Randomized Query Processing in Robot Path Planning
The subject of this paper is the analysis of a randomized preprocessing scheme that has been used for query processing in robot path planning. The attractiveness of the scheme stems from its general applicability to virtually any path-planning problem, and its empirically observed success. In this p...
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| Published in | Journal of computer and system sciences Vol. 57; no. 1; pp. 50 - 60 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.08.1998
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| Online Access | Get full text |
| ISSN | 0022-0000 1090-2724 |
| DOI | 10.1006/jcss.1998.1578 |
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| Abstract | The subject of this paper is the analysis of a randomized preprocessing scheme that has been used for query processing in robot path planning. The attractiveness of the scheme stems from its general applicability to virtually any path-planning problem, and its empirically observed success. In this paper we initiate a theoretical basis for explaining this empirical success. Under a simple assumption about the configuration space, we show that it is possible to perform preprocessing following which queries can be answered quickly. En route, we consider related problems on graph connectivity in the evasiveness model and art-gallery theorems. |
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| AbstractList | The subject of this paper is the analysis of a randomized preprocessing scheme that has been used for query processing in robot path planning. The attractiveness of the scheme stems from its general applicability to virtually any path-planning problem, and its empirically observed success. In this paper we initiate a theoretical basis for explaining this empirical success. Under a simple assumption about the configuration space, we show that it is possible to perform preprocessing following which queries can be answered quickly. En route, we consider related problems on graph connectivity in the evasiveness model and art-gallery theorems. |
| Author | Motwani, Rajeev Raghavan, Prabhakar Latombe, Jean-Claude Kavraki, Lydia E. |
| Author_xml | – sequence: 1 givenname: Lydia E. surname: Kavraki fullname: Kavraki, Lydia E. organization: Robotics Laboratory – sequence: 2 givenname: Jean-Claude surname: Latombe fullname: Latombe, Jean-Claude organization: Robotics Laboratory – sequence: 3 givenname: Rajeev surname: Motwani fullname: Motwani, Rajeev organization: Department of Computer Science, Stanford University, Stanford, California, 94305-2140 – sequence: 4 givenname: Prabhakar surname: Raghavan fullname: Raghavan, Prabhakar organization: IBM Research Division, Almaden Research Center, 650 Harry Road, San Jose, California, 95120 |
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| Cites_doi | 10.21236/ADA459660 10.1145/359156.359164 10.1177/027836498600500106 10.1109/TC.1983.1676196 10.1109/ROBOT.1994.351060 10.1137/0215055 10.1177/027836499101000604 10.1109/TSMC.1981.4308589 10.1109/21.148426 10.1016/0022-0000(86)90007-3 10.1109/SFCS.1979.10 10.1145/323233.323242 10.1137/0214025 10.1137/0213038 10.1177/027836498400300405 10.1109/ROBOT.1994.350966 10.1145/225058.225159 10.1109/SFCS.1985.36 10.1016/0196-8858(83)90014-3 |
