Abstract
This paper deals with the surveillance problem of computing the motions of one or more robot observers in order to maintain visibility of one or several moving targets. The targets are assumed to move unpredictably, and the distribution of obstacles in the workspace is assumed to be known in advance. Our algorithm computes a motion strategy by maximizing the shortest distance to escape—the shortest distance the target must move to escape an observer's visibility region. Since this optimization problem is intractable, we use randomized methods to generate candidate surveillance paths for the observers. We have implemented our algorithms, and we provide experimental results using real mobile robots for the single target case, and simulation results for the case of two targets-two observers.
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References
Başar, T. and Olsder, G. 1982. Dynamic Noncooperative Game Theory, Academic Press.
Balkcom, D.J. and Mason, M.T. 2000. Geometric construction of time optimal trajectories for differential drive robots. Fourth Workshop on Algorithmic Foundations of Robotics, pp 1–13.
Barraquand, J., Langlois, L., and Latombe, J.C. 1989. Robot motion planning with many degrees of freedom and dynamic constraints. In Proc Fifth Int. Symposium on Robotics Research.
Barraquand, J. and Latombe, J.C. 1991. Robot motion planning: A distributed representation approach. Int. Journal on Robotics Research, 10(6):628–649.
Becker, C., Gonz·lez-Baños, H., Latombe, J.-L., and Tomasi, C. 1995. An intelligent observer. In Int. Symposium on Experimental Robotics.
Becker, C., Salas, J., Tokusei, K., and Latombe, J.C. 1995. Reliable navigation using landmarks. In IEEE Int. Conf. on Robotics and Automation.
Bullen, P.S. 2003. The Power Means, Chapter 3, in Handbook of Means and Their Inequalities. In Kluwer.
Canny, J.F. 1988. The Complexity of the Robot Motion Planning, MIT Press: Cambridge, MA.
Espiau, B., Chaumette, F., and Rives, P. 1992. A new approach to visual servoing in robotics. IEEE Trans. Robot and Autom., 8(3):313–326.
Fabiani, P. and Latombe, J.C. 1999. Tracking a partially predictable object with uncertainty and visibility constraints: a game-theoretic approach. IJCAI.
Geraerts, R. and Overmars, M.H. 2002. A comparative study of probabilistic roadmap planners. In Proceedings of Workshop on Algorithmic Foundations of Robotics, pp. 43–57.
Guibas, L., Latombe, J.-C., LaValle, S.M., Lin, D., and Motwani, R. 1997. Visibility-based pursuit-evasion in a polygonal environment. In Proc 5th Workshop on Algorithms and Data Structures.
Isaccs, R. 1975. Differential Games, Wiley: New York, NY.
Hájek, O. 1965. Pursuit Games, Academic Press: New York.
Han, Li and Amato, Nancy M. 2000. A kinematics-based probabilistic roadmap method for closed chain systems. In Proceedings of Workshop on Algorithmic Foundations of Robotics.
Hespanha, J., Prandini, M., and Sastry, S. 2000. Probabilistic Pursuit-Evasion Games: A one-step Nash approach. In Proc. Conference on Decision and Control.
Hsu, D., Kindel, R., Latombe, J.C., and Rock, S. 2000. Randomized Kinodynamic Motion Planning with Moving Obstacles. In Workshop on Algorithm Foundations of Robotics.
Huttenlocher, D.P., Rucklidge, W.J., and Noh, J.J. 1993. Tracking non-rigid objects in complex scenes. In Fourth Int. Conf. on Computer Vision.
Hutchinson, S. 1991. Exploiting visual constraints in robot motion planning. In IEEE Int. Conf. on Robotics and Automation.
Hutchinson, S., Hager, G., and Coke, P. 1996. A tutorial on visual servo control. IEEE Transactions on Robotics and Automation, 12(5).
González-Baños, H.H., Lee, C.-Y., and Latombe, J.-C. 2002. Real-Time Combinatorial Tracking of a Target Moving Unpredictably Among Obstacles. In Proc IEEE Int. Conf. on Robotics and Automation.
