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Homotopic Roadmap Generation for Robot Motion Planning

  • Rahul KalaEmail author
Article

Abstract

Two robot paths are said to be in the same homotopic group if one can be obtained from the other by multiple small deformations. Knowledge of robot homotopic groups gives information regarding the obstacle structure and enables timely computation of optimal path. Making a roadmap which misses out on a single homotopic group in such approaches may lead to sub-optimal decisions. E.g. one may prefer to go through a very narrow corridor if that reduces the path length significantly, but not if the resulting path has too many such narrow segments. Similarly knowledge of homotopic groups may enable distribution and scheduling of robots across homotopic groups for decentralized planning of multiple robots. For an unstructured robot environment, sampling based approaches give an insight into homotopic groups. The aim of the work is to make a homotopy conscious Probabilistic Roadmap such that the roadmap is capable of generating paths corresponding to as many homotopic groups as possible. Experimental results confirm that the proposed approach gives the best results as compared to the other sampling techniques subject to the test scenarios run.

Keywords

Sampling Robot motion planning Homotopy identification Probabilistic roadmap Multi-robotics 

Mathematics Subject Classification (2010)

68T40 Robotics 

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References

  1. 1.
    Kala, R.: Rapidly-exploring Random Graphs: Motion Planning of Multiple Mobile Robots. Adv. Rob 27(14), 1113–1122 (2013)CrossRefGoogle Scholar
  2. 2.
    Kala, R.: Coordination in Navigation of Multiple Mobile Robots. Cybern. Syst 45(1), 1–24 (2014)CrossRefzbMATHGoogle Scholar
  3. 3.
    Kala, R., Warwick, K.: Multi-Level Planning for Semi-Autonomous Vehicles in Traffic Scenarios based on Separation Maximization. J. Intell. Rob. Syst 72(3-4), 559–590 (2013)CrossRefGoogle Scholar
  4. 4.
    Kala, R., Warwick, K.: Planning Autonomous Vehicles in the Absence of Speed Lanes using an Elastic Strip. IEEE Trans. Intell. Transp. Syst 14(4), 1743–1752 (2013)CrossRefGoogle Scholar
  5. 5.
    Kavraki, L.E., Svestka, P., Latombe, J.-C., Overmars, M.H.: Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Trans. Rob. Automat 12(4), 566–580 (1996)CrossRefGoogle Scholar
  6. 6.
    Bohlin, R., Kavraki, L.E.: Path planning using lazy prm. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 521–528. IEEE (2000)Google Scholar
  7. 7.
    Nieuwenhuisen, D., Overmars, M.H.: Useful cycles in probabilistic roadmap graphs. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 446–452. IEEE (2004)Google Scholar
  8. 8.
    Marble, J.D., Bekris, K.E.: Computing spanners of asymptotically optimal probabilistic roadmaps. In: Proceedings of the 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 4292–4298. IEEE (2011)Google Scholar
  9. 9.
    Marble, J.D., Bekris, K.E.: Asymptotically Near-Optimal Planning With Probabilistic Roadmap Spanners. IEEE Trans. Rob 29(2), 432–444 (2013)CrossRefGoogle Scholar
  10. 10.
    Gayle, R., Sud, A., Andersen, E., Guy, S.J., Lin, M.C., Manocha, D.: Interactive Navigation of Heterogeneous Agents Using Adaptive Roadmaps. IEEE Trans. Visual. Comput. Graph 15(1), 34–48 (2009)CrossRefGoogle Scholar
  11. 11.
    Gayle, R., Sud, A., Lin, M.C., Manocha, D.: Reactive Deformation Roadmaps: Motion Planning of Multiple Robots in Dynamic Environments. In: Proceedings of the 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3777–3783. IEEE, San Diego (2007)Google Scholar
  12. 12.
    Hilgert, J., Hirsch, K., Bertram, T., Hiller, M.: Emergency path planning for autonomous vehicles using elastic band theory. In: Proceedings of the 2003 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, vol. 2, pp. 1390–1395. IEEE (2003)Google Scholar
