Abstract
Asymptotically optimal planners like prm* guarantee that solutions approach optimal as iterations increase. Roadmaps with this property, however, may grow too large. If optimality is relaxed, asymptotically near-optimal solutions produce sparser graphs by not including all edges. The idea stems from graph spanners, which produce sparse subgraphs that guarantee near-optimal paths. Existing asymptotically optimal and near-optimal planners, however, include all sampled configurations as roadmap nodes, meaning only infinite graphs have the desired properties. This work proposes an approach, called spars, that provides the following asymptotic properties: (a) completeness, (b) near-optimality and (c) the probability of adding nodes to the spanner converges to zero as iterations increase, which suggests that finite-size data structures may exist that have near-optimality properties. The method brings together ideas from various planners but deviates from existing integrations of prm* with graph spanners. Simulations for rigid bodies show that spars indeed provides small roadmaps and results in faster query resolution. The rate of node addition is shown to decrease over time and the quality of solutions is even better than the theoretical bounds.
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References
Agarwal, P.: Compact Representations for Shortest-Path Queries. Appeared at the IROS 2012 Workshop on Progress and Open Problems in Motion Planning (2011)
Amato, N.M., Bayazit, O.B., Dale, L.K., Jones, C., Vallejo, D.: OBPRM: An Obstacle-based PRM for 3D Workspaces. In: WAFR, pp. 155–168 (1998)
Baswana, S., Sen, S.: A Simple and Linear Time Randomized Algorithm for Computing Spanners in Weighted Graphs. Random Structures and Algorithms 30(4), 532–563 (2007)
Geraerts, R., Overmars, M.H.: Creating High-Quality Roadmaps for Motion Planning in Virtual Environments. In: IROS, Beijing, China, pp. 4355–4361 (2006)
Hsu, D., Kavraki, L., Latombe, J.C., Motwani, R., Sorkin, S.: On Finding Narrow Passages with Probabilistic Roadmap Planners. In: WAFR, Houston, TX (1998)
Hsu, D., Kindel, R., Latombe, J.C., Rock, S.: Randomized Kinodynamic Motion Planning with Moving Obstacles. IJRR 21(3), 233–255 (2002)
Jaillet, L., Simeon, T.: Path Deformation Roadmaps. In: Akella, S., Amato, N.M., Huang, W.H., Mishra, B. (eds.) Algotithmic Foundation Robotics VII. STAR, vol. 47, pp. 19–34. Springer, Heidelberg (2008)
Kallman, M., Mataric, M.: Motion Planning Using Dynamic Roadmaps. In: ICRA, New Orleands, LA, vol. 5, pp. 4399–4404 (2004)
Karaman, S., Frazzoli, E.: Sampling-based Algorithms for Optimal Motion Planning. IJRR 30(7), 846–894 (2011)
Kavraki, L.E., Kolountzakis, M.N., Latombe, J.C.: Analysis of Probabilistic Roadmaps for Path Planning. IEEE TRA 14(1), 166–171 (1998)
Kavraki, L.E., Svestka, P., Latombe, J.C., Overmars, M.: Probabilistic Roadmaps for Path Planning in High-Dimensional Configuration Spaces. IEEE TRA 12(4), 566–580 (1996)
Ladd, A.M., Kavraki, L.E.: Measure Theoretic Analysis of Probabilistic Path Planning. IEEE TRA 20(2), 229–242 (2004)
LaValle, S.M., Kuffner, J.J.: Randomized Kinodynamic Planning. IJRR 20, 378–400 (2001)
Li, Y., Bekris, K.E.: Learning Approximate Cost-to-Go Metrics to Improve Sampling-based Motion Planning. In: IEEE ICRA, Shanghai, China (2011)
Marble, J.D., Bekris, K.E.: Asymptotically Near-Optimal is Good Enough for Motion Planning. In: ISRR, Flagstaff, AZ (2011)
Marble, J.D., Bekris, K.E.: Towards Small Asymptotically Near-Optimal Roadmaps. In: IEEE ICRA, Minnesota, MN (2012)
Nechushtan, O., Raveh, B., Halperin, D.: Sampling-Diagram Automata: A Tool for Analyzing Path Quality in Tree Planners. In: Hsu, D., Isler, V., Latombe, J.-C., Lin, M.C. (eds.) Algorithmic Foundations of Robotics IX. STAR, vol. 68, pp. 285–301. Springer, Heidelberg (2010)
Nieuwenhuisen, D., Overmars, M.H.: Using Cycles in Probabilistic Roadmap Graphs. In: IEEE ICRA, pp. 446–452 (2004)
Peleg, D., Schäffer, A.: Graph Spanners. Journal of Graph Theory 13(1), 99–116 (1989)
Raveh, B., Enosh, A., Halperin, D.: A Little More, a Lot Better: Improving Path Quality by a Path-Merging Algorithm. IEEE TRO 27(2), 365–370 (2011)
Sanchez, G., Latombe, J.C.: A Single-Query, Bi-Directional Probabilistic Roadmap Planner with Lazy Collision Checking. In: ISRR, pp. 403–418 (2001)
Schmitzberger, E., Bouchet, J.L., Dufaut, M., Wolf, D., Husson, R.: Capture of Homotopy Classes with Probabilistic Roadmap. In: IEEE/RSJ IROS, pp. 2317–2322 (2002)
Simeon, T., Laumond, J.P., Nissoux, C.: Visibility-based Probabilistic Roadmaps for Motion Planning. Advanced Robotics Journal 41(6), 477–494 (2000)
Varadhan, G., Manocha, D.: Star-shaped Roadmaps: A Deterministic Sampling Approach for Complete Motion Planning. IJRR (2007)
Xie, D., Morales, M., Pearce, R., Thomas, S., Lien, J.L., Amato, N.M.: Incremental Map Generation (IMG). In: Akella, S., Amato, N.M., Huang, W.H., Mishra, B. (eds.) Algorithmic Foundations of Robotics. STAR, vol. 47, pp. 53–68. Springer, Heidelberg (2008)
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Dobson, A., Krontiris, A., Bekris, K.E. (2013). Sparse Roadmap Spanners. In: Frazzoli, E., Lozano-Perez, T., Roy, N., Rus, D. (eds) Algorithmic Foundations of Robotics X. Springer Tracts in Advanced Robotics, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36279-8_17
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DOI: https://doi.org/10.1007/978-3-642-36279-8_17
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