Autonomous Robots

, Volume 19, Issue 3, pp 285–300 | Cite as

A Sampling-Based Motion Planning Approach to Maintain Visibility of Unpredictable Targets

  • Rafael Murrieta-Cid
  • BenjamÍn Tovar
  • Seth Hutchinson
Article

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.

Keywords

pursuit-evasion motion planning visibility 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Başar, T. and Olsder, G. 1982. Dynamic Noncooperative Game Theory, Academic Press.Google Scholar
  2. 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.Google Scholar
  3. 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.Google Scholar
  4. Barraquand, J. and Latombe, J.C. 1991. Robot motion planning: A distributed representation approach. Int. Journal on Robotics Research, 10(6):628–649.Google Scholar
  5. Becker, C., Gonz·lez-Baños, H., Latombe, J.-L., and Tomasi, C. 1995. An intelligent observer. In Int. Symposium on Experimental Robotics.Google Scholar
  6. Becker, C., Salas, J., Tokusei, K., and Latombe, J.C. 1995. Reliable navigation using landmarks. In IEEE Int. Conf. on Robotics and Automation.Google Scholar
  7. Bullen, P.S. 2003. The Power Means, Chapter 3, in Handbook of Means and Their Inequalities. In Kluwer.Google Scholar
  8. Canny, J.F. 1988. The Complexity of the Robot Motion Planning, MIT Press: Cambridge, MA.Google Scholar
  9. 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.Google Scholar
  10. Fabiani, P. and Latombe, J.C. 1999. Tracking a partially predictable object with uncertainty and visibility constraints: a game-theoretic approach. IJCAI.Google Scholar
  11. 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.Google Scholar
  12. 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.Google Scholar
  13. Isaccs, R. 1975. Differential Games, Wiley: New York, NY.Google Scholar
  14. Hájek, O. 1965. Pursuit Games, Academic Press: New York.Google Scholar
  15. 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.Google Scholar
  16. Hespanha, J., Prandini, M., and Sastry, S. 2000. Probabilistic Pursuit-Evasion Games: A one-step Nash approach. In Proc. Conference on Decision and Control.Google Scholar
  17. 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.Google Scholar
  18. 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.Google Scholar
  19. Hutchinson, S. 1991. Exploiting visual constraints in robot motion planning. In IEEE Int. Conf. on Robotics and Automation.Google Scholar
  20. Hutchinson, S., Hager, G., and Coke, P. 1996. A tutorial on visual servo control. IEEE Transactions on Robotics and Automation, 12(5).Google Scholar
  21. 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.Google Scholar
  22. Jiansho, S. and Tomasi, C. 1994. Good features to track. In Conf. on Computer Vision and Pattern Recognition.Google Scholar
  23. Jung, B. and Sukhatme, G. 2002. Tracking targets using multiple robots: The effect of environment occlusion. Journal Autonomous Robots, 12:191–205.Google Scholar
  24. 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.CrossRefGoogle Scholar
  25. 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.Google Scholar
  26. 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.Google Scholar
  27. Kanatani, K. 1993. Geometric Computation for Machine Vision, Oxford Science Publications.Google Scholar
  28. Latombe, J.-C. 1991. Robot Motion Planning, Kluwer Academic Publishers.Google Scholar
  29. 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.Google Scholar
  30. 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.Google Scholar
  31. 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.Google Scholar
  32. Lazanas, A. and Latombe, J.C. 1995. Landmark-based robot navigation. Algorithmica, 13:472–501.CrossRefMathSciNetGoogle Scholar
  33. Leven, P. and Hutchinson, S. 2003. A Framework for real-time path planning in changing environments. Int. Journal of Robotics Research, 21(12).Google Scholar
  34. 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.Google Scholar
  35. 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.Google Scholar
  36. 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.Google Scholar
  37. 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.Google Scholar
  38. 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.Google Scholar
  39. O'Rourke, J. 1997. Visibility. In J.E. Goodman and J. O'Rourke (eds.) Handbook of Discrete and Computational Geometry, pp. 467–479,.Google Scholar
  40. Parker L. 2002. Algorithms for Multi-Robot Observation of Multiple Targets. Journal Autonomous Robots, 12:231–255.MATHGoogle Scholar
  41. 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.Google Scholar
  42. 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.Google Scholar
  43. 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.Google Scholar
  44. Spletzer, J.R. and Taylor, C.J. 2003. Dynamic Sensor Planning and Control for Optimally Tracking Targets. Int. Journal of Robotics Research, 22(1).Google Scholar
  45. Suzuki, I. and Yamashita, M. 1992. Searching for a mobile intruder in a polygonal region. SIAM J. Comput, 21(5):863–888.CrossRefMathSciNetGoogle Scholar
  46. 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.Google Scholar
  47. 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.CrossRefGoogle Scholar
  48. Welzl, E. 1985. Constructing the visibility graph for n-line segments in O(n2) time. In Proceedings of Information Processing Letters, pp. 167–171.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Rafael Murrieta-Cid
    • 1
  • BenjamÍn Tovar
    • 2
  • Seth Hutchinson
    • 3
  1. 1.Mechatronics Research Center, EGIC, Tec de MonterreyEdo de MéxicoMéxico
  2. 2.Department of Computer Science, Siebel CenterUniversity of IllinoisUrbanaUSA
  3. 3.Department of Electrical and Computer Engineering, The Beckman InstituteUniversity of IllinoisUrbanaUSA

Personalised recommendations