  13. 13.
    Quinlan, S., Khatib, O.: Elastic bands: connecting path planning and control. In: Proceedings of the 1993 IEEE International Conference on Robotics and Automation, pp. 802–807. IEEE (1993)Google Scholar
  14. 14.
    LaValle, S.M., Kuffner, J.J.: Randomized kinodynamic planning. Int. J. Robot. Res. 20(5), 378–400 (2001)CrossRefGoogle Scholar
  15. 15.
    Kuffner, J.J., LaValle, S.M.: RRT-connect: An efficient approach to single-query path planning. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 995–1001. IEEE (2000)Google Scholar
  16. 16.
    Lie, T.Y., Shie, Y.C.: An incremental approach to motion planning with roadmap management. In: Proceedings of the IEEE International Conference on Robotics and Automation, vol. 4, pp. 3411–3416. IEEE (2002)Google Scholar
  17. 17.
    Morales, M., Rodriguez, S., Amato, N.: Improving the connectivity of PRM roadmaps. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 4427–4432. IEEE (2003)Google Scholar
  18. 18.
    Plaku, E., Bekris, K.E., Chen, B.Y., Ladd, A.M., Kavraki, E.E.: Sampling-Based Roadmap of Trees for Parallel Motion Planning. IEEE Trans. Rob 21(4), 597–608 (2005)CrossRefGoogle Scholar
  19. 19.
    Raveh, B., Enosh, A., Halperin, D.: A little more, a lot better: improving path quality by a path-merging algorithm. IEEE Trans. Rob 27, 365–371 (2011)CrossRefGoogle Scholar
  20. 20.
    Amato, N.M., Bayazit, O.B., Dale, L.K., Jones, C., Vallejo, D.: Obprm: An obstacle-based prm for 3d workspaces. In: Agarwal, P., Kavraki, L.E., Mason, M. (eds.) Robotics: The Algorithmic Perspective, pp. 155–168. A.K. Peters (1998)Google Scholar
  21. 21.
    Yeh, H.Y., Thomas, S., Eppstein, D., Amato, N.M.: UOBPRM: A uniformly distributed obstacle-based PRM. In: Proceedings of the 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2655–2662. IEEE (2012)Google Scholar
  22. 22.
    Hsu, D., Jiang, T., Reif, J., Sun, Z.: The bridge test for sampling narrow passages with probabilistic roadmap planners. In: Proceedings of the 2003 IEEE International Conference on Robotics and Automation, vol. 3, pp. 4420–4426. IEEE (2003)Google Scholar
  23. 23.
    Boor, V., Overmars, M.H., van der Stappen, A.F.: The Gaussian sampling strategy for probabilistic roadmap planners. In: Proceedings of the 1999 IEEE International Conference on Robotics and Automation, vol. 2, pp. 1018–1023. IEEE (1999)Google Scholar
  24. 24.
    Sun, Z., Hsu, D., Jiang, T., Kurniawati, H., Reif, J.H.: Narrow passage sampling for probabilistic roadmap planning. IEEE Trans. Rob 21(6), 1105–1115 (2005)CrossRefGoogle Scholar
  25. 25.
    Denny, J., Amato, N.M.: Toggle PRM: A Coordinated Mapping of C-free and C-obstacle in Arbitrary Dimension. In: Proceedings of the International Workshop on Algorithmic Foundations of Robotics, pp. 297–312. Springer, Boston (2012)Google Scholar
  26. 26.
    Wilmarth, S.A., Amato, N.M., Stiller, P.F.: MAPRM: 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. Detroit (1999)Google Scholar
  27. 27.
    Holleman, C., Kavraki, L.E.: A framework for using the workspace medial axis in prm planners. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1408–1413. IEEE (2000)Google Scholar
  28. 28.
    Schmitzberger, E., Bouchet, J.L., Dufaut, M., Wolf, D., Husson, R.: Capture of homotopy classes with probabilistic road map. In: Proceedings of the 2002. IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 3, pp. 2317–2322. IEEE (2002)Google Scholar
  29. 29.
    Bhattacharya, S., Likhachev, M., Kumar, V.: Topological constraints in search-based robot path planning. Auton Rob 33(3), 273–290 (2012)CrossRefGoogle Scholar
  30. 30.
    Demyen, D., Buro, M.: Effιcient triangulation-based pathfιnding. In: 21st National conference on Artifιcial Intelligence, pp. 942–947. IEEE (2006)Google Scholar
  31. 31.
    Grigoriev, D., Slissenko, A.: Polytime algorithm for the shortest path in a homotopy class amidst semi-algebraic obstacles in the plane. In: Proceedings of the 1998 international symposium on Symbolic and algebraic computation, pp. 17–24. IEEE (1998)Google Scholar
  32. 32.
    Hsu, D., Sanchez-Ante, G., Sun, Z.: Hybrid PRM Sampling with a Cost-Sensitive Adaptive Strategy. In: Proceedings of the 2005 IEEE International Conference on Robotics and Automation, pp. 3874–3880. IEEE (2005)Google Scholar
  33. 33.
    Shi, K., Denny, J., Amato, N.M.: Spark PRM: Using RRTs within PRMs to efficiently explore narrow passages. In: Proceedings of the 2014 IEEE International Conference on Robotics and Automation, pp. 4659–4666. IEEE (2014)Google Scholar
  34. 34.
    Siméon, T., Laumond, J.P., Nissoux, C.: Visibility-based probabilistic roadmaps for motion planning. Adv. Rob 14(6), 477–493 (2000)CrossRefGoogle Scholar
  35. 35.
    Jaillet, L., Cortes, J., Simeon, T.: Transition-based RRT for path planning in continuous cost spaces. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2145–2150. IEEE, France (2008)Google Scholar
  36. 36.
    Dobson, A., Bekris, K.E.: Sparse roadmap spanners for asymptotically near-optimal motion planning. Int. J. Rob. Res 33, 18–47 (2014)CrossRefGoogle Scholar
  37. 37.
    Littlefield, Z., Li, Y., Bekris, K.E.: Efficient sampling-based motion planning with asymptotic near-optimality guarantees for systems with dynamics. In: Proceedings of the 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1779–1785. IEEE (2013)Google Scholar
  38. 38.
    Dobson, A., Krontiris, A., Bekris, K.E.: Sparse Roadmap Spanners. In: Algorithmic Foundations of Robotics X, Springer Tracts in Advanced Robotics, vol. 86, pp. 279–296. Springer (2013)Google Scholar
  39. 39.
    Ferguson, D., Stentz, A.: Anytime RRTs. In: Proceedings of the IEEE International Conference on Intelligent Robots and Systems, pp. 5369–5375. IEEE, Beijing (2006)Google Scholar
  40. 40.
    Kalisiak, M., van de Panne, M.: RRT-blossom: RRT with a local flood-fill behavior, pp. 1237–1242. IEEE, Orlando (2006)Google Scholar
  41. 41.
    Strandberg, M.: Augmenting RRT-planners with local trees. In: Proceedings of the 2004 IEEE International Conference on Robotics and Automation, vol. 4, pp. 3258–3262. IEEE (2004)Google Scholar
  42. 42.
    Urmson, C., Simmons, R.: Approaches for heuristically biasing RRT growth. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 2, pp. 1178–1183. IEEE, Las Vegas (2003)Google Scholar
  43. 43.
    Kala, R., Shukla, A., Tiwari, R.: Robotic Path Planning using Evolutionary Momentum based Exploration. J. Exp. Theor. Artif. Intell 23(4), 469–495 (2011)CrossRefGoogle Scholar
  44. 44.
    Bennewitz, M., Burgard, W., Thrun, S.: Optimizing schedules for prioritized path planning of multi -robot systems. In: Proceedings of the 2001 IEEE international conference on robotics and automation, pp. 271–276. IEEE (2001)Google Scholar
  45. 45.
    Bennewitz, M., Burgard, W., Thrun, S.: Finding and optimizing solvable priority schemes for decoupled path planning techniques for teams of mobile robots. Rob. Auton. Syst. 41(2-3), 89–99 (2002)CrossRefGoogle Scholar
  46. 46.
    Clark, C.M., Bretl, T., Rock, S.: Applying kinodynamic randomized motion planning with a dynamic priority system to multi-robot space systems. In: Proceedings of the 2002 IEEE Aerospace Conference Proceedings, vol. 7, pp. 3621–3631. IEEE (2002)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Robotics and Artificial Intelligence LaboratoryIndian Institute of Information Technology AllahabadAllahabadIndia

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