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| References | O'Rourke (SS981578RF28) 1987 Hopcroft, Schwartz, Sharir (SS981578RF7) 1984; 3 Latombe (SS981578RF21) 1991 Overmars, Švestka (SS981578RF29) 1994 Udupa (SS981578RF35) 1977 Kavraki, Švestka, Latombe, Overmans (SS981578RF15) 1994 Lozano-Pérez (SS981578RF24) 1981; SMC-11 Kantabutra, Kosaraju (SS981578RF13) 1986; 32 Koga (SS981578RF20) 1994 Canny, Reif (SS981578RF4) 1987 Lay (SS981578RF22) 1982 G. Kalai, J. Matoušek, Guarding galleries in which every point can see a large area, Israel J. Math. D. A. Joseph, W. H. Plantiga, On the complexity of reachability and motion planning questions, Proceedings, First ACM Symposium on Computational Geometry, Baltimore, MD, 1985, 62, 66 Overmars (SS981578RF30) 1992 N. J. Nilsson, A mobile automaton: An application of artificial intelligence techniques, Proceedings, 1st International Joint Conference on Artificial Intelligence, Washington, DC, 1969, 509, 520 Kavraki (SS981578RF17) 1995 Lozano-Pérez, Wesley (SS981578RF26) 1979; 22 S. Quinlan, Efficient distance computation between non-convex objects, Proceedings, IEEE International Conference on Robotics and Automation, 1994, 3324, 3329 J. H. Reif, Complexity of the Mover's Problem and Generalizations, Proceedings, 20th IEEE Symposium on Foundations of Computer Science, 1979, 421, 427 Barraquand, Langois, Latombe (SS981578RF1) 1992; 22 Lovász, Young (SS981578RF23) 1991 Canny (SS981578RF3) 1988 Kavraki (SS981578RF18) 1997 Lozano-Pérez (SS981578RF25) 1983; 32 L. Kavraki, J.-C. Latombe, R. Motwani, P. Raghavan, Randomized query processing in robot path planning, Proceedings, 27th Annual ACM Symposium on Theory of Computing, Las Vegas, NV, 1995, 353, 362 P. Valtr, Guarding galleries where no point sees a small area, Israel J. Math. L. Kavraki, J.-C. Latombe, Randomized preprocessing of configuration space for fast path planning, Proceedings, IEEE International Conference on Robotics and Automation, San Diego, CA, 1994, 2138, 2145 D. Hsu, J.-C. Latombe, R. Motwani, Path planning in expansive configuration spaces, Proceedings, IEEE International Conference on Robotics and Automation, Minneapolis, MN, 1997 Barraquand, Latombe (SS981578RF2) 1991; 10 Khatib (SS981578RF19) 1986; 5 Hopcroft, Joseph, Whitesides (SS981578RF5) 1984; 13 Hopcroft, Joseph, Whitesides (SS981578RF6) 1985; 14 Schwartz, Sharir (SS981578RF34) 1983; 4 Hopcroft, Wilfong (SS981578RF8) 1984; 15 Th. Horsch, F. Schwarz, H. Tolle, Motion planning for many degrees of freedom—Random reflections at c-space obstacles, Proceedings of the IEEE International Conference on Robotics and Automation, San Diego, CA, 1994, 3318, 3323 J. H. Reif, M. Sharir, Motion planning in the presence of moving obstacles, Proceedings, 25th IEEE Symposium on Foundations of Computer Science, 1985, 144, 154 Kantabutra (10.1006/jcss.1998.1578_SS981578RF13) 1986; 32 Hopcroft (10.1006/jcss.1998.1578_SS981578RF8) 1984; 15 Lozano-Pérez (10.1006/jcss.1998.1578_SS981578RF24) 1981; SMC-11 Hopcroft (10.1006/jcss.1998.1578_SS981578RF6) 1985; 14 Udupa (10.1006/jcss.1998.1578_SS981578RF35) 1977 10.1006/jcss.1998.1578_SS981578RF9 Overmars (10.1006/jcss.1998.1578_SS981578RF30) 1992 Lovász (10.1006/jcss.1998.1578_SS981578RF23) 1991 Overmars (10.1006/jcss.1998.1578_SS981578RF29) 1994 10.1006/jcss.1998.1578_SS981578RF31 10.1006/jcss.1998.1578_SS981578RF11 10.1006/jcss.1998.1578_SS981578RF33 10.1006/jcss.1998.1578_SS981578RF10 10.1006/jcss.1998.1578_SS981578RF32 Kavraki (10.1006/jcss.1998.1578_SS981578RF15) 1994 10.1006/jcss.1998.1578_SS981578RF12 10.1006/jcss.1998.1578_SS981578RF14 10.1006/jcss.1998.1578_SS981578RF36 10.1006/jcss.1998.1578_SS981578RF16 Canny (10.1006/jcss.1998.1578_SS981578RF3) 1988 Hopcroft (10.1006/jcss.1998.1578_SS981578RF7) 1984; 3 Kavraki (10.1006/jcss.1998.1578_SS981578RF18) 1997 Canny (10.1006/jcss.1998.1578_SS981578RF4) 1987 Lay (10.1006/jcss.1998.1578_SS981578RF22) 