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Distributed Multi-robot Circumnavigation with Dynamic Spacing and Time Delay

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Abstract

Circumnavigation is the process whereby a single agent or multiple agents rotate around a target while preserving a circular formation, which has promising potential in real-world applications such as entrapping a malicious target or escorting an important member. For the multi-robot circumnavigation problem, spacing (i.e., the angle differences) among robots plays an important role in forming a desirable circular formation. The spacing is usually assumed to be a unified constant in most of the studies. However, when robots have different or even time-varying kinematic capabilities, a fixed and equal spacing is probably not effective for accomplishing such task as preventing an enclosed target from fleeing, and thus dynamic spacing is naturally proposed and preferred. The variations of spacing are caused by the “weights” (termed utilities) of robots. This paper relaxes the condition of piecewise constant utilities and provides the ultimate bound and the input-to-state (ISS) stability conditions for the spacing error and its dynamics respectively. In addition, since time delay is ubiquitous in practical engineering systems while seldom considered in the current studies on circumnavigation, the maximum allowable time delay within which the circumnavigation remains stable is derived using both the frequency domain method and the Lambert-W function. Finally, the theoretical results are validated by a practical simulation system.

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References

  1. Cao, Y.: Uav circumnavigating an unknown target under a gps-denied environment with range-only measurements. Automatica 55, 150–158 (2015)

    Article  MathSciNet  Google Scholar 

  2. Clarke, F.H.: Optimization and nonsmooth analysis, vol. 5. Siam (1990)

  3. Corless, R.M., Gonnet, G.H., Hare, D.E., Jeffrey, D.J., Knuth, D.E.: On the lambertw function. Adv. Comput. Math. 5(1), 329–359 (1996)

    Article  MathSciNet  Google Scholar 

  4. Dai, W., Yao, W., Luo, S., Ma, J., Wang, R., Hong, S., Zhou, Z., Li, X., Han, B., Xiao, J., et al.: Nubot team description paper (2018)

  5. Deghat, M., Shames, I., Anderson, B.D., Yu, C.: Localization and circumnavigation of a slowly moving target using bearing measurements. IEEE Trans. Autom. Control 59(8), 2182–2188 (2014)

    Article  MathSciNet  Google Scholar 

  6. Dong, Y., Hu, X.: Distributed control of periodic formations for multiple under-actuated autonomous vehicles. IET Control Theory Appl. 11(1), 66–72 (2016)

    Article  MathSciNet  Google Scholar 

  7. Dugard, L., Verriest, E.I.: Stability and control of time-delay systems, vol. 228. Springer (1998)

  8. Fax, J.A., Murray, R.M.: Information flow and cooperative control of vehicle formations. IEEE Trans. Autom. Control 35(1), 115–120 (2002)

    Google Scholar 

  9. Franchi, A., Stegagno, P., Oriolo, G.: Decentralized multi-robot encirclement of a 3D target with guaranteed collision avoidance. Auton. Robot. 40(2), 245–265 (2016). https://doi.org/10.1007/s10514-015-9450-3

    Article  Google Scholar 

  10. Goodwin, G.C., Graebe, S.F., Salgado, M.E.: Control System Design, 1st edn. Prentice Hall PTR, Upper Saddle River (2000)

  11. Gu, K., Chen, J., Kharitonov, V.L.: Stability of time-delay systems. Springer Science & Business Media (2003)

  12. Horn, R.A., Johnson, C.R.: Matrix analysis. Cambridge University Press (2012)

  13. Khalil, H.K.: Noninear systems. Prentice-Hall New Jersey 2(5), 5–1 (1996)

    Google Scholar 

  14. Krasovskii, N.N.: Stability of motion. Stanford University Press (1963)

  15. Li, R., Shi, Y., Song, Y.: Localization and circumnavigation of multiple agents along an unknown target based on bearing-only measurement: a three dimensional solution. Automatica 94, 18–25 (2018)

