L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. Visibility-based pursuit-evasion in a polygonal environment. In F. Dehne, A. Rau-Chaplin, J.-R. Sack, and R. Tamassia, editors, WADS '97 Algorithms and Data Structures (Lecture Notes in Computer Science, 1272), pages 17-30. Springer-Verlag, Berlin, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....placing sensors at appropriate locations to ensure the visibility of certain objects. Installing a minimal number of sensors in a static manner is the so called art gallery problem [2] 15] while allowing the sensors (usually cameras) to move actively is the so called pursuit evasion problem 0[5]. The camera motions are usually controlled via an active vision system, and the motion can also be integrated into control servo loops [7] 16] Similar planning problems about object tracking were considered in [10] for robotics applications. A general dynamic programming approach was used to ....

L. J. Guibas, J.-C. Latombe, S. M. LeVa lle, D. Lin, and R. Motwani, "Visibility-Based Pursuit-Evasion in a Polygonal Environment," Proceedings of the 5th Workshop on Algorithms and Data Structures, Springer Verlag, pp. 17-30, 1997.

....2.3.2 Optimal Placement Another approach to addressing the deployment problem is to formulate it as an optimal placement problem. Optimal placement problems have been studied in various contexts by researchers including facility location (theory [CGS99] and pursuit evasion problems in robotics ( [GLL99]) 2.3.2.1 Art Gallery and Pursuit Evasion In robotics, art gallery and pursuit evasion [GLL99] problems have been well studied. In the art gallery analogy, the robot s goal is to move from one position to another to maximize visual coverage of its surroundings, as a human might try to do in a ....

....as an optimal placement problem. Optimal placement problems have been studied in various contexts by researchers including facility location (theory [CGS99] and pursuit evasion problems in robotics ( GLL99] 2.3.2. 1 Art Gallery and Pursuit Evasion In robotics, art gallery and pursuit evasion [GLL99] problems have been well studied. In the art gallery analogy, the robot s goal is to move from one position to another to maximize visual coverage of its surroundings, as a human might try to do in a gallery. A complementary set of approaches addresses the pursuit evasion problem in which a robot ....

Leonidas Guibas, D Lin, Jean Claude Latombe, S LaValle, and Rajeev Motwani. "Visibility-based pursuit evasion in a polygonal environment." International Journal of Computational Geometry Applications, 9(5):471-- 494, October 1999.

.... case of k flashlights) for k 1, or the 1 searcher having full 360 ffi vision (the case of a light bulb) The problem was first discussed in [13] as a dynamic version of the well known art gallery problem [11] The following two factors seem to have contributed to the recent outburst of papers [3] [6] 7] 9] 10] 14] 15] 16] on polygon search and its variants in both computational geometry conferences and robotics conferences: 1. Despite its seeming simplicity, the problem has proven quite challenging. Indeed, the algorithm given in [3] for computing a schedule of the 1 searcher to ....

....have contributed to the recent outburst of papers [3] 6] 7] 9] 10] 14] 15] 16] on polygon search and its variants in both computational geometry conferences and robotics conferences: 1. Despite its seeming simplicity, the problem has proven quite challenging. Indeed, the algorithm given in [3] for computing a schedule of the 1 searcher to search a given polygon through state space enumeration has exponential worst case running time, and the exact complexity of the problem of generating a schedule to clear a given polygon by one 1 searcher is still unknown. The capabilities of various ....

[Article contains additional citation context not shown here]

L.J. Guibas, J.-C. Latombe, S.M. LaValle, D. Lin and R. Motwani, "Visibilitybased pursuit-evasion in a polygonal environment," in F. Dehne et al. Eds., WADS '97 Algorithms and Data Structures (LNCS 1272), 1997, 17-30, Springer.

....of placing sensors at appropriate locations to ensure the visibility of certain objects. Installing a minimal number of sensors in a static manner is the so called art gallery problem [1] 16] while allowing the sensors (usually cameras) to move actively is the so called pursuit evasion problem [5]. Camera motions are usually controlled via an active vision system, and the motion can also be integrated into control servo loops [7] 17] Similar planning problems about maintaining object visibility were considered in [10] for robotics applications. A general dynamic programming approach was ....

L. J. Guibas, J.-C. Latombe, S. M. LeValle, D. Lin, and R. Motwani, "Visibility-Based Pursuit-Evasion in a Polygonal Environment," Proceedings of the 5th Workshop on Algorithms and Data Structures, Springer Verlag, pp. 17-30, 1997.

