Skip to main content
SpringerLink
Log in

Roadmaps for Robot Motion Planning with Groups of Robots

  • Group Robotics (M Gini and F Amigoni, Section Editors)
  • Published:
Current Robotics Reports Aims and scope Submit manuscript

Abstract

Purpose of Review

Autonomous robotic systems require the core capability of planning motions and actions. Centralized motion planning exhibits significant challenges when applied to multi-robot problems. Reasoning about groups of robots typically cause an exponential increase in the size of the search space that an algorithm has to explore. Moreover, each robot by itself might be an articulated mechanism with a large number of controllable joints, or degrees of freedom which can pose its own difficulties in planning. Roadmaps have been a popular graph-based method of representing the connectivity of valid motions in such large search spaces including specialized variants for multi-robot motion planning.

Recent Findings

This article primarily covers recent algorithmic advances that are based on roadmaps for motion planning, with specific optimizations necessary for the multi-robot domain. The structure of the multi-robot problem domain leads to efficient graphical decomposition of the problem on roadmaps. These algorithms provide some desired theoretical properties of being guaranteed to find a solution, as well as optimality of the discovered solution. Extensions to richer planning applications are also discussed.

Summary

The design of efficient multi-robot planning algorithms like the roadmap-based ones discussed in this article provides the cornerstone for the deployment of large-scale multi-robot teams to solve real-world problems.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Notes

  1. In general, the robots can be non-uniform and have different degrees of freedom.

  2. Typically these are straight-line interpolations, but in general, the edge only needs a guarantee that the path connects the two vertices xu and xv. This is denoted by steerability of the system, i.e., the ability to steer to a specific configuration xv from xu, and is not a valid assumption for robots with non-trivial dynamics.

  3. Note that the construction phase and the solution recovery phase are distinct. This means that for scenarios where the environment is known beforehand, a roadmap can be constructed and reused for all motion planning problems in the same (or a similar) environment. Conversely, a roadmap optimistically constructed ignoring some or all obstacles can also be reused to recover the solution on the subgraph that is collision-free.

  4. Deterministic sampling strategies have also been proposed for PRM methods. The motivation remains the same that the chosen sampling strategy has to effectively cover the space as the number of samples increases. Uniform sampling is the classical technique, though for simpler domains grids, or other informed samples preserve the same arguments.

  5. Though the optimality is stated for shortest path lengths, the optimality at this step describing paths for individual robots which can be combined into a multi-robot optimal path.

  6. Optimality was shown for different cost functions: Euclidean arc length in \(\mathcal {Q}_{\text {free}}\), and any linear combination of individual robot shortest paths including makespan distance.

  7. Each robot’s individual shortest path to the goal proves a very reliable heuristic in the multi-robot configuration space. An efficient way to precompute this would be to maintain an all-pairs shortest path data structure tied to each \(\mathcal {G}^{i}\). This is feasible when each individual roadmap is reasonably sized.

References

  1. Erdmann M, Lozano-Perez T. On multiple moving objects. Algorithmica 1987;2(1-4):477.

    Article  MathSciNet  Google Scholar 

  2. Ghrist R, O’Kane JM, LaValle SM. Computing pareto optimal coordinations on roadmaps. IJRR 2005;24(11):997–1010.

    Google Scholar 

  3. LaValle SM, Hutchinson S. Optimal motion planning for multiple robots having independent goals. IEEE TRA 1998;14(6):912–925.

    Google Scholar 

  4. Peng J, Akella S. Coordinating multiple robots with kinodynamic constraints along specified paths. IJRR 2005;24(4):295–310.

    Google Scholar 

  5. van den Berg J, Overmars M. Prioritized motion planning for multiple robots. IROS; 2005. p. 430–435.

  6. van den Berg J, Snoeyink J, Lin M, Manocha D. Centralized path planning for multiple robots: optimal decoupling into sequential plans. RSS; 2009.

  7. Khan A, Zhang C, Li S, Wu J, Schlotfeldt B, Tang S, Ribeiro A, Bastani O, Kumar V. Learning safe unlabeled multi-robot planning with motion constraints. IEEE/RSJ IROS; 2019 . p. 7558–7565.

  8. Tang S, Kumar V. A complete algorithm for generating safe trajectories for multi-robot teams. ISRR; 2015.

  9. Kloder S, Hutchinson S. Path planning for permutation-invariant multi-robot formations. ICRA; 2005. p. 650–665.

  10. O’Donnell PA, Lozano-Pérez T. Deadlock-free and collision- free coordination of two robot manipulators. IEEE ICRA; 1989. p. 484–489.

  11. Salzman O, Hemmer M, Halperin D. On the power of manifold samples in exploring configuration spaces and the dimensionality of narrow passages. IEEE TASE 2015;12(2):529–538.

    Google Scholar 

  12. Solovey K, Salzman O, Halperin D. Finding a needle in an exponential haystack: discrete RRT for exploration of implicit roadmaps in multi-robot motion planning. IJRR 2016;35(5):501–513.

    Google Scholar 

  13. Svestka P, Overmars M. Coordinated path planning for multiple robots. RAS 1998;23:125–152.

    Google Scholar 

  14. •• Shome R, Solovey K, Dobson A, Halperin D, Bekris KE. dRRT: scalable and informed asymptotically-optimal multi-robot motion planning. AURO 2020;44(3):443–467.

    Google Scholar 

  15. •• Wagner G, Choset H. Subdimensional expansion for multirobot path planning. Artif Intell J 2015;219:1–24.