    Article  MathSciNet  Google Scholar 

  16. Luo, S., Yao, W., Yu, Q., Xiao, J., Lu, H., Zhou, Z.: Object Detection Based on Gpu Parallel Computing for Robocup Middle Size League. In: 2017 IEEE International Conference on Robotics and Biomimetics (ROBIO), pp. 86–91. IEEE (2017)

  17. Ma, J., Yao, W., Dai, W., Lu, H., Xiao, J., Zheng, Z.: Cooperative Encirclement Control for a Group of Targets by Decentralized Robots with Collision Avoidance. In: 2018 37Th Chinese Control Conference (CCC), pp. 6848–6853. IEEE (2018)

  18. Marshall, B.J.A., Broucke, M.E., Francis, B.A.: Formation of vehicles in cyclic pursuit. IEEE Trans. Autom. Control 49(11), 1963–1974 (2015)

    Article  MathSciNet  Google Scholar 

  19. Matveev, A.S., Semakova, A.A., Savkin, A.V.: Range-only based circumnavigation of a group of moving targets by a non-holonomic mobile robot. Automatica 65, 76–89 (2016)

    Article  MathSciNet  Google Scholar 

  20. Mesbahi, M., Egerstedt, M.: Graph theoretic methods in multiagent networks. Princeton University Press (2010)

  21. Miao, Z., Wang, Y., Fierro, R.: Cooperative circumnavigation of a moving target with multiple nonholonomic robots using backstepping design. Syst. Control Lett. 103, 58–65 (2017)

    Article  MathSciNet  Google Scholar 

  22. Oh, K.K., Park, M.C., Ahn, H.S.: A survey of multi-agent formation control. Automatica 53, 424–440 (2015)

    Article  MathSciNet  Google Scholar 

  23. Olfati-Saber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)

    Article  MathSciNet  Google Scholar 

  24. Olfati-Saber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004). https://doi.org/10.1109/TAC.2004.834113

    Article  MathSciNet  Google Scholar 

  25. Pavone, M., Frazzoli, E.: Decentralized Policies for Geometric Pattern Formation and Path Coverage. J. Dyn. Syst. Measur. Control 129(5), 633–643 (2007)

    Article  Google Scholar 

  26. Razumikhin, B.S.: On the stability of systems with a delay. Prikl. Mat. Mekh. 20(4), 500–512 (1956)

    Google Scholar 

  27. Richard, J.P.: Time-delay systems: an overview of some recent advances and open problems. Automatica 39 (10), 1667–1694 (2003)

    Article  MathSciNet  Google Scholar 

  28. Sastry, S.: Nonlinear systems: analysis, stability, and control, vol. 10. Springer Science & Business Media (2013)

  29. Tang, S., Shinzaki, D., Lowe, G.C., Clark, C.M.: Multi-robot control for circumnavigation of particle distributions. Springer Tracts Adv. Robot. 104, 149–152 (2014)

    Article  Google Scholar 

  30. Wang, C., Xie, G., Cao, M.: Forming Circle Formations of Anonymous Mobile Agents With Order Preservation. IEEE Trans. Autom. Control 58(12), 3248–3254 (2013)

    Article  Google Scholar 

  31. Wang, C., Xie, G., Cao, M.: Controlling anonymous mobile agents with unidirectional locomotion to form formations on a circle. Automatica 50(4), 1100–1108 (2014)

    Article  MathSciNet  Google Scholar 

  32. Wang, X., Zeng, Z., Cong, Y.: Multi-agent distributed coordination control: Developments and directions via graph viewpoint. Neurocomputing 199, 204–218 (2016). https://doi.org/10.1016/j.neucom.2016.03.021

    Article  Google Scholar 

  33. Xiao, J., Lu, H., Zeng, Z., Xiong, D., Yu, Q., Huang, K., Cheng, S., Yang, X., Dai, W., Ren, J., et al.: Nubot team description paper 2015. Proceedings of RoboCup (2015)

  34. Xiao, J., Xiong, D., Yao, W., Yu, Q., Lu, H., Zheng, Z.: Building Software System and Simulation Environment for Robocup Msl Soccer Robots Based on Ros and Gazebo. In: Robot Operating System (ROS), pp. 597–631. Springer (2017)

  35. Xiong, D., Xiao, J., Lu, H., Zeng, Z., Yu, Q., Huang, K., Yi, X., Zheng, Z.: The design of an intelligent soccer-playing robot. Ind. Robot. 43, 91–102 (2016). https://doi.org/10.1108/IR-05-2015-0092

    Article  Google Scholar 

  36. Yao, W., Dai, W., Xiao, J., Lu, H., Zheng, Z.: A Simulation System Based on Ros and Gazebo for Robocup Middle Size League. In: 2015 IEEE International Conference On Robotics and Biomimetics (ROBIO), pp. 54–59. IEEE (2015)

  37. Yao, W., Kapitanyuk, Y.A., Cao, M.: Robotic Path Following in 3D Using a Guiding Vector Field. In: 2018 IEEE Conference on Decision and Control (CDC), pp. 4475–4480. IEEE (2018)

  38. Yao, W., Lu, H., Zeng, Z., Xiao, J., Zheng, Z.: Distributed static and dynamic circumnavigation control with arbitrary spacings for a heterogeneous multi-robot system. Journal of Intelligent & Robotic Systems 94 (3-4), 883–905 (2019)

    Article  Google Scholar 

  39. Yao, W., Luo, S., Lu, H., Xiao, J.: Distributed circumnavigation control with dynamic spacings for a heterogeneous multi-robot system 2018. RoboCup Symposium (2018)

  40. Yao, W., Zeng, Z., Wang, X., Lu, H., Zheng, Z.: Distributed Encirclement Control with Arbitrary Spacing for Multiple Anonymous Mobile Robots. In: 2017 Chinese Control Conference (CCC). Dalian, China (2017)

  41. Yi, S., Nelson, P.W., Ulsoy, A.G.: Time-delay systems: analysis and control using the Lambert W function. World Scientific (2010)

  42. Yu, X., Liu, L.: Distributed circular formation control of ring-networked nonholonomic vehicles. Automatica 68, 92–99 (2016). https://doi.org/10.1016/j.automatica.2016.01.056

    Article  MathSciNet  Google Scholar 

  43. Zheng, R., Lin, Z., Fu, M., Sun, D.: Distributed Circumnavigation by Unicycles with Cyclic Repelling Strategies. In: 2013 9Th Asian Control Conference (ASCC), pp. 1–6. IEEE (2013)

  44. Zheng, R., Lin, Z., Fu, M., Sun, D.: Distributed control for uniform circumnavigation of ring-coupled unicycles. Automatica 53, 23–29 (2015). https://doi.org/10.1016/j.automatica.2014.11.012

    Article  MathSciNet  Google Scholar 

  45. Zheng, R., Liu, Y., Sun, D.: Enclosing a target by nonholonomic mobile robots with bearing-only measurements. Automatica 53, 400–407 (2015)

    Article  MathSciNet  Google Scholar 

  46. Zhou, Z., Yao, W., Ma, J., Lu, H., Xiao, J., Zheng, Z.: Simatch: a Simulation System for Highly Dynamic Confrontations between Multi-Robot Systems. In: 2018 Chinese Automation Congress (CAC), pp. 3934–3939. IEEE (2018)

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Acknowledgments

This work is supported by National Science Foundation of China (No. 61773393, No. U1813205).

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Authors and Affiliations

  1. Robotics Research Center, College of Intelligence Science and Technology, National University of Defense Technology, Changsha, Hunan, China

    Huimin Lu & Weijia Yao

  2. Department of Control Science and Engineering, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Liangming Chen

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