Skip to main content
SpringerLink
Log in

Pareto-optimal coordination of multiple robots with safety guarantees

  • Published:
Autonomous Robots Aims and scope Submit manuscript

Abstract

This paper investigates the coordination of multiple robots with pre-specified paths, considering motion safety and minimizing the traveling time. A method to estimate possible collision point along the local paths of the robots is proposed. The repulsive potential energy is computed based on the distances between the robots and the potential collision points. This repulsive potential energy is used as the cost map of the probabilistic roadmap (PRM), which is constructed in the coordination space for multiple robots taking into account both motion time cost and safety cost. We propose a search method on the PRM to obtain the Pareto-optimal coordination solution for multiple robots. Both simulation and experimental results are presented to demonstrate the effectiveness of the algorithms.

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

Similar content being viewed by others

References

  • Barraquand, J., & Latombe, J. (1991). Robot motion planning: a distributed representation approach. Int. J. Robot. Res., 10(6), 628–649.

    Article  Google Scholar 

  • Chakravarthy, A., & Ghose, D. (1998). Obstacle avoidance in a dynamic environment: a collision cone approach. IEEE Trans. Syst. Man Cybern., Part A, Syst. Hum., 28(5), 562–574.

    Article  Google Scholar 

  • Chitsaz, H., O’Kane, J. M., & LaValle, S. M. (2004). Exact Pareto-optimal coordination of two translating polygonal robots on an acyclic roadmap. In Proceedings of 2004 IEEE international conference on robotics and automation (Vol. 4, pp. 3981–3986).

    Chapter  Google Scholar 

  • Choset, H., Lynch, K.M., Hutchinson, S., Kantor, G., Burgard, W., Kavraki, L.E., & Thrun, S. (2005). Principles of robot motion: theory, algorithms and implementation. Cambridge: MIT Press.

    MATH  Google Scholar 

  • Cui, R., Ge, S. S., How, V. E. B., & Choo, Y. S. (2010). Leader-Follower formation control of underactuated autonomous underwater vehicles. Ocean Eng., 37(17–18), 1491–1502.

    Article  Google Scholar 

  • Durfee, E. H. (1999). Distributed continual planning for unmanned ground vehicle teams. AI Mag., 20(4), 55–61.

    Google Scholar 

  • Fua, C. H., Ge, S. S., Do, K. D., & Lim, K. W. (2007). Multirobot formations based on the queue-formation scheme with limited communication. IEEE Trans. Robot., 23(6), 1160–1169.

    Article  Google Scholar 

  • Ge, S. S., & Cui, Y. J. (2002a). New potential functions for mobile robot path planning. IEEE Trans. Robot. Autom., 16(5), 615–620.

    Article  Google Scholar 

  • Ge, S. S., & Cui, Y. J. (2002b). Dynamic motion planning for mobile robots using potential field method. Auton. Robots, 13(3), 207–222.

    Article  MATH  Google Scholar 

  • Ge, S. S., & Fua, C. H. (2004). Queues and artificial potential trenches for multirobot formations. IEEE Trans. Robot., 21(4), 646–656.

    Article  Google Scholar 

  • Ghrist, R., O’Kane, J. M., & LaValle, S. M. (2005a). Computing Pareto optimal coordinations on roadmaps. Int. J. Robot. Res., 24(11), 997–1010.

    Article  Google Scholar 

  • Ghrist, R., O’Kane, J. M., & LaValle, S. M. (2005b). Pareto optimal coordination on roadmaps. In Algorithmic foundations of robotics VI (pp. 171–186).

    Chapter  Google Scholar 

  • Hsu, D. (2000). Randomized single-query motion planning in expansive spaces. Ph.D. dissertation, Stanford University.

  • Hu, H., Brady, M., & Probert, P. (2002). Coping with uncertainty in control and planning for a mobile robot. In Proceedings of IEEE/RSJ international workshop on intelligent robots and systems (pp. 1025–1030).

    Google Scholar 

  • Hu, J., Prandini, M., & Sastry, S. (2002). Optimal coordinated maneuvers for three-dimensional aircraft conflict resolution. J. Guid. Control Dyn., 25(5), 888–900.

    Article  Google Scholar 

  • Kant, K., & Zucker, S. (1986). Toward efficient trajectory planning: the path velocity decomposition. Int. J. Robot. Res., 5(3), 72–89.