Jiansho, S. and Tomasi, C. 1994. Good features to track. In Conf. on Computer Vision and Pattern Recognition.
Jung, B. and Sukhatme, G. 2002. Tracking targets using multiple robots: The effect of environment occlusion. Journal Autonomous Robots, 12:191–205.
Kavraki, L., Svestka, E., Latombe, J.C., and Overmars, M.H. 1996. Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Trans. on Robotics and Automation, 12(4):556–580.
Kim, D., Guibas, L., Yong, S., and Shin, S. 1998. Fast Collision Detection Among Multiple Moving Spheres. IEEE Trans. Visualization and Computer Graphics, 4(3):230–242.
Kriegmen, D.J., Triendl, E., and Binford, T.O. 1991. Stereo vision and navigation in buildings for mobile robots. IEEE Trans. on Robotics and Automation, 5(6):1722–1727.
Kanatani, K. 1993. Geometric Computation for Machine Vision, Oxford Science Publications.
Latombe, J.-C. 1991. Robot Motion Planning, Kluwer Academic Publishers.
Lavalle, S., González-Banos, H.H., Becker, C., and Latombe, J.C. 1997. Motion strategies for maintaining visibility of a moving target. In IEEE Int. Conf. on Robotics and Automation, vol. 1, pp. 731–736.
LaValle, S.M., and Hinrichsen, J. 1999. Visibility-based pursuit-evasion: An extension to curved environments. In Proc IEEE Int. Conf. on Robotics and Automation.
Lavalle, S., Branicky, M.S., and Lindemann, S.R. 2003. On the relationship between classical grid search and probabilistic roadmaps. In Int. Journal of Robotics Research.
Lazanas, A. and Latombe, J.C. 1995. Landmark-based robot navigation. Algorithmica, 13:472–501.
Leven, P. and Hutchinson, S. 2003. A Framework for real-time path planning in changing environments. Int. Journal of Robotics Research, 21(12).
Murrieta-Cid, R., Briot, M., and Vandapel, N. 1998. Landmark identification and tracking in natural environment. In IEEE/RSJ Int. Conf. on Intelligent Robots and Systems.
Murrieta-Cid, R., Parra, C., and Devy, M. 2002. Visual Navigation in Natural Environments: From Range and Color Data to a Landmark-based Model. Journal Autonomous Robots, 13(2):143–168.
Murrieta-Cid, R., González-Baños, H.H., and Tovar, B. 2002. A Reactive Motion Planner to Maintain Visibility of Unpredictable Targets. In Proc IEEE Int. Conf. on Robotics and Automation.
Murrieta-Cid, R., Sarmiento, A., and Hutchinson, S. 2003. On the Existence of a Strategy to Maintain a Moving Target within the Sensing Range of an Observer Reacting with Delay. In IEEEs/RSJ Int. Conf. on Intelligent Robots and Systems.
Murrieta-Cid, R., Sarmiento, A., Bhattacharya, S., and Hutchinson, S. 2004. Maintaining Visibility of a Moving Target at a Fixed Distance: The Case of Observer Bounded Speed. In IEEE Int. Conf. on Robotics and Automation.
O'Rourke, J. 1997. Visibility. In J.E. Goodman and J. O'Rourke (eds.) Handbook of Discrete and Computational Geometry, pp. 467–479,.
Parker L. 2002. Algorithms for Multi-Robot Observation of Multiple Targets. Journal Autonomous Robots, 12:231–255.
Papanikolopous, N.P., Khosla, P.K., and Kanade, T. 1993. Visual tracking of a moving target by a camera mounted on a robot: A combination of control and vision. IEEE Trans. Robotics and Automation, 9(1):14–35.
Parsons, T.D. 1976. Pursuit-evasion in a graph. In Y. Alani and D.R. Lick (eds.), Theory and Application of Graphs, Springer-Verlag: Berlin, pp. 426–441.
