Skip to main content
SpringerLink
Log in

Decentralized Three Dimensional Formation Building Algorithms for a Team of Nonholonomic Mobile Agents

  • Regular Papers
  • Robot and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This article studies 3D formation building in three dimensional spaces by a team of mobile robotic sensors. The multi-agent system consists of mobile robotic sensors defined by the three degrees of freedom kinematics equations with the constraints on their linear and angular velocities. First, we propose a distributed consensus-based control algorithm for the mobile agents which result in forming a desired geometric configuration in 3D environments. Then, we present a decentralized random motion coordination law for the mobile robotic sensors for the case when the agents are unaware of their positions in the configuration in three dimensional environments. The proposed algorithms use some simple consensus rules for motion coordination and building desired geometric patterns. Convergence of the mobile agents to the given configurations are shown by extensive simulations. Moreover, performance of the proposed control laws have been proved mathematically.

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

  1. K. Sakurama, Y. Kosaka, and S. Nishida, “Formation control of swarm robots with multiple proximity distance sensors,” International Journal of Control, Automation and Systems, vol. 16, no. 1, pp. 16–26, 2018.

    Article  Google Scholar 

  2. Y. Liu and R. Bucknall, “A survey of formation control and motion planning of multiple unmanned vehicles,” Robotica, pp. 1–29, 2018.

    Google Scholar 

  3. V. Nazarzehi and A. V. Savkin, “Distributed selfdeployment of mobile wireless 3d robotic sensor networks for complete sensing coverage and forming specific shapes,” Robotica, vol. 36, no. 1, pp. 1–18, 2018.

    Article  Google Scholar 

  4. K.-K. Oh and H.-S. Ahn, “Leader-follower type distancebased formation control of a group of autonomous agents,” International Journal of Control, Automation and Systems, vol. 15, no. 4, pp. 1738–1745, 2017.

    Article  Google Scholar 

  5. Z. Peng, G. Wen, A. Rahmani, and Y. Yu, “Distributed consensus-based formation control for multiple nonholonomic mobile robots with a specified reference trajectory,” International Journal of Systems Science, pp. 1–11, 2013.

    Google Scholar 

  6. T. Nguyen, H. M. La, T. D. Le, and M. Jafari, “Formation control and obstacle avoidance of multiple rectangular agents with limited communication ranges,” IEEE Trans. on Control of Network Systems, vol. 4, no. 4, pp. 680–691, Dec 2017.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Jin and N. Gans, “Collision-free formation and heading consensus of nonholonomic robots as a pose regulation problem,” Robotics and Autonomous Systems, vol. 95, pp. 25–36, 2017.

    Article  Google Scholar 

  8. W. Xie, B. Ma, T. Fernando, and H. H.-C. Iu, “A new formation control of multiple underactuated surface vessels,” International Journal of Control, vol. 91, no. 5, pp. 1011–1022, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  9. A. V. Savkin, C. Wang, A. Baranzadeh, Z. Xi, and H. T. Nguyen, “Distributed formation building algorithms for groups of wheeled mobile robots,” Robotics and Autonomous Systems, vol. 75, pp. 463–474, 2016.

    Article  Google Scholar 

  10. J. Liu, H. Ma, X. Ren, T. Shi, P. Li, and X. Ma, “The continuous-discrete pso algorithm for shape formation problem of multiple agents in two and three dimensional space,” Applied Soft Computing, 2018.

    Google Scholar 

  11. N. Moshtagh and A. Jadbabaie, “Distributed geodesic control laws for flocking of nonholonomic agents,” IEEE Trans. on Automatic Control, vol. 52, no. 4, pp. 681–686, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  12. V. Nazarzehi had and A. V. Savkin, “Decentralized navigation of nonholonomic robots for 3d formation building,” Proc., of the 2014.IEEE International Conference on Robotics and Biomimetics, IEEE, 2014.

    Google Scholar 

  13. G. Roussos, D. V. Dimarogonas, and K. J. Kyriakopoulos, “3d navigation and collision avoidance for nonholonomic aircraft-like vehicles,” International Journal of Adaptive Control and Signal Processing, vol. 24, no. 10, pp. 900–920, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  14. C. Wang, A. V. Savkin, and M. Garratt, “A strategy for safe 3d navigation of non-holonomic robots among moving obstacles,” Robotica, vol. 36, no. 2, pp. 275–297, 2018.

    Article  Google Scholar 

  15. A. Jadbabaie, J. Lin, and A. S. Morse, “Coordination of groups of mobile autonomous agents using nearest neighbor rules,” IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 988–1001, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  16. A. V. Savkin, “Coordinated collective motion of groups of autonomous mobile robots: analysis of Vicsek’s model,” IEEE Trans. on Automatic Control, vol. 49, no. 6, pp. 981–983, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  17. H. Teimoori and A. V. Savkin, “Equiangular navigation and guidance of a wheeled mobile robot based on rangeonly measurements,” Robotics and Autonomous Systems, vol. 58, no. 2, pp. 203–215, 2010.

    Article  Google Scholar 

  18. A. V. Savkin and R. J. Evans, Hybrid Dynamical Systems: Controller and Sensor Switching Problems, Birkhauser, Boston, 2002.

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chabahar Maritime and Marine University, Chabahar, Iran

    Valimohammad Nazarzehi

  2. School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, Australia

    Andrey V. Savkin

Authors
  1. Valimohammad Nazarzehi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrey V. Savkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Valimohammad Nazarzehi.

Additional information

Recommended by Associate Editor Jongrae Kim under the direction of Editor Fuchun Sun. This work was supported in part by the Australian Research Council.

Valimohammad Nazarzehihad received his Ph.D. degree in 2016 from the University of New South Wales, Australia. Currently, he is an assistant professor in the department of Electrical Engineering, Chabahr Maritime University, Iran. His research interests include decentralized control, marine control systems, and control of mobile robots.

Andrey V. Savkin received his M.S. and Ph.D. degrees from the Leningrad University, USSR, in 1987 and 1991, respectively. Since 2000, he has been a Professor with the School of Electrical Engineering and Telecommunications, the University of New South Wales, Sydney. His current research interests include robust control and filtering, hybrid dynamical systems, networked control systems, control of mobile robots.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nazarzehi, V., Savkin, A.V. Decentralized Three Dimensional Formation Building Algorithms for a Team of Nonholonomic Mobile Agents. Int. J. Control Autom. Syst. 17, 1283–1292 (2019). https://doi.org/10.1007/s12555-018-0283-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-018-0283-7

Keywords

Search

Navigation