    Article  Google Scholar 

  • Kavraki, L. E., Svestka, P., Latombe, J. C., & Overmars, M. H. (1996). Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Trans. Robot. Autom., 12(4), 566–580.

    Article  Google Scholar 

  • Kuchar, J. K., & Yang, L. C. (2002). A review of conflict detection and resolution modeling methods. IEEE Trans. Intell. Transp. Syst., 1(4), 179–189.

    Article  Google Scholar 

  • Kuffner, J. (2004). Effective sampling and distance metrics for 3d rigid body path planning. In Proceedings of IEEE international conference on robotics and automation (Vol. 4, pp. 3993–3998).

    Google Scholar 

  • Kuffner, J. J., & LaValle, S. M. (2000). Rrt-connect: an efficient approach to single-query path planning. In Proceedings of IEEE international conference on robotics and automation (Vol. 2, pp. 995–1001).

    Google Scholar 

  • Ladd, A., & Kavraki, L. E. (2002). Generalizing the analysis of PRM. In Proceedings of IEEE international conference on robotics and automation (Vol. 2, pp. 2120–2125).

    Google Scholar 

  • Laffary, M. (2002). MobileRobots advanced robotics interface for applications (ARIA) developer’s reference manual. http://robots.mobilerobots.com/wiki/ARIA.

  • LaValle, S. M. (2006). Planning algorithms. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  • LaValle, S. M., & Hinrichsen, J. (2001). Visibility-based pursuit-evasion: the case of curved environments. IEEE Trans. Robot. Autom., 17(2), 196–202.

    Article  Google Scholar 

  • Liu, G., & Li, Z. (2002). A unified geometric approach to modeling and control of constrained mechanical systems. IEEE Trans. Robot. Autom., 18(4), 574–587.

    Article  Google Scholar 

  • Mataric, M. (1995). Issues and approaches in the design of collective autonomous agents. Robot. Auton. Syst., 16(2), 321–332.

    Article  Google Scholar 

  • Mortezaie, F. (1991). Constrained voronoi diagram and its application to autonomous mobile robot path planning. Ph.D. dissertation, University of California, Irvine.

  • Parker, L. E. (1997). ‘Cooperative motion control for multi-target observation. In Proceedings of the 1997 IEEE/RSJ international conference on intelligent robots and systems (Vol. 3, pp. 1591–1597).

    Google Scholar 

  • Plaku, E., & Kavraki, L. (2005). Distributed sampling-based roadmap of trees for large-scale motion planning. In IEEE international conference on robotics and automation (Vol. 4, pp. 3868–3873).

    Google Scholar 

  • Purwin, O., D’Andrea, R., & Lee, J. W. (2008). Theory and implementation of path planning by negotiation for decentralized agents. Robot. Auton. Syst., 56(5), 422–436.

    Article  Google Scholar 

  • Schouwenaars, T., How, J., & Feron, E. (2004). Decentralized cooperative trajectory planning of multiple aircraft with hard safety guarantees. In Proceedings of the AIAA guidance, navigation and control conference.

    Google Scholar 

  • Schwarzer, F., Saha, M., & Latombe, J. C. (2003). Exact collision checking of robot paths. In Algorithmic foundations of robotics V (pp. 25–42).

    Google Scholar 

  • Shanmugavel, M., Tsourdos, A., White, B., & Zbikowski, R. (2009). Co-operative path planning of multiple UAVs using Dubins paths with clothoid arcs. Control Eng. Pract., 18(9), 1084–1092.

    Article  Google Scholar 

  • Shin, K. G., & Zheng, Q. (1992). Minimum-time collision free trajectory planning for dual robot systems. IEEE Trans. Robot. Autom., 8(5), 641–644.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Marine Engineering, Northwestern Polytechnical University, Xi’an, 710072, P.R. China

    Rongxin Cui & Bo Gao

  2. College of Physics and Electrical Engineering, Anyang Normal University, Anyang, 455000, P.R. China

    Ji Guo

Authors
  1. Rongxin Cui
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bo Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ji Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rongxin Cui.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cui, R., Gao, B. & Guo, J. Pareto-optimal coordination of multiple robots with safety guarantees. Auton Robot 32, 189–205 (2012). https://doi.org/10.1007/s10514-011-9265-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10514-011-9265-9

Keywords

Search

Navigation