1982 O'Rourke (10.1006/jcss.1998.1578_SS981578RF28) 1987 Hopcroft (10.1006/jcss.1998.1578_SS981578RF5) 1984; 13 Lozano-Pérez (10.1006/jcss.1998.1578_SS981578RF26) 1979; 22 Khatib (10.1006/jcss.1998.1578_SS981578RF19) 1986; 5 Barraquand (10.1006/jcss.1998.1578_SS981578RF2) 1991; 10 Koga (10.1006/jcss.1998.1578_SS981578RF20) 1994 Kavraki (10.1006/jcss.1998.1578_SS981578RF17) 1995 Schwartz (10.1006/jcss.1998.1578_SS981578RF34) 1983; 4 Latombe (10.1006/jcss.1998.1578_SS981578RF21) 1991 Barraquand (10.1006/jcss.1998.1578_SS981578RF1) 1992; 22 10.1006/jcss.1998.1578_SS981578RF27 Lozano-Pérez (10.1006/jcss.1998.1578_SS981578RF25) 1983; 32 |
| References_xml | – reference: N. J. Nilsson, A mobile automaton: An application of artificial intelligence techniques, Proceedings, 1st International Joint Conference on Artificial Intelligence, Washington, DC, 1969, 509, 520 – year: 1995 ident: SS981578RF17 publication-title: Random Networks in Configuration Space for Fast Path Planning – volume: 32 start-page: 136 year: 1986 end-page: 153 ident: SS981578RF13 article-title: New algorithms for multilink robot arms publication-title: J. Comput. System Sci. – volume: 14 start-page: 315 year: 1985 end-page: 333 ident: SS981578RF6 article-title: On the movement of robot arms in 2-dimensional bounded regions publication-title: SIAM J. Comput. – year: 1991 ident: SS981578RF21 publication-title: Robot Motion Planning – volume: 5 start-page: 90 year: 1986 end-page: 98 ident: SS981578RF19 article-title: Real-time obstacle avoidance for manipulators and mobile robots publication-title: Internat. J. Robot. Res. – year: 1992 ident: SS981578RF30 publication-title: Technical Report – volume: 22 start-page: 224 year: 1992 end-page: 241 ident: SS981578RF1 article-title: Potential Fields for Robot motion planning publication-title: IEEE Trans. Systems Man Cybern. – volume: 22 start-page: 560 year: 1979 end-page: 570 ident: SS981578RF26 article-title: An algorithm for planning collision-free paths among polyhedral obstacles publication-title: Comm. ACM – volume: 13 start-page: 610 year: 1984 end-page: 629 ident: SS981578RF5 article-title: Movement problems for 2-dimensional linkages publication-title: SIAM J. Comput. – year: 1988 ident: SS981578RF3 publication-title: The Complexity of Robot Motion Planning – year: 1977 ident: SS981578RF35 publication-title: Collision Detection and Avoidance in Computer Controlled Manipulators – volume: 4 start-page: 298 year: 1983 end-page: 351 ident: SS981578RF34 article-title: On the “Piano Movers” Problem. II. General techniques for computing topological properties of real algebraic manifolds publication-title: Adv. Appl. Math. – year: 1982 ident: SS981578RF22 publication-title: Convex Sets and Their Applications – reference: J. H. Reif, M. Sharir, Motion planning in the presence of moving obstacles, Proceedings, 25th IEEE Symposium on Foundations of Computer Science, 1985, 144, 154 – reference: Th. Horsch, F. Schwarz, H. Tolle, Motion planning for many degrees of freedom—Random reflections at c-space obstacles, Proceedings of the IEEE International Conference on Robotics and Automation, San Diego, CA, 1994, 3318, 3323 – volume: SMC-11 start-page: 681 year: 1981 end-page: 698 ident: SS981578RF24 article-title: Automatic planning of manipulator transfer movements publication-title: IEEE Trans. Systems Man Cybern. – reference: S. Quinlan, Efficient distance computation between non-convex objects, Proceedings, IEEE International Conference on Robotics and Automation, 1994, 3324, 3329 – reference: G. Kalai, J. Matoušek, Guarding galleries in which every point can see