Skip to main content
SpringerLink
Log in

Algorithmic Motion Planning: The Randomized Approach

  • Chapter
General Theory of Information Transfer and Combinatorics

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4123))

Abstract

Algorithms based on randomized sampling proved to be the only viable algorithmic tool for quickly solving motion planning problems involving many degrees of freedom. Information on the configuration space is acquired by generating samples and finding simple paths among them. Paths and samples are stored in a suitable data structure. According to this paradigm, in the recent years a wide number of algorithmic techniques have been proposed and some approaches are now widely used. This survey reviews the main algorithms, outlining their advantages and drawbacks, as well as the knowledge recently acquired in the field.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amato, N.M., Burchand Bayazit, O., Dale, L.K., Jones, H., Vallejo, D.: Obprm: an obstacle-based prm for 3d workspaces. In: Agarwal, P.K., Kavraki, L.E., Mason, M.T. (eds.) Robotics: The Algorithmic Perspective, The Third Workshop on the Algorithmic Foundations of Robotics, pp. 156–168. A.K. Peters (1998)

    Google Scholar 

  2. Amato, N.M., Bayazit, O.B., Dale, L.K., Jone, C.: Choosing good distances metrics and local planners for probabilistic roadmap methods. IEEE Transactions on Robotics and Automation 16(4), 442–447 (2000)

    Article  Google Scholar 

  3. Amato, N.M., Dale, L.K.: Probabilistic roadmaps are embarrassingly parallel. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 688–694 (1999)

    Google Scholar 

  4. Amato, N.M., Dill, K.A., Song, G.: Using motion planning to map protein folding landscapes and analyze folding kinetics of known native structures. In: Proceedings the 6th International Conference on Computational Molecular Biology (RECOMB), pp. 2–11 (2002)

    Google Scholar 

  5. Amato, N.M., Wu, Y.: A randomized roadmap method for path and manipulation planning. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 113–120 (1996)

    Google Scholar 

  6. Atramentov, A., LaValle, S.M.: Efficient nearest neighbor searching for motion planning. In: Proceedings of the IEEE Conference on Robotics and Automation, Washington, May 2002, pp. 632–637 (2002)

    Google Scholar 

  7. Barraquand, J., Kavraki, L., Latombe, J.C., Li, T., Motwani, R., Raghavan, P.: A random sampling scheme for robot path planning. International Journal of Robotics Research 15(6), 759–774 (1997)

    Google Scholar 

  8. Barraquand, J., Latombe, J.C.: Robot motion planning: a distributed representation approach. The International Journal of Robotics Research 10(6), 628–649 (1991)

    Article  Google Scholar 

  9. Burchan Bayazit, O., Lien, J.-M., Amato, N.M.: Probabilistic roadmap motion planning for deformable objects. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 2126–2133 (2002)

    Google Scholar 

  10. Burchan Bayazit, O., Song, G., Amato, N.M.: Ligand binding with obprm and user input. In: Proceedings of the IEEE International Conference on Robotics and Automation (2001)

    Google Scholar 

  11. Bohlin, R., Kavraki, L.E.: Path planning using lazy prm. In: Proceedings of the IEEE International Conference on Robotics and Automation, Seoul, May 2000, pp. 1469–1474 (2000)

    Google Scholar 

  12. Boor, V., Overmars, M.H., van der Stappen, A.F.: The gaussian sampling theory for probabilistic roadmap planners. In: Proceedings of the IEEE International Conference on Robotics and Automation, Detroit, May 1999, pp. 1018–1023 (1999)

    Google Scholar 

  13. Bruce, J., Veloso, M.: Real-time randomized path planning for robot navigation. In: Proceedings of the IEEE/RSJ Intl. Conference on Intelligent Robots and Systems, pp. 2383–2388 (2002)

    Google Scholar 

  14. Cameron, S.: Enhancing gjk: computing minimum distance and penetration between convex polyhedra. In: Proceedings of the IEEE Conference on Robotics and Automation, pp. 3112–3117 (1997)

