving this problem that combines low-level multi-robot control with higher-level reasoning control based on the ALLIANCE formalism. We analyze the effectiveness of our approach by comparing it to three other feasible algorithms for cooperative control, showing the superiority of our approach for a large class of problems.
A Region-based Approach for Cooperative Multi-Target Tracking in a Structured Environment
, 2002
"... This paper addresses the problem of tracking multiple anonymous targets using a network of communicating robots and stationary sensors. We introduce a regionbased approach which controls robot deployment at two levels. A coarse deployment controller distributes robots across regions using a topologi ..."
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Cited by 26 (3 self)
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This paper addresses the problem of tracking multiple anonymous targets using a network of communicating robots and stationary sensors. We introduce a regionbased approach which controls robot deployment at two levels. A coarse deployment controller distributes robots across regions using a topological map and density estimates, and a target-following controller attempts to maximize the number of tracked targets within a region. A behavior-based system is presented implementing the region-based approach. Intensive simulations were performed to investigate the correlation between our approach and the degree of occlusion in the environment. The region-based approach shows better performance than a `naive' local-following strategy when the environment has significant occlusion. We performed real-robot experiments to validate the system. These experiments open up a new line of research, which suggests that an optimal ratio of robots to stationary sensors may exist for a given environment with certain occlusion characteristics. 1
A point-based POMDP planner for target tracking
- in Proc. ICRA
, 2008
"... Abstract-Target tracking has two variants that are often studied independently with different approaches: target searching requires a robot to find a target initially not visible, and target following requires a robot to maintain visibility on a target initially visible. In this work, we use a part ..."
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Cited by 25 (7 self)
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Abstract-Target tracking has two variants that are often studied independently with different approaches: target searching requires a robot to find a target initially not visible, and target following requires a robot to maintain visibility on a target initially visible. In this work, we use a partially observable Markov decision process (POMDP) to build a single model that unifies target searching and target following. The POMDP solution exhibits interesting tracking behaviors, such as anticipatory moves that exploit target dynamics, informationgathering moves that reduce target position uncertainty, and energy-conserving actions that allow the target to get out of sight, but do not compromise long-term tracking performance. To overcome the high computational complexity of solving POMDPs, we have developed SARSOP, a new point-based POMDP algorithm based on successively approximating the space reachable under optimal policies. Experimental results show that SARSOP is competitive with the fastest existing pointbased algorithm on many standard test problems and faster by many times on some.
Pursuit-Evasion on Trees by Robot Teams
, 2010
"... We present Graph-Clear, a novel pursuit-evasion 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 Graph-Clear, a novel pursuit-evasion 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 Graph-Clear 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 NP-hard. 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.
An Algorithm for Searching a Polygonal Region with a Flashlight
- International Journal of Computational Geometry and Applications
, 2000
"... We present an algorithm for a single pursuer with one ashlight that searches for an unpredictable, moving target with unbounded speed in a polygonal environment. The algorithm decides whether a simple polygon with n edges and m concave regions (m is typically much less than n, and always bounded ..."
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Cited by 24 (3 self)
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We present an algorithm for a single pursuer with one ashlight that searches for an unpredictable, moving target with unbounded speed in a polygonal environment. The algorithm decides whether a simple polygon with n edges and m concave regions (m is typically much less than n, and always bounded by n) can be cleared by the pursuer, and if so, constructs a search schedule in time O(m 2 + m log n + n). The key ideas in this algorithm include a representation called the \visibility obstruction diagram" and its \skeleton," which is a combinatorial decomposition based on a number of critical visibility events. An implementation is presented along with a computed example. 1 Introduction Consider the following scenario: in a dark polygonal region there are two moving points. The rst one, called the pursuer, has the task to nd the second one, called the evader. The evader can move arbitrarily fast, and his movements are unpredictable by the pursuer. The pursuer is equipped with a...