    Article  MathSciNet  Google Scholar 

  16. •• Yu J, LaValle SM. Optimal multirobot path planning on graphs: complete algorithms and effective heuristics. IEEE T-RO 2016;32(5):1163–1177.

    Article  Google Scholar 

  17. Lozano-Perez T. Spatial planning: a configuration space approach. Autonomous robot vehicles. Springer; 1990 . p. 259–271.

  18. Kavraki LE, Svestka P, Latombe J, Overmars M. Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Trans Robot Autom 1996;12(4):566–580.

    Article  Google Scholar 

  19. LaValle SM, Kuffner JJ. Randomized kinodynamic planning. IJRR 2001;20:378–400.

    Google Scholar 

  20. Karaman S, Frazzoli E. Sampling-based algorithms for optimal motion planning. IJRR 2011; 30(7):846–894.

    MATH  Google Scholar 

  21. Janson L, Schmerling A, Clark A, Pavone M. Fast marching tree: a fast marching sampling-based method for optimal motion planning in many dimensions. IJRR 2015;34(7):883–921.

    Google Scholar 

  22. Sȧnchez-Ante G, Latombe J. Using a PRM planner to compare centralized and decoupled planning for multi-robot systems. IEEE ICRA; 2002. p. 2112–2119.

  23. Hart PE, Nilsson NJ, Raphael B. A formal basis for the heuristic determination of minimum cost paths. IEEE Trans Syst Sci Cybern 1968;4(2):100–107.

    Article  Google Scholar 

  24. Gravot F, Alami R. A method for handling multiple roadmaps and its use for complex manipulation planning. IEEE ICRA; 2003. p. 2914–2919.

  25. Gharbi M, Cortés J, Siméon T. Roadmap composition for multi-arm systems path planning. IEEE/RSJ IROS; 2009. p. 2471–2476.

  26. Wagner G, Choset H. M*: a complete multirobot path planning algorithm with performance bounds. IROS. IEEE; 2011. p. 3260–3267.

  27. Wagner G, Kang M, Choset H. Probabilistic path planning for multiple robots with subdimensional expansion. IEEE ICRA; 2012. p. 2886–2892.

  28. Dobson A, Solovey K, Shome R, Halperin D, Bekris K. Scalable asymptotically-optimal multi-robot motion planning. IEEE MRS; 2017. p. 120–127.

  29. Kornhauser DM, Miller GL, Spirakis PG. 1984. Coordinating pebble motion on graphs, the diameter of permutation groups, and applications. Master’s thesis, M. I. T., Dept of Electrical Engineering and Computer Science.

  30. Luna R, Bekris K. An efficient and complete approach for cooperative path-finding. Conference on artificial intelligence, San Francisco, California, USA; 2011. p. 1804–1805.

  31. Yu J. Constant factor time optimal multi-robot routing on high-dimensional grids. RSS; 2018.

  32. Chinta R, Han SD, Yu J. Coordinating the motion of labeled discs with optimality guarantees under extreme density. WAFR. Springer; 2018. p. 817–834.

  33. Ma H, Li J, Kumar TS, Koenig S. Lifelong multi-agent path finding for online pickup and delivery tasks. AAMAS; 2017. p. 837–845.

  34. Ho F, Salta A, Geraldes R, Goncalves A, Cavazza M, Prendinger H. Multi-agent path finding for uav traffic management. AAMAS; 2019. p. 131–139.

  35. Choudhury S, Solovey K, Kochenderfer MJ, Pavone M. Efficient large-scale multi-drone delivery using transit networks. ICRA. IEEE; 2020. p. 4543–4550.

  36. Adler A, de Berg M, Halperin D, Solovey K. Efficient multi-robot motion planning for unlabeled discs in simple polygons. IEEE TASE 2015;12(4):1–17.

    MathSciNet  Google Scholar 

  37. Solovey K, Yu J, Zamir O, Halperin D. Motion planning for unlabeled discs with optimality guarantees. RSS; 2015.

  38. Turpin M, Michael N, Kumar V. Concurrent assignment and planning of trajectories for large teams of interchangeable robots. IEEE ICRA; 2013. p. 842–848.

  39. Solomon I, Halperin D. Motion planning for multiple unit-ball robots in Rd. WAFR. Springer; 2018. p. 799–816.

  40. Cohen JB, Phillips M, Likhachev M. Planning single-arm manipulations with n-Arm robots. RSS; 2014.

  41. Krontiris A, Shome R, Dobson A, Kimmel A, Bekris K. Rearranging similar objects with a manipulator using pebble graphs. IEEE humanoids; 2014. p. 1081–1087.

  42. Shome R, Bekris K. Anytime multi-arm task and motion planning for pick-and-place of individual objects via handoffs. IEEE MRS. IEEE; 2019. p. 37–43.

  43. Shome R, Solovey K, Yu J, Bekris K, Halperin D. Fast and high-quality dual-arm rearrangement in synchronous, monotone tabletop setups. WAFR; 2018. p. 778–795.

  44. Shome R, Bekris K. Synchronized multi-arm rearrangement guided by mode graphs with capacity constraints. WAFR; 2020.

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Rice University, Houston, TX, USA

    Rahul Shome

Authors
  1. Rahul Shome
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rahul Shome.

Ethics declarations

Conflict of Interest

The author declares no competing interest.

Human and Animal Rights and Informed Consent

This article does not contain any studies with human or animal subjects performed by the author.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article belongs to the Topical Collection on Group Robotics

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shome, R. Roadmaps for Robot Motion Planning with Groups of Robots. Curr Robot Rep 2, 85–94 (2021). https://doi.org/10.1007/s43154-021-00043-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s43154-021-00043-8

Keywords

Search

Navigation