    Google Scholar 

  15. Canny, J.: The Complexity of Robot Motion Planning. MIT Press, Cambridge (1988)

    Google Scholar 

  16. Canny, J.: Some algebraic and geometric computations in pspace. In: Proceedings of the IEEE Symposium on foundations of computer science, pp. 460–467 (1988)

    Google Scholar 

  17. Carpin, S., Pagello, E.: On parallel rrts for multi-robot systems. In: Proceedings of the 8th conference of the Italian Association for Artificial Intelligence, pp. 834–841 (2002)

    Google Scholar 

  18. Carpin, S., Pillonetto, G.: Robot motion planning using adaptive random walks. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 3809–3814 (2003)

    Google Scholar 

  19. Challou, D., Boley, D., Gini, M., Kumar, V., Olson, C.: Parallel search algorithms for robot motion planning. In: Gupta, K., del Pobil, A.P. (eds.) Practical Motion Planning, pp. 115–132. John Wiley & Sons, Chichester (1998)

    Google Scholar 

  20. Cheng, P., LaValle, S.M.: Resolution complete rapidly-exploring random trees. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 267–272 (2002)

    Google Scholar 

  21. Cheng, P., LaValle, S.M.: Reducing metric sensitivity in randomized trajectory design. In: Procceedings of the IEEE/RSJ Conference on Intelligent Robots and Systems (2001)

    Google Scholar 

  22. Cheng, P., Shen, Z., LaValle, S.M.: RRT-based trajectory design for autonomous automobiles and spacecraft. Archives of Control Sciences 11(3–4), 167–194 (2001)

    Google Scholar 

  23. Cortes, J., Simeon, T., Laumond, J.P.: A random loop generator for planning the motions of closed kinematics chains using prm methods. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 2141–2146 (2002)

    Google Scholar 

  24. Dale, L.K., Amato, N.M.: Probabilistic roadmaps - putting it all together. In: Proceedings of the IEEE International Conference on Robotics and Automation, Seoul, May 2001, pp. 1940–1947 (2001)

    Google Scholar 

  25. Donald, B., Xavier, P.: Provably good approximation algorithms for optimal kinodynamic planning for cartesian robots and open chain manipulators. Algorithmica 14(6), 480–530 (1995)

    Article  MathSciNet  Google Scholar 

  26. Donald, B., Xavier, P.: Provably good approximation algorithms for optimal kinodynamic planning: robots with decoupled dynamic bounds. Algorithmica 14(6), 443–479 (1995)

    Article  MathSciNet  Google Scholar 

  27. Donald, B., Xavier, P., Canny, J., Reif, J.: Kinodynamic motion planning. Journal of the ACM 40(5), 1048–1066 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  28. Geraerters, R., Overmars, M.H.: A comparative study of probabilistic roadmap planners. In: Boissonat, J.D., Burdick, J., Goldberg, K., Hutchinson, S. (eds.) Workshop on Algorithmic Foundations of Robotics. Advanced Robotics Series. Springer, Heidelberg (2002)

    Google Scholar 

  29. Gilbert, E.G., Johnson, D.W., Keerthi, S.S.: A fast procedure for computing the distance between complex objects in three-dimensional space. IEEE Journal of Robotics and Automation 4(2), 193–203 (1988)

    Article  Google Scholar 

  30. Glavina, B.: Solving findpath by combination of goal-directed and randomized search. In: Proceedings of the IEEE Conference on Robotics and Automation, pp. 1718–1723 (1990)

    Google Scholar 

  31. Gottschalk, S., Lin, M.C., Manocha, D.: Obb-tree: a hierarchical structure for rapid interference detection. In: Proc. of ACM Siggraph 1996 (1996)

    Google Scholar 

  32. Halperin, D., Kavraki, L., Latombe, J.C.: Robotics. In: Goodman, J.E., O’Rourke, J. (eds.) CRC Handbook of Discrete and Computational Geometry, ch. 41, pp. 755–778. CRC Press, Boca Raton (1997)

    Google Scholar 

  33. Han, L., Amato, N.: A kinematics-based probabilistic roadmap method for closed chain systems. In: Donald, B., Lynch, K., Rus, D. (eds.) Algorithmic and Computational Robotics - New Directions, pp. 233–246. A.K. Peters (2000)