a large area, Israel J. Math. – year: 1994 ident: SS981578RF29 article-title: A probabilistic learning approach to motion planning publication-title: Proceedings, Workshop on Algorithmic Foundations of Robotics – year: 1987 ident: SS981578RF4 article-title: New lower bound techniques for robot motion planning problems publication-title: Proceedings, 28th IEEE Symposium on Foundations of Computer Science – volume: 3 start-page: 76 year: 1984 end-page: 88 ident: SS981578RF7 article-title: On the complexity of motion planning for multiple independent objects: PSPACE-hardness of the “Warehouseman's Problem publication-title: Internat. J. Robot. Res. – volume: 15 start-page: 768 year: 1984 end-page: 785 ident: SS981578RF8 article-title: Motions of objects in contact publication-title: SIAM J. Comput. – year: 1987 ident: SS981578RF28 publication-title: Art Gallery Theorems and Algorithms – reference: P. Valtr, Guarding galleries where no point sees a small area, Israel J. Math. – reference: L. Kavraki, J.-C. Latombe, Randomized preprocessing of configuration space for fast path planning, Proceedings, IEEE International Conference on Robotics and Automation, San Diego, CA, 1994, 2138, 2145 – reference: L. Kavraki, J.-C. Latombe, R. Motwani, P. Raghavan, Randomized query processing in robot path planning, Proceedings, 27th Annual ACM Symposium on Theory of Computing, Las Vegas, NV, 1995, 353, 362 – reference: J. H. Reif, Complexity of the Mover's Problem and Generalizations, Proceedings, 20th IEEE Symposium on Foundations of Computer Science, 1979, 421, 427 – reference: D. Hsu, J.-C. Latombe, R. Motwani, Path planning in expansive configuration spaces, Proceedings, IEEE International Conference on Robotics and Automation, Minneapolis, MN, 1997 – volume: 32 start-page: 108 year: 1983 end-page: 120 ident: SS981578RF25 article-title: Spatial planning: A configuration space approach publication-title: IEEE Trans. Comput. – reference: D. A. Joseph, W. H. Plantiga, On the complexity of reachability and motion planning questions, Proceedings, First ACM Symposium on Computational Geometry, Baltimore, MD, 1985, 62, 66 – year: 1994 ident: SS981578RF15 publication-title: Technical Report – volume: 10 start-page: 628 year: 1991 end-page: 649 ident: SS981578RF2 article-title: Robot motion planning: A distributed representation approach publication-title: Internat. J. Robot. Res. – year: 1991 ident: SS981578RF23 publication-title: Technical Report – year: 1997 ident: SS981578RF18 article-title: Geometry and the discovery of new ligands publication-title: Algorithms for Robotic Motion and Manipulation – year: 1994 ident: SS981578RF20 publication-title: Technical Report – ident: 10.1006/jcss.1998.1578_SS981578RF27 doi: 10.21236/ADA459660 – volume: 22 start-page: 560 year: 1979 ident: 10.1006/jcss.1998.1578_SS981578RF26 article-title: An algorithm for planning collision-free paths among polyhedral obstacles publication-title: Comm. ACM doi: 10.1145/359156.359164 – year: 1994 ident: 10.1006/jcss.1998.1578_SS981578RF29 article-title: A probabilistic learning approach to motion planning – year: 1994 ident: 10.1006/jcss.1998.1578_SS981578RF15 publication-title: Technical Report – year: 1987 ident: 10.1006/jcss.1998.1578_SS981578RF4 article-title: New lower bound techniques for robot motion planning problems – volume: 5 start-page: 90 year: 1986 ident: 10.1006/jcss.1998.1578_SS981578RF19 article-title: Real-time obstacle avoidance for manipulators and mobile robots publication-title: Internat. J. Robot. Res. doi: 10.1177/027836498600500106 – year: 1991 ident: 10.1006/jcss.1998.1578_SS981578RF23 