AI helps you reading Science

AI generates interpretation videos

AI extracts and analyses the key points of the paper to generate videos automatically


pub
Go Generating

AI Traceability

AI parses the academic lineage of this thesis


Master Reading Tree
Generate MRT

AI Insight

AI extracts a summary of this paper


Weibo:
This paper presented the results of a thorough analysis of the Rapidly-exploring Random Trees and Rapidly-exploring Random Graph algorithms for optimal motion planning

Incremental Sampling-Based Algorithms For Optimal Motion Planning

ROBOTICS: SCIENCE AND SYSTEMS VI, (2011): 267-274

Cited: 708|Views80
EI
Full Text
Bibtex
Weibo

Abstract

During the last decade, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs), have been shown to work well in practice and to possess theoretical guarantees such as probabilistic completeness. However, no theoretical bounds on the quality of the solution obtained by these algorithms, e. ...More

Code:

Data:

0
Introduction
  • The robotic motion planning problem has received a considerable amount of attention, especially over the last decade, as robots started becoming a vital part of modern industry as well as the daily life.
  • Algorithmic approaches to the motion planning problem mainly focused on developing complete planners for, e.g., polygonal robots moving among polygonal obstacles [7], and later for more general cases using algebraic techniques [8]
  • These algorithms, suffered severely from computational complexity, which prohibited their practical implementations; for instance, the algorithm in [8] had doubly
Highlights
  • The robotic motion planning problem has received a considerable amount of attention, especially over the last decade, as robots started becoming a vital part of modern industry as well as our daily life
  • Algorithmic approaches to the motion planning problem mainly focused on developing complete planners for, e.g., polygonal robots moving among polygonal obstacles [7], and later for more general cases using algebraic techniques [8]
  • We propose a novel variant of the Rapidly-exploring Random Graph algorithm, called Rapidly-exploring Random Trees∗, which inherits the asymptotic optimality of the Rapidly-exploring Random Graph algorithm while maintaining a tree structure
  • This paper presented the results of a thorough analysis of the Rapidly-exploring Random Trees and Rapidly-exploring Random Graph algorithms for optimal motion planning
  • The Rapidly-exploring Random Graph and the Rapidly-exploring Random Trees∗ were shown to have no significant overhead when compared to the Rapidly-exploring Random Trees algorithm in terms of asymptotic computational complexity
Conclusion
  • This paper presented the results of a thorough analysis of the RRT and RRG algorithms for optimal motion planning.
  • As the number of samples increases, the RRT algorithm converges to a sub-optimal solution almost surely.
  • It is proven that the RRG algorithm has the asymptotic optimality property, i.e., almost sure convergence to an optimum solution, which the RRT algorithm lacked.
  • The paper proposed a novel algorithm called the RRT∗, which inherits the asymptotic optimality property of the RRG, while maintaining a tree structure rather than a graph.
  • Experimental evidence that demonstrate the effectiveness of the algorithms proposed and support the theoretical claims were provided
Funding
  • This research was supported in part by the Michigan/AFRL Collaborative Center on Control Sciences, AFOSR grant no
  • Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the supporting organizations
Reference
  • J. Latombe. Motion planning: A journey of robots, molecules, digital actors, and other artifacts. International Journal of Robotics Research, 18(11):1119–1128, 1999.
    Google ScholarLocate open access versionFindings
  • A. Bhatia and E. Frazzoli. Incremental search methods for reachability analysis of continuous and hybrid systems. In R. Alur and G.J. Pappas, editors, Hybrid Systems: Computation and Control, number 2993 in Lecture Notes in Computer Science, pages 142–156. Springer-Verlag, Philadelphia, PA, March 2004.
    Google ScholarLocate open access versionFindings
  • M. S. Branicky, M. M. Curtis, J. Levine, and S. Morgan. Samplingbased planning, control, and verification of hybrid systems. IEEE Proc. Control Theory and Applications, 153(5):575–590, Sept. 2006.
    Google ScholarLocate open access versionFindings
  • J. Cortes, L. Jailet, and T. Simeon. Molecular disassembly with RRTlike algorithms. In IEEE International Conference on Robotics and Automation (ICRA), 2007.
    Google ScholarLocate open access versionFindings