    Google Scholar 

  34. Hsu, D.: Randomized single-query motion planning in expansive spaces, PhD thesis, Department of Computer Sciece, Stanford University (2000)

    Google Scholar 

  35. Hsu, D., Kavraki, L.E., Latombe, J.C., Motwani, R.: Capturing the connectivity of high-dimensional geometric spaces by parallelizable random sampling techniques. In: Pardalos, P.M., Rajasekaran, S. (eds.) Advances in Randomized Parallel Computing, pp. 159–182. Kluwer Academic Publishers, Boston (1999)

    Google Scholar 

  36. Hsu, D., Kavraki, L.E., Latombe, J.C., Motwani, R., Sorkin, S.: On finding narrow passages with probabilistic roadmap planners. In: Agarwal, P.K., Kavraki, L.E., Mason, M.T. (eds.) Robotics: The Algorithmic Perspective, The Third Workshop on the Algorithmic Foundations of Robotics, pp. 142–153. A.K. Peters (1998)

    Google Scholar 

  37. Hsu, D., Kindel, R., Latombe, J.C., Rock, S.: Randomized kinodynamic motion planning with moving obstacles. In: Donald, B., Lynch, K., Rus, D. (eds.) Algorithmic and Computational Robotics - New Directions. A.K. Peters Ltd (2000)

    Google Scholar 

  38. Hsu, D., Latombe, J.C., Motwani, R.: Path planning and expansive configuration spaces. International Journal of Computational Geometry and Applications 9, 495–512 (1999)

    Article  MathSciNet  Google Scholar 

  39. Hwang, Y.K., Ahuja, N.: Gross motion planning - a survey. ACM Computational Surveys 24(3), 219–290 (1992)

    Article  Google Scholar 

  40. Kavraki, L., Latombe, J.C.: Randomized preprocessing of configuration space for fast path planning. In: Proceedings of the IEEE Conference on Robotics and Automation, pp. 2138–2145 (1994)

    Google Scholar 

  41. Kavraki, L.E., Kolountzakis, M.N., Latombe, J.C.: Analysis of probabilistic roadmaps for path planning. IEEE Transactions on Robotics and Automation 14(1), 166–171 (1998)

    Article  Google Scholar 

  42. Kavraki, L.E., Latombe, J.C., Motwani, R., Raghavan, P.: Randomized query processing in robot path planning. Journal of Computer and Systems Science 57(1), 50–60 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  43. Kavraki, L.E., Švestka, P., Latombe, J.C., Overmars, M.H.: Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Transactions on Robotics and Automation 12(4), 566–580 (1996)

    Article  Google Scholar 

  44. Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. International Journal of Robotic Research 5(1), 90–98 (1986)

    Article  MathSciNet  Google Scholar 

  45. Kindel, R., Hsu, D., Latombe, J.C., Rock, S.: Kinodynamic motion planning admnist moving obstacles. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 537–543 (2000)

    Google Scholar 

  46. Kufner, J., Nishiwaki, K., Kagami, S., Inaba, M., Inoue, H.: Motion planning for humanoid robots under obstacle and dynamic balance constraints. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 692–698 (2001)

    Google Scholar 

  47. Kufner, J.J., LaValle, S.M.: Rrt-connect: an efficient approach to single-query path planning. In: Proceedings of the IEEE Conference on Robotics and Automation, San Francisco, April 2001, pp. 995–1001 (2001)

    Google Scholar 

  48. Ladd, A., Kavraki, L.E.: Generalizing the analysis of prm. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 2120–2125 (2002)

    Google Scholar 

  49. Lamiraux, F., Kavraki, L.E.: Planning paths for elastic objects under manipulation constraints. International Journal of Robotics Research 20(3), 188–208 (2001)

    Article  Google Scholar 

  50. Larsen, E., Gottschalk, S., Lin, M.C., Manocha, D.: Fast distance queries with rectangular swept sphere volumes. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 3719–3726 (2000)