....include placing sensors at appropriate locations to ensure the visibility of certain objects. Installing a minimal number of sensors in a static manner is the so called art gallery problem[15] while allowing the sensors (usually cameras) to move actively is the so called pursuitevasion problem[5]. The camera motions are usually controlled via an active vision system, and the motion can also be integrated into control servo loops [6] 16] Similar planning problems about object tracking were considered in [3] for robotics applications. A general dynamic programming approach was used to ....

L. J. Guibas, J.-C. Latombe, S. M. LeValle, D. Lin, and R. Motwani, "Visibility-Based Pursuit-Evasion in a Polygonal Environment," Proceedings of the 5th Workshop on Algorithms and Data Structures, Springer Verlag, pp. 17-30, 1997.

....contexts. A common abstraction is the so called art gallery analogy, where the robot s goal is to move from one position to another so as to maximize visual coverage of its surroundings, as one might try to do in a gallery. A complementary set of approaches address the pursuit evasion problem [5] in which a robot tries to move so as to evade observation or capture by a group of moving trackers. Several approaches to exploration have been developed, addressing the related goals of searching for a specific location object, space coverage, and maximizing some measure of novelty. ....

L. J. Guibas, D. Lin J-C. Latombe, S. M. LaValle, and R. Motwani. Visibility-based pursuit-evasion in a polygonal environment. International Journal of Computational Geometry and Applications, To Appear.

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L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. Visibility-based pursuit-evasion in a polygonal environment. In F. Dehne, A. Rau-Chaplin, J.-R. Sack, and R. Tamassia, editors, WADS '97 Algorithms and Data Structures (Lecture Notes in Computer Science, 1272), pages 17-30. Springer-Verlag, Berlin, 1997.

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L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. Visibility-based pursuit-evasion in a polygonal environment. International Journal of Computational Geometry and Applications, 9(5):471-- 494, 1999.

No context found.

L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. Visibility-based pursuit-evasion in a polygonal environment. International Journal of Computational Geometry and Applications, 9(5):471--494, 1999.

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L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. Visibility-based pursuit-evasion in a polygonal environment. In Workshop on Algorithms and Data Structures, pages 17-30, 1997.

No context found.

Leonidas J. Guibas, Jean-Claude Latombe, Steven M. LaValle, David Lin, and Rajeev Motwani. Visibility-based pursuit-evasion in a polygonal environment. In F. Dehne, A. Rau-Chaplin, J.-R. Sack, and R. Tamassia, editors, WADS '97 Algorithms and Data Structures, volume 1272 of Lecture Notes in Computer Science, pages 17--30. Springer-Verlag, Berlin, 1997.

....[7,10] Originally, the problem of 1 searchability of a polygon was introduced in Ref. 12] together with a more general problem in which the pursuer (a.k.a. k searcher) has k ashlights; when k is not bounded this corresponds to a 360 vision. For results concerning 360 vision refer to Refs. [2,4,11,12] for search in polygons and to Ref. 8] for curved planar environments. Our model is motivated in part by the need in mobile robotics systems to develop simple sensing mechanisms and to minimize localization requirements (knowing the precise location of the robot) The ashlight could be ....

....Observation 3.8 For each i, 0 i m 1, let C i be a concave region of P with hiding places a i and b i and associated walls i , i . Then the tile bordering the diagonal and the walls i , as well as the tile bordering the diagonal These are the green segments de ned in Ref. [4]. 17 and walls i are both empty. Moreover, every other tile which borders the diagonal is nonempty and its boundary contains a con guration hp; pi, where p is a nonre ex vertex of the polygon P . The next lemma establishes that every tile contains at most one conservative region. Lemma ....

L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. Visibilitybased pursuit-evasion in a polygonal environment. In F. Dehne, A. Rau-Chaplin, J.-R. Sack, and R. Tamassia, editors, WADS '97 Algorithms and Data Structures (Lecture Notes in Computer Science, 1272), pages 17-30. Springer-Verlag, Berlin, 1997.

....been cleared by the guards, but if the target can find a way to enter the region again, it becomes recontaminated and must again be cleared. Thus, unless one has su#ciently many guards, the target finding problem is not always solvable. Crass et al. 9] Suzuki and Yamashita [28] Guibas et al. [12], and LaValle et al. 21] study various versions of this problem where the guards move independently. Guibas et al. prove that for a simple polygon with n vertices and h holes, #( # h log n) guards are needed in the worst case to detect all targets. They also prove that computing the smallest ....

L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. Visibility-based pursuit evasion in a polygonal environment. In Proc. 5th Workshop Algorithms and Data Structures, pages 17--30, 1997.

....abilities. The following lemma is straightforward to establish: Lemma 4.1 If there exists a solution path, 0; 1] R, then there exists another solution path 0 such that 0 (0) 2 R 0 and 0 (1) 2 R 0 . 5 We now use information space concepts, which are de ned formally in [6, 9]. The information state represents set of all places in which an evader could be hiding, and is speci ed in the present context by identifying the gaps that appear in the gap sensor, and assigning a binary label to each. The label represents clear or contaminated, as in the case of the status from ....

....3, which can be considered as the information states at junctions. Due to appear lines, however, a sequence of information states are traversed during the execution of a primitive motion. The present de nition of information states can be reduced to more basic information states as described in [6] by de ning equivalence classes; however, we forego this discussion in this paper. A partial ordering can be de ned on the set of information states by considering one information state, 1 to dominate another, 2 if each involves the same set of gaps, and for each gap the label for 1 is 0 ....

[Article contains additional citation context not shown here]

L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. Visibility-based pursuit-evasion in a polygonal environment. In F. Dehne, A. Rau-Chaplin, J.-R. Sack, and R. Tamassia, editors, WADS '97 Algorithms and Data Structures (Lecture Notes in Computer Science, 1272), pages 17-30. Springer-Verlag, Berlin, 1997.

No context found.

L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. Visibility-based pursuit-evasion in a polygonal environment. In F. Dehne, A. Rau-Chaplin, J.-R. Sack, and R. Tamassia, editors, WADS '97 Algorithms and Data Structures (Lecture Notes in Computer Science, 1272), pages 17-30. Springer-Verlag, Berlin, 1997.

....have been cleared by the guards, but if the target can nd a way to enter the region again, it becomes recontaminated and must again be cleared. Thus, unless one has suciently many guards, the target nding problem is not always solvable. Crass et al. 9] Suzuki and Yamashita [28] Guibas et al. [12], and LaValle et al. 21] study various versions of this problem where the guards move independently. Guibas et al. prove that for a polygon with n vertices and h holes, p h logn) guards are needed in the worst case to detect all targets. They also prove that computing the smallest number of ....

L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. Visibility-based pursuit evasion in a polygonal environment. In Proc. 5th Workshop Algorithms and Data Structures, pages 17-30, 1997.

No context found.

L.J. Guibas, J.C. Latombe, S.M. LaValle, D. Lin, and R. Motwani, \Visibility-Based Pursuit-Evasion in a Polygonal Environment," Proc. 5th Workshop on Algorithms and Data Structures (WADS'97), Springer-Verlag, pp. 17-30, 1997.

....an area that has already been explored. The planner uses the input layout to compute a robot s motion such that, for any point p along this path, the section of the environmemt that has already been explored before reaching p is fully separated from the unexplored one by the region visible from p [19]. In the target tracking task, the robot must visually track a target that may try to escape its field of view, for instance, by hiding behind an obstacle. The online planner uses a 2 D layout to decide how the robot should move. At each step, it computes the visibility region of the robot at ....

Guibas, L.J., J.C. Latombe, S.M. LaValle, D. Lin, and R. Motwani (1997). Visibility-based pursuit-evasion in a polygonal environment. Proc. 5th Workshop on Algorithms and Data Structures (WADS'97), Springer, New York (NY), 17--30.

.... show that it is a nontrivial generalization of the variants of 1 searchability de ned in [7] and [9] Originally, the problem of 1 searchability of a polygon was introduced together with a more general problem in which the pursuer has 360 vision [11] For results concerning 360 vision refer to [11, 2, 4, 10] for search in polygons and to [8] for curved planar environments. Our models are motivated in part by the desire in mobile robotics systems to develop simple sensing mechanisms and to minimize localization requirements (knowing the precise location of the robot) The ashlight could be ....

L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. Visibility-based pursuit-evasion in a polygonal environment. In F. Dehne, A. Rau-Chaplin, J.-R. Sack, and R. Tamassia, editors, WADS '97 Algorithms and Data Structures (Lecture Notes in Computer Science, 1272), pages 17-30. Springer-Verlag, Berlin, 1997.

....robot knows. In the intruder example, we can associate a visibility region with each configuration of the robot. In a polygonal environment, this region is a polygon bounded by both obstacle edges and free edges. The information state defines the free edges behind which the intruder may still hide [22]. The planner must compute a trajectory of the robot leading to an information state such that the intruder cannot be hiding behind any of the free edges of the current visibility region. Executing that path guarantees that the intruder will eventually be detected. 3.5 Integration Most motion ....

Guibas, L.J., Latombe, J.C., LaValle, S.M., Lin, D., and Motwani. , R. 1997. Visibility-Based PursuitEvasion in a Polygonal Environment. Proc. 5th Int. Workshop on Algorithms and Data Structures (WADS'97), Dehne, F., Rau-Chaplin, A., Sack, J.R., and Tamassia, R. (eds.), Lecture Notes in Computer Science, Vol. 1272, 17-30.

....been cleared by the guards, but if the target can find a way to enter the region again, it becomes recontaminated and must again be cleared. Thus, unless one has sufficiently many guards, the target finding problem is not always solvable. Crass et al. 9] Suzuki and Yamashita [28] Guibas et al. [12], and LaValle et al. 21] study various versions of this problem where the guards move independently. Guibas et al. prove that for a simple polygon with n vertices and h holes, Theta( p h log n) guards are needed in the worst case to detect all targets. They also prove that computing the ....

L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani. Visibility-based pursuit evasion in a polygonal environment. In Proc. 5th Workshop Algorithms and Data Structures, pages 17--30, 1997.

....moves through a workspace. As explained in [5] when the presence of visual and motion obstructions are considered, the tracking problem trascends the machine vision context into motion control and planning domains. Another example of vision as end effector is the hide andseek problem presented in [3]. Here the task is to move a team of robots in order to localize an unpredictable and arbitrary fast target with absolute certainty. This problem is very interesting from the theoretical point of view as it is a generalization of the art gallery problem when the museum guards are not restricted to ....

L. Guibas, J.C. Latombe, S.M. LaValle, D. Lin, and R. Motwani. Visibility-based pursuit-evasion in a polygonal environment. In Proc. 5th Workshop on Algorihtms and Data Structures (WADS'97), pages 17--30. Springer Verlag, 1997.

No context found.

L. Guibas, J.-C. Latombe, S.M. LaValle, D. Lin and R. Motwani. Visibility-based pursuit-evasion in a polygonal environment. In Proc 5th Workshop on Algorithms and Data Structures, 1997.

No context found.

L.J Guibas, J.C Latombe, S.M LaValle, D. Lin and R. Motwani. Visibility-based pursuit-evasion in a polygonal environment. In 5th Workshop on Algorithms and Data Structures, 1997.

No context found.

L. Guibas, J.-C. Latombe,S.M. LaValle, D. Lin, R. Motwani, Visibilitybased pursuit-evasion in a polygonal environment, In Proc 5th Workshop on Algorithms and Data Structures, 1997.

No context found.

L. Guibas, J.-C. Latombe,S.M. LaValle, D. Lin, R. Motwani, Visibilitybased pursuit-evasion in a polygonal environment, In Proc 5th Workshop on Algorithms and Data Structures, 1997.

No context found.

L. J. Guibas, J.-C. Latombe, S. M. LaValle, D. Lin, and R. Motwani, "Visibility-based pursuit-evasion in a polygonal environment," in WADS '97 Algorithms and Data Structures (Lecture Notes in Computer Science, 1272). Springer-Verlag, 1977.

No context found.

L. Guibas, J.-C. Latombe, S. LaValle, D. Lin and R. Motwani, "Visibility-Based PursuitEvasion in a Polygonal Environment", International Journal of Computational Geometry and Applications, 9(5), 1999, pp. 471-494.

No context found.

Leonidas Guibas, D Lin, Jean Claude Latombe, S LaValle, and Rajeev Motwani. Visibilitybased pursuit evasion in a polygonal environment. International Journal of Computational Geometry Applications, 2000.

No context found.

L. Guibas, D. Lin, J. C. Latombe, S. LaValle, and R. Motwani. Visibility-based pursuit evasion in a polygonal environment. International Journal of Computational Geometry Applications, 2000.

No context found.

L. Guibas, D. Lin, J. C. Latombe, S. LaValle, and R. Motwani. Visibility-based pursuit evasion in a polygonal environment. International Journal of Computational Geometry Applications, 2000.

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