  • Y. Liu and N.I. Badler. Real-time reach planning for animated characters using hardware acceleration. In IEEE International Conference on Computer Animation and Social Characters, pages 86–93, 2003.
    Google ScholarLocate open access versionFindings
  • P.W. Finn and L.E. Kavraki. Computational approaches to drug design. Algorithmica, 25:347–371, 1999.
    Google ScholarLocate open access versionFindings
  • T. Lozano-Perez and M. A. Wesley. An algorithm for planning collisionfree paths among polyhedral obstacles. Communications of the ACM, 22(10):560–570, 1979.
    Google ScholarLocate open access versionFindings
  • J. T. Schwartz and M. Sharir. On the ‘piano movers’ problem: II. general techniques for computing topological properties of real algebraic manifolds. Advances in Applied Mathematics, 4:298–351, 1983.
    Google ScholarLocate open access versionFindings
  • J.H. Reif. Complexity of the mover’s problem and generalizations. In Proceedings of the IEEE Symposium on Foundations of Computer Science, 1979.
    Google ScholarLocate open access versionFindings
  • R. Brooks and T. Lozano-Perez. A subdivision algorithm in configuration space for findpath with rotation. In International Joint Conference on Artificial Intelligence, 1983.
    Google ScholarLocate open access versionFindings
  • J. Barraquand and J. C. Latombe. Robot motion planning: A distributed representation approach. International Journal of Robotics Research, 10(6):628–649, 1993.
    Google ScholarLocate open access versionFindings
  • O. Khatib. Real-time obstacle avoidance for manipulators and mobile robots. International Journal of Robotics Research, 5(1):90–98, 1986.
    Google ScholarLocate open access versionFindings
  • J. Canny. The Complexity of Robot Motion Planning. MIT Press, 1988.
    Google ScholarFindings
  • S. S. Ge and Y.J. Cui. Dynamic motion planning for mobile robots using potential field method. Autonomous Robots, 13(3):207–222, 2002.
    Google ScholarLocate open access versionFindings
  • Y. Koren and J. Borenstein. Potential field methods and their inherent limitations for mobile robot navigation. In IEEE Conference on Robotics and Automation, 1991.
    Google ScholarLocate open access versionFindings
  • L. Kavraki and J. Latombe. Randomized preprocessing of configuration space for fast path planning. In IEEE International Conference on Robotics and Automation, 1994.
    Google ScholarLocate open access versionFindings
  • L.E. Kavraki, P. Svestka, J Latombe, and M.H. Overmars. Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Transactions on Robotics and Automation, 12(4):566–580, 1996.
    Google ScholarLocate open access versionFindings
  • S. M. LaValle and J. J. Kuffner. Randomized kinodynamic planning. International Journal of Robotics Research, 20(5):378–400, May 2001.
    Google ScholarLocate open access versionFindings
  • S. Prentice and N. Roy. The belief roadmap: Efficient planning in blief space by factoring the covariance. International Journal of Robotics Research, 28(11–12):1448–1465, 2009.
    Google ScholarLocate open access versionFindings
  • R. Tedrake, I. R. Manchester, M. M. Tobekin, and J. W. Roberts. LQR-trees: Feedback motion planning via sums of squares verification. International Journal of Robotics Research (to appear), 2010.
    Google ScholarLocate open access versionFindings
  • B. Luders, S. Karaman, E. Frazzoli, and J. P. How. Bounds on tracking error using closed-loop rapidly-exploring random trees. In American Control Conference, 2010.
    Google ScholarLocate open access versionFindings
  • D. Berenson, J. Kuffner, and H. Choset. An optimization approach to planning for mobile manipulation. In IEEE International Conference on Robotics and Automation, 2008.
    Google ScholarLocate open access versionFindings
  • A. Yershova and S. Lavalle. Motion planning in highly constrained spaces. Technical report, University of Illinois at Urbana-Champaign, 2008.
    Google ScholarFindings
  • M. Stilman, J. Schamburek, J. Kuffner, and T. Asfour. Manipulation planning among movable obstacles. In IEEE International Conference on Robotics and Automation, 2007.
    Google ScholarLocate open access versionFindings
  • E. Koyuncu, N.K. Ure, and G. Inalhan. Integration of path/manuever planning in complex environments for agile maneuvering UCAVs. Jounal of Intelligent and Robotic Systems, 57(1–4):143–170, 2010.
    Google ScholarLocate open access versionFindings
  • J. Barraquand, L. Kavraki, J. Latombe, T. Li, R. Motwani, and P. Raghavan. A random sampling scheme for path planning. International Journal of Robotics Research, 16:759–774, 1997.
    Google ScholarLocate open access versionFindings
  • D. Hsu, J. Latombe, and H. Kurniawati. On the probabilistic foundations of probabilistic roadmap planning. International Journal of Robotics Research, 25:7, 2006.