    Google Scholar 

  51. Latombe, J.C.: Robot Motion Planning. Kluwer Academic Publishers, Dordrecht (1990)

    Google Scholar 

  52. Latombe, J.C.: Motion planning: a journey of robots, molecules, digital actors, and other artifacts. The International Journal of Robotics Research - Special Issue on Robotics at the Millennium 18(11), 1119–1128 (1999)

    Google Scholar 

  53. LaValle, S.M.: From dynamic programming to RRTs: algorithmic design of feasible trajectories. In: Bicchi, A., Christensen, H.I., Prattichizzo, D. (eds.) Control Problems in Robotics, pp. 19–37. Springer, Berlin (2002)

    Google Scholar 

  54. LaValle, S.M.: Msl - the motion strategy library software, version 2.0, http://msl.cs.uiuc.edu

  55. LaValle, S.M.: Rapidly-exploring random trees, Technical Report TR 98-11, Computer Science Department Iowa State University (October 1998)

    Google Scholar 

  56. LaValle, S.M., Kuffner, J.J.: Randomized kinodynamic planning. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 473–479 (1999)

    Google Scholar 

  57. LaValle, S.M., Kufner, J.J.: Randomized kinodynamic planning. International Journal of Robotics Research 20(5), 378–400 (2001)

    Article  Google Scholar 

  58. LaValle, S.M., Kufner, J.J.: Rapidly-exploring random trees: progress and prospects. In: Donald, B., Lynch, K., Rus, D. (eds.) Algorithmic and Computational Robotics, New Directions, pp. 45–59. A.K. Peters (2001)

    Google Scholar 

  59. Lien, J.-M., Thomas, S.L., Amato, N.M.: A general framework for sampling on the medial axis of the free space. In: Proceedings of the IEEE International Conference on Robotics and Automation (2003)

    Google Scholar 

  60. Lin, M.C., Canny, J.F.: A fast algorithm for incremental distance calculation. In: Proceedings of the IEEE Conference on Robotics and Automation, pp. 1008–1014 (1991)

    Google Scholar 

  61. Lozano-Pérez, T.: Spatial planning: a configuration space approach. IEEE Transactions on Computers C-32(2), 108–120 (1983)

    Article  Google Scholar 

  62. Mazer, E., Ahuactzin, J.M., Bessiére, P.: The ariadne’s clew algorithm. Journal of Artificial Intelligence Research 9, 295–316 (1998)

    MATH  Google Scholar 

  63. Mirtich, B.: V-clip: fast and robust polyhedral collision detection. ACM Transaction on Graphics 17(3), 177–203 (1998)

    Article  Google Scholar 

  64. Nielsen, C., Kavraki, L.E.: A two-level fuzzy prm for manipulation planning. In: Proceedings of The IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1716–1722 (2000)

    Google Scholar 

  65. Overmars, M., Švestka, P.: A probabilistic learning approach to motion planning. In: Goldberg, K., Halperin, D., Latombe, J.C., Wilson, R. (eds.) Algorithmics Foundations of Robotics. A.K. Peters Ltd. (1995)

    Google Scholar 

  66. Reif, J.H.: Complexity of the mover’s problem and generalization. In: Proceedings of the 20th IEEE Symposium on Foundations of Computer Science, pp. 421–427 (1979)

    Google Scholar 

  67. Russel, S., Norwig, P.: Artificial Intelligence - A modern approach. Prentice Hall International, Englewood Cliffs (1995)

    Google Scholar 

  68. Sánchez, G., Latombe, J.C.: A single-query bi-directional probabilistic roadmap planner with lazy collision checking. International Journal of Robotics Reserach 21(1), 5–26 (2002)

    Article  Google Scholar 

  69. Sánchez-Ante, G.: Path planning using a single-query bi-directional lazy collision checking planner. In: Coello Coello, C.A., de Albornoz, Á., Sucar, L.E., Battistutti, O.C. (eds.) MICAI 2002. LNCS (LNAI), vol. 2313, pp. 41–50. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  70. Schwartz, J.T., Sharir, M.: Algorithmic motion planning in robotics. In: Handbook of Theoretical Computer Science, ch. 8, vol. 1, pp. 392–430. Elsevier, Amsterdam (1990)