publication-title: Technical Report – volume: 32 start-page: 108 year: 1983 ident: 10.1006/jcss.1998.1578_SS981578RF25 article-title: Spatial planning: A configuration space approach publication-title: IEEE Trans. Comput. doi: 10.1109/TC.1983.1676196 – year: 1988 ident: 10.1006/jcss.1998.1578_SS981578RF3 – ident: 10.1006/jcss.1998.1578_SS981578RF9 doi: 10.1109/ROBOT.1994.351060 – year: 1995 ident: 10.1006/jcss.1998.1578_SS981578RF17 – volume: 15 start-page: 768 year: 1984 ident: 10.1006/jcss.1998.1578_SS981578RF8 article-title: Motions of objects in contact publication-title: SIAM J. Comput. doi: 10.1137/0215055 – volume: 10 start-page: 628 year: 1991 ident: 10.1006/jcss.1998.1578_SS981578RF2 article-title: Robot motion planning: A distributed representation approach publication-title: Internat. J. Robot. Res. doi: 10.1177/027836499101000604 – ident: 10.1006/jcss.1998.1578_SS981578RF31 – ident: 10.1006/jcss.1998.1578_SS981578RF10 – ident: 10.1006/jcss.1998.1578_SS981578RF12 – year: 1994 ident: 10.1006/jcss.1998.1578_SS981578RF20 publication-title: Technical Report – volume: SMC-11 start-page: 681 year: 1981 ident: 10.1006/jcss.1998.1578_SS981578RF24 article-title: Automatic planning of manipulator transfer movements publication-title: IEEE Trans. Systems Man Cybern. doi: 10.1109/TSMC.1981.4308589 – volume: 22 start-page: 224 year: 1992 ident: 10.1006/jcss.1998.1578_SS981578RF1 article-title: Potential Fields for Robot motion planning publication-title: IEEE Trans. Systems Man Cybern. doi: 10.1109/21.148426 – year: 1991 ident: 10.1006/jcss.1998.1578_SS981578RF21 – year: 1992 ident: 10.1006/jcss.1998.1578_SS981578RF30 publication-title: Technical Report – year: 1982 ident: 10.1006/jcss.1998.1578_SS981578RF22 – volume: 32 start-page: 136 year: 1986 ident: 10.1006/jcss.1998.1578_SS981578RF13 article-title: New algorithms for multilink robot arms publication-title: J. Comput. System Sci. doi: 10.1016/0022-0000(86)90007-3 – year: 1977 ident: 10.1006/jcss.1998.1578_SS981578RF35 – year: 1997 ident: 10.1006/jcss.1998.1578_SS981578RF18 article-title: Geometry and the discovery of new ligands – ident: 10.1006/jcss.1998.1578_SS981578RF32 doi: 10.1109/SFCS.1979.10 – ident: 10.1006/jcss.1998.1578_SS981578RF11 doi: 10.1145/323233.323242 – volume: 14 start-page: 315 year: 1985 ident: 10.1006/jcss.1998.1578_SS981578RF6 article-title: On the movement of robot arms in 2-dimensional bounded regions publication-title: SIAM J. Comput. doi: 10.1137/0214025 – volume: 13 start-page: 610 year: 1984 ident: 10.1006/jcss.1998.1578_SS981578RF5 article-title: Movement problems for 2-dimensional linkages publication-title: SIAM J. Comput. doi: 10.1137/0213038 – year: 1987 ident: 10.1006/jcss.1998.1578_SS981578RF28 – ident: 10.1006/jcss.1998.1578_SS981578RF36 – volume: 3 start-page: 76 year: 1984 ident: 10.1006/jcss.1998.1578_SS981578RF7 article-title: On the complexity of motion planning for multiple independent objects: PSPACE-hardness of the “Warehouseman's Problem publication-title: Internat. J. Robot. Res. doi: 10.1177/027836498400300405 – ident: 10.1006/jcss.1998.1578_SS981578RF14 doi: 10.1109/ROBOT.1994.350966 – ident: 10.1006/jcss.1998.1578_SS981578RF16 doi: 10.1145/225058.225159 – ident: 10.1006/jcss.1998.1578_SS981578RF33 doi: 10.1109/SFCS.1985.36 – volume: 4 start-page: 298 year: 1983 ident: 10.1006/jcss.1998.1578_SS981578RF34 article-title: On the “Piano Movers” Problem. II. General techniques for computing topological properties of real algebraic manifolds publication-title: Adv. Appl. Math. doi: 10.1016/0196-8858(83)90014-3 |
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