    Google ScholarLocate open access versionFindings
  • L. E. Kavraki, M. N. Kolountzakis, and J. Latombe. Analysis of probabilistic roadmaps for path planning. IEEE Transactions on Roborics and Automation, 14(1):166–171, 1998.
    Google ScholarLocate open access versionFindings
  • J.J. Kuffner and S.M. LaValle. RRT-connect: An efficient approach to single-quert path planning. In Proceedings of the IEEE International Conference on Robotics and Automation, 2000.
    Google ScholarLocate open access versionFindings
  • S. LaValle. Planning Algorithms. Cambridge University Press, 2006.
    Google ScholarFindings
  • S.R. Lindemann and S.M. LaValle. Current issues in sampling-based motion planning. In P. Dario and R. Chatila, editors, Eleventh International Symposium on Robotics Research, pages 36–54.
    Google ScholarLocate open access versionFindings
  • M. S. Branicky, S. M. LaValle, K. Olson, and L. Yang. Quasirandomized path planning. In IEEE Conference on Robotics and Automation, 2001.
    Google ScholarLocate open access versionFindings
  • A. L. Ladd and L. Kavraki. Measure theoretic analysis of probabilistic path planning. IEEE Transactions on Robotics and Automation, 20(2):229–242, 2004.
    Google ScholarLocate open access versionFindings
  • D. Hsu, R. Kindel, J. Latombe, and S. Rock. Randomized kinodynamic motion planning with moving obstacles. International Journal of Robotics Research, 21(3):233–255, 2002.
    Google ScholarLocate open access versionFindings
  • E. Frazzoli, M. Dahleh, and E. Feron. Real-time motion planning for agile autonomous vehicles. Journal of Guidance, Control, and Dynamics, 25(1):116–129, 2002.
    Google ScholarLocate open access versionFindings
  • M. S. Branicky, M. M. Curtis, J. A. Levine, and S. B. Morgan. RRTs for nonlinear, discrete, and hybrid planning and control. In IEEE Conference on Decision and Control, 2003.
    Google ScholarLocate open access versionFindings
  • M. Zucker, J. Kuffner, and M. Branicky. Multiple RRTs for rapid replanning in dynamic environments. In IEEE Conference on Robotics and Automation, 2007.
    Google ScholarLocate open access versionFindings
  • J. Bruce and M.M. Veloso. Real-Time Randomized Path Planning for Robot Navigation, volume 2752 of Lecture Notes in Computer Science, chapter RoboCup 2002: Robot Soccer World Cup VI, pages 288–295.
    Google ScholarLocate open access versionFindings
  • Y. Kuwata, J. Teo, G. Fiore, S. Karaman, E. Frazzoli, and J.P. How. Realtime motion planning with applications to autonomous urban driving. IEEE Transactions on Control Systems, 17(5):1105–1118, 2009.
    Google ScholarLocate open access versionFindings
  • S. Teller, M. R. Walter, M. Antone, A. Correa, R. Davis, L. Fletcher, E. Frazzoli, J. Glass, J.P. How, A. S. Huang, J. Jeon, S. Karaman, B. Luders, N. Roy, and T. Sainath. A voice-commandable robotic forklift working alongside humans in minimally-prepared outdoor environments. In IEEE International Conference on Robotics and Automation, 2010.
    Google ScholarLocate open access versionFindings
  • A. Shkolnik, M. Levashov, I. R. Manchester, and R. Tedrake. Bounding on rough terrain with the LittleDog robot. Under review.
    Google ScholarFindings
  • J. J. Kuffner, S. Kagami, K. Nishiwaki, M. Inaba, and H. Inoue. Dynamically-stable motion planning for humanoid robots. Autonomous Robots, 15:105–118, 2002.
    Google ScholarLocate open access versionFindings
  • S. Karaman and E. Frazzoli. Sampling-based motion planning with deterministic μ-calculus specifications. In IEEE Conference on Decision and Control (CDC), 2009.
    Google ScholarLocate open access versionFindings
  • E.M. Clarke, O. Grumberg, and D.A. Peled. Model Checking. Springer, 1999.
    Google ScholarFindings
  • C. Urmson and R. Simmons. Approaches for heuristically biasing RRT growth. In Proceedings of the IEEE/RSJ International Conference on Robotics and Systems (IROS), 2003.
    Google ScholarLocate open access versionFindings
  • D. Ferguson and A. Stentz. Anytime RRTs. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2006.
    Google ScholarLocate open access versionFindings
  • N. A. Wedge and M.S. Branicky. On heavy-tailed runtimes and restarts in rapidly-exploring random trees. In Twenty-third AAAI Conference on Artificial Intelligence, 2008.
    Google ScholarLocate open access versionFindings
  • M. Likhachev, G. Gordon, and S. Thrun. Anytime A* with provable bounds on sub-optimality. In Advances in Neural Information Processing Systems, 2004.
    Google ScholarLocate open access versionFindings
  • M. Likhachev, D. Ferguson, G. Gordon, A. Stentz, and S. Thrun. Anytime search in dynamic graphs. Artificial intelligence Journal, 172(14):1613–1643, 2008.