Shas, S., Rajko, S., and LaValle, S.M. 2003. Visibility-based pursuit-evasion in an unknown planar environment. Submited to Int. Journal on Robotics Research.
Spletzer, J.R. and Taylor, C.J. 2003. Dynamic Sensor Planning and Control for Optimally Tracking Targets. Int. Journal of Robotics Research, 22(1).
Suzuki, I. and Yamashita, M. 1992. Searching for a mobile intruder in a polygonal region. SIAM J. Comput, 21(5):863–888.
Tovar, B., Murrieta-Cid, R., and Esteves, C. 2002. Robot Motion Planning for Map Building. In IEEE/RSJ Int. Conf. on Intelligent Robots and Systems.
Vidal, R., Shakernia, O., Jin, H., Hyunchul, D., and Sastry, S. 2002. Probabilistic Pursuit-Evasion Games: Theory, Implementation, and Experimental Evaluation. IEEE Trans. Robotics and Automation, 18(5):662–669.
Welzl, E. 1985. Constructing the visibility graph for n-line segments in O(n2) time. In Proceedings of Information Processing Letters, pp. 167–171.
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Rafael Murrieta-Cid received the B.S degree in Physics Engineering (1990), and the M.Sc. degree in Automatic Manufacturing Systems (1993), both from “Instituto Tecnológico y de Estudios Superiores de Monterrey” (ITESM) Campus Monterrey. He received his Ph.D. from the “Institut National Polytechnique” (INP) of Toulouse, France (1998). His Ph.D research was done in the Robotics and Artificial Intelligence group of the LAAS/CNRS. In 1998–1999, he was a postdoctoral researcher in the Computer Science Department at Stanford University. From January 2000 to July 2002 he was an assistant professor in the Electrical Engineering Department at ITESM Campus México City, México. In 2002–2004, he was working as a postdoctoral research associate in the Beckman Institute and Department of Electrical and Computer Engineering of the University of Illinois at Urbana-Champaign. Since August 2004, he is director of the Mechatronics Research Center in the ITESM Campus Estado de México, México. He is mainly interested in sensor-based robotics motion planning and computer vision.
Benjamin Tovar received the B.S degree in electrical engineering from ITESM at Mexico City, Mexico, in 2000, and the M.S. in electrical engineering from University of Illinois, Urbana-Champaign, USA, in 2004. Currently (2005) he is pursuing the Ph.D degree in Computer Science at the University of Illinois. Prior to M.S. studies he worked as a research assistant at Mobile Robotics Laboratory at ITESM Mexico City. He is mainly interested in motion planning, visibility-based tasks, and minimal sensing for robotics.
Seth Hutchinson received his Ph. D. from Purdue University in West Lafayette, Indiana in 1988. He spent 1989 as a Visiting Assistant Professor of Electrical Engineering at Purdue University. In 1990 Dr. Hutchinson joined the faculty at the University of Illinois in Urbana-Champaign, where he is currently a Professor in the Department of Electrical and Computer Engineering, the Coordinated Science Laboratory, and the Beckman Institute for Advanced Science and Technology. Dr. Hutchinson is currently a senior editor of the IEEE Transactions on Robotics and Automation. In 1996 he was a guest editor for a special section of the Transactions devoted to the topic of visual servo control, and in 1994 he was co-chair of an IEEE Workshop on Visual Servoing. In 1996 and 1998 he co-authored papers that were finalists for the King-Sun Fu Memorial Best Transactions Paper Award. He was co-chair of IEEE Robotics and Automation Society Technical Committee on Computer and Robot Vision from 1992 to 1996, and has served on the program committees for more than thirty conferences related to robotics and computer vision. He has published more than 100 papers on the topics of robotics and computer vision.
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Murrieta-Cid, R., Tovar, B. & Hutchinson, S. A Sampling-Based Motion Planning Approach to Maintain Visibility of Unpredictable Targets. Auton Robot 19, 285–300 (2005). https://doi.org/10.1007/s10514-005-4052-0
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DOI: https://doi.org/10.1007/s10514-005-4052-0