    Google Scholar 

  71. Schwartz, J.T., Sharir, M., Hopcroft, J. (eds.): Planning, Geometry, and Complexity of Robot Motion. Ablex Publishing, Greenwich (1987)

    Google Scholar 

  72. Schwarzer, F., Saha, M., Latombe, J.C.: Exact collision checking of robot paths. In: Boissonat, J.D., Burdick, J., Goldberg, K., Hutchinson, S. (eds.) Workshop on Algorithmic Foundations of Robotics. Advanced Robotics Series. Springer, Heidelberg (2002)

    Google Scholar 

  73. Sharir, M.: Algorithmic motion planning. IEEE Computer 22(3), 9–20 (1989)

    Google Scholar 

  74. Siméon, T., Leroy, S., Laumond, J.P.: Path coordination for multiple mobile robots: a resolution-complete algorithm. IEEE Transactions on Robotics and Automation 18(1), 42–49 (2002)

    Article  Google Scholar 

  75. Singh, A.P., Latombe, J.C., Brutlag, D.L.: A motion planning approach to flexible ligand binding. In: Proceedings of the Int. Conf. on Intelligent Systems for Molecular Biology, pp. 252–261 (1999)

    Google Scholar 

  76. Song, G., Amato, N.M.: A motion planning approach to folding: from paper craft to protein folding. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 948–953 (2001)

    Google Scholar 

  77. Song, G., Amato, N.M.: Using motion planning to study protein folding. In: Proceedings the 5th International Conference on Computational Molecular Biology (RECOMB), pp. 287–296 (2001)

    Google Scholar 

  78. Song, G., Amato, N.M.: A motion-planning approach to folding: from paper craft to protein folding. IEEE Transactions on Robotics and Automation 20(1), 60–71 (2004)

    Article  Google Scholar 

  79. Song, G., Miller, S., Amato, N.M.: Customizing prm roadmaps at query time. In: Proceedings of the IEEE International Conference on Robotics and Automation, Seoul, May 2001, pp. 1500–1505 (2001)

    Google Scholar 

  80. Song, G., Thomas, S., Amato, N.M.: A general framework for prm motion planning. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 4445–4450 (2003)

    Google Scholar 

  81. Švestka, P., Overmars, M.H.: Coordinated path planning for multiple robots. Robotics and Autonomous Systems 23(3), 125–152 (1998)

    Article  Google Scholar 

  82. Wilmarth, S.A., Amato, N.M., Stiller, P.F.: Motion planning for a rigid body using random networks on the medial axis of the free space. In: Proceedings of the 15th Annual ACM Symposium on Computational Geometry, pp. 173–180 (1999)

    Google Scholar 

  83. Wilmarth, S.A., Amato, N.M., Stiller, P.F.: A probabilistic roadmap planner with sampling on the medial axis of the free space. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1024–1031 (1999)

    Google Scholar 

  84. Yakey, J.H., LaValle, S.M., Kavraki, L.E.: Randomized path planning for linkages with closed kinematic chains. IEEE Transactions on Robotics and Automation 17(6), 951–958 (2001)

    Article  Google Scholar 

Download references

Authors
  1. S. Carpin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, 100131, 33501, Bielefeld, Germany

    Rudolf Ahlswede

  2. Fakultät für Mathematik, Universität Bielefeld, Universitätsstr. 25, 33615, Bielefeld, Germany

    Lars Bäumer , Ning Cai , Harout Aydinian  & Christian Deppe , ,  & 

  3. Russian Academy of Sciences Institute of Problems of Information Transmission, Bol’shoi Karetnyi per. 19, 101447, Moscow, Russia

    Vladimir Blinovsky

  4. Universität Bielefeld, Fakultät für Mathematik, Universitätsstr. 25, 33615, Bielefeld, Germany

    Haik Mashurian

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Carpin, S. (2006). Algorithmic Motion Planning: The Randomized Approach. In: Ahlswede, R., et al. General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol 4123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889342_48

Download citation

  • DOI: https://doi.org/10.1007/11889342_48

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46244-6

  • Online ISBN: 978-3-540-46245-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation