Skip to main content
SpringerLink
Log in

Distributed Range-Based Relative Localization of Robot Swarms

  • Chapter
  • First Online:
Algorithmic Foundations of Robotics XI

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 107))

Abstract

This paper studies the problem of having mobile robots in a multi-robot system maintain an estimate of the relative position and relative orientation of near-by robots in the environment. This problem is studied in the context of large swarms of simple robots which are capable of measuring only the distance to near-by robots. We compare two distributed localization algorithms with different trade-offs between their computational complexity and their coordination requirements. The first algorithm does not require the robots to coordinate their motion. It relies on a non-linear least squares based strategy to allow robots to compute the relative pose of near-by robots. The second algorithm borrows tools from distributed computing theory to coordinate which robots must remain stationary and which robots are allowed to move. This coordination allows the robots to use standard trilateration techniques to compute the relative pose of near-by robots. Both algorithms are analyzed theoretically and validated through simulations.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Many swarm of platforms, including the Kilobots [20], use the same hardware (i.e., infrared transceivers) as a cost-effective way to implement both communication and sensing.

  2. 2.

    The iterated logarithm function counts the number of times the logarithm is applied to the argument before the result is less or equal to 1. It is an extremely slowly growing function, for instance the iterated logarithm of the number of atoms in the universe is less than 5.

References

  1. Turgut, A., et al.: Self-organized flocking in mobile robot swarms. Swarm Intell. 2(2–4), 97–120 (2008)

    Article  Google Scholar 

  2. Balch, T., Arkin, R.C.: Behavior-based formation control for multirobot teams. Trans. Robot. Autom. (TRA) 14(6), 926–939 (1998)

    Article  Google Scholar 

  3. Thrun, S., Burgard, W., Fox, D.: A real-time algorithm for mobile robot mapping with applications to multi-robot and 3D mapping. In: International Conference on Robotics and Automation (ICRA), vol. 1, pp. 321–328 (2000)

    Google Scholar 

  4. Luo, J., Zhang, Q.: Relative distance based localization for mobile sensor networks. In: Global Telecommunications Conference (GlobeCom), pp. 1076–1080 (2007)

    Google Scholar 

  5. Savvides, A., Han, C., Strivastava, M.: Dynamic fine-grained localization in ad-hoc networks of sensors. In: International Conference on Mobile Computing and Networking (MobiCom), pp. 166–179 (2001)

    Google Scholar 

  6. Djugash, J., et al.: Range-only slam for robots operating cooperatively with sensor networks. In: International Conference on Robotics and Automation (ICRA), pp. 2078–2084 (2006)

    Google Scholar 

  7. Olson, E., Leonard, J., Teller, S.: Robust range-only beacon localization. IEEE J. Ocean. Eng. 31(4), 949–958 (2006)

    Article  Google Scholar 

  8. Moore, D., et al.: Robust distributed network localization with noisy range measurements. In: International Conference on Embedded Networked Sensor Systems (SenSys), pp. 50–61 (2004)

    Google Scholar 

  9. Trawny, N., Roumeliotis, S.I.: On the global optimum of planar, range-based robot-to-robot relative pose estimation. In: International Conference on Robotics and Automation (ICRA), pp. 3200–3206. IEEE (2010)

    Google Scholar 

  10. Kurazume, R., Nagata, S., Hirose, S.: Cooperative positioning with multiple robots. In: International Conference on Robotics and Automation (ICRA), vol. 2, pp. 1250–1257 (1994)

    Google Scholar 

  11. Navarro-Serment, L., Paredis, P., Khosla, C.: A beacon system for the localization of distributed robotic teams. In: International Conference on Field and Service Robotics (FSR), vol. 6 (1999)

    Google Scholar 

  12. Fox, D., et al.: A probabilistic approach to collaborative multi-robot localization. Auton. Robots 8(3), 325–344 (2000)

    Article  Google Scholar 

  13. Roumeliotis, S.I., Bekey, G.A.: Collective localization: a distributed Kalman filter approach to localization of groups of mobile robots. In: International Conference on Robotics and Automation (ICRA), vol. 3, pp. 2958–2965 (2000)