    Google ScholarLocate open access versionFindings
  • D. Stentz. The focussed D* algorithm for real-time replanning. In International Joint Conference on Artificial Intelligence, 1995.
    Google ScholarLocate open access versionFindings
  • M. Likhachev and D. Ferguson. Planning long dynamically-feasible maneuvers for autonomous vehicles. International Journal of Robotics Research, 28(8):933–945, 2009.
    Google ScholarLocate open access versionFindings
  • D. Dolgov, S. Thrun, M. Montemerlo, and J. Diebel. Experimental Robotics, chapter Path Planning for Autonomous Driving in Unknown Environments, pages 55–64.
    Google ScholarFindings
  • M. Penrose. Random Geometric Graphs. Oxford University Press, 2003.
    Google ScholarFindings
  • J. Dall and M. Christensen. Random geometric graphs. Physical Review E, 66(1):016121, Jul 2002.
    Google ScholarLocate open access versionFindings
  • S.M. LaValle, M.S. Branicky, and S.R. Lindemann. On the relationship between classical grid search and probabilistic roadmaps. International Journal of Robotics Research, 23(7–8):673–692, 2004.
    Google ScholarLocate open access versionFindings
  • H. Samet. Applications of Spatial Data Structures: Computer Graphics, Image Processesing and Gis. Addison-Wesley, 1989.
    Google ScholarFindings
  • H. Samet. Design and Analysis of Spatial Data Structures. AddisonWesley, 1989.
    Google ScholarFindings
  • A. Atramentov and S. M. LaValle. Efficient nearest neighbor searching for motion planning. In IEEE International Conference on Robotics and Automation, 2002.
    Google ScholarLocate open access versionFindings
  • T. H. Cohen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. MIT Press, 1990.
    Google ScholarFindings
  • H. Edelsbrunner. Algorithms in Computational Geometry. SpringerVerlag, 1987.
    Google ScholarFindings
  • K. L. Clarkson. A randomized algorithm for closest-point querries. SIAM Journal of Computation, 17:830–847, 1988.
    Google ScholarLocate open access versionFindings
  • S. Arya, D. M. Mount, R. Silverman, and A. Y. Wu. An optimal algorithm for approximate nearest neighbor search in fixed dimensions. Journal of the ACM, 45(6):891–923, November 1999.
    Google ScholarLocate open access versionFindings
  • E. Plaku and L. E. Kavraki. Quantitative analysis of nearest-neighbors search in high-dimensional sampling-based motion planning. In Workshop on Algorithmic Foundations of Robotics (WAFR), 2008.
    Google ScholarLocate open access versionFindings
  • D. T. Lee and C. K. Wong. Worst-case analysis for region and partial region searches in multidimensional binary search trees and quad trees. Acta Informatica, 9:23–29, 1977.
    Google ScholarLocate open access versionFindings
  • P. Chanzy, L. Devroye, and C. Zamora-Cura. Analysis of range search for random k-d trees. Acta Informatica, 37:355–383, 2001.
    Google ScholarLocate open access versionFindings
  • S. Arya and D. M. Mount. Approximate range searching. Computational Geometry: Theory and Applications, 17:135–163, 2000.
    Google ScholarLocate open access versionFindings
  • S. Arya, T. Malamatos, and D. M. Mount. Space-time tradeoffs for approximate speherical range counting. In Symposium on Discrete Algorithms, 2005.
    Google ScholarLocate open access versionFindings
  • S. LaValle and J. Kuffner. Space filling trees. Technical Report CMURI-TR-09-47, Carnegie Mellon University, The Robotics Institute, 2009.
    Google ScholarFindings
  • N.C. Rowe and R.S. Alexander. Finding optimal-path maps for path planning across weighted regions. The International Journal of Robotics Research, 19:83–95, 2000.
    Google ScholarLocate open access versionFindings
  • H. A. David and H. N. Nagaraja. Order Statistics. Wiley, 2003.
    Google ScholarFindings
  • G. Grimmett and D. Stirzaker. Probability and Random Processes. Oxford University Press, Third edition, 2001.
    Google ScholarFindings
  • M. Mitzenmacher and E. Upfal. Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press, 2005.
    Google ScholarFindings
  • S. Muthukrishnan and G. Pandurangan. The bin-covering technique for thresholding random geometric graph properties. In Proceedings of the sixteenth annual ACM-SIAM symposium on discrete algorithms, 2005.
    Google ScholarLocate open access versionFindings
  • 2. Then, by the Borel-Cantelli Lemma [71], one can conclude that the probability that Dk,j occurs for infinitely many j is zero, i.e., P(lim supj→∞ Dk,j) = 0, which implies the claim.
    Google ScholarFindings
0
Your rating :

No Ratings

Tags
Comments
数据免责声明
页面数据均来自互联网公开来源、合作出版商和通过AI技术自动分析结果,我们不对页面数据的有效性、准确性、正确性、可靠性、完整性和及时性做出任何承诺和保证。若有疑问,可以通过电子邮件方式联系我们:report@aminer.cn