    Google Scholar 

  14. Martinelli, A., Pont, F., Siegwart, R.: Multi-robot localization using relative observations. In: International Conference on Robotics and Automation (ICRA), pp. 2797–2802 (2005)

    Google Scholar 

  15. Leung, K.Y.K., Barfoot, T.D., Liu, H.H.T.: Decentralized localization of sparsely-communicating robot networks: a centralized-equivalent approach. IEEE Trans. Robot. 26(1) (2010)

    Google Scholar 

  16. Carrillo-Arce, L.C., et al.: Decentralized multi-robot cooperative localization using covariance intersection. In: Intelligent Robots and Systems (IROS), pp. 1412–1417 (2013)

    Google Scholar 

  17. Nerurkar, E.D., Roumeliotis, S.I.: A communication-bandwidth-aware hybrid estimation framework for multi-robot cooperative localization. In: Intelligent Robots and Systems (IROS), pp. 1418–1425 (2013)

    Google Scholar 

  18. Prorok, A., Bahr, A., Martinoli, A.: Low-cost collaborative localization for large-scale multi-robot systems. In: International Conference on Robotics and Automation (ICRA), pp. 4236–4241 (2012)

    Google Scholar 

  19. Awerbuch, B.: Complexity of network synchronization. J. ACM (JACM) 32(4), 804–823 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  20. Rubenstein, M., Ahler, C., Nagpal, R.: Kilobot: a low cost scalable robot system for collective behaviors. In: International Conference on Robotics and Automation (ICRA), pp. 3293–3298 (2012)

    Google Scholar 

  21. Ueda, K., Yamashita, N.: On a global complexity bound Levenberg-Marquardt method. J. Optim. Theory Appl. 147(3), 443–453 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  22. Servatius, B., Servatius, H.: Generic and abstract rigidity (1999)

    Google Scholar 

  23. Luby, M.: A simple parallel algorithm for the maximal independent set problem. SIAM J. Comput. 15, 1036–1053 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  24. Schneider, J., Wattenhofer, R.: A log-star maximal independent set algorithm for growth-bounded graphs. In: International Symposium on Principles of Distributed Computing (PODC) (2008)

    Google Scholar 

  25. Afek, Y., et al.: Beeping a maximal independent set. In: International Symposium on Distributed Computing (DISC), pp. 32–50 (2011)

    Google Scholar 

  26. Métivier, Y., et al.: An optimal bit complexity randomized distributed MIS algorithm. In: Colloquim on Structural Information and Communication Complexity (SIROCCO) (2009)

    Google Scholar 

  27. Vicsek, T., et al.: Novel type of phase transition in a system of self-driven pinproceedings. Phys. Rev. Lett. 75(6), 1226 (1995)

    Article  Google Scholar 

  28. Olfati-Saber, R.: Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Autom. Control 51(3), 401–420 (2006)

    Article  MathSciNet  Google Scholar 

  29. Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom. Control 48(6), 988–1001 (2003)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA

    Alejandro Cornejo & Radhika Nagpal

Authors
  1. Alejandro Cornejo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Radhika Nagpal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alejandro Cornejo .

Editor information

Editors and Affiliations

  1. Department of Computer Engineering, Bogazici University, Istanbul, Turkey

    H. Levent Akin

  2. Department of Computer Science and Engineering, Texas A&M University, College Station, Texas, USA

    Nancy M. Amato

  3. Department of Computer Science and Engineering, University of Minnesota, Minneapolis, Minnesota, USA

    Volkan Isler

  4. Department of Information and Computing Sciences, Utrecht University, Utrecht, Utrecht, The Netherlands

    A. Frank van der Stappen

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Cornejo, A., Nagpal, R. (2015). Distributed Range-Based Relative Localization of Robot Swarms. In: Akin, H., Amato, N., Isler, V., van der Stappen, A. (eds) Algorithmic Foundations of Robotics XI. Springer Tracts in Advanced Robotics, vol 107. Springer, Cham. https://doi.org/10.1007/978-3-319-16595-0_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-16595-0_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16594-3

  • Online ISBN: 978-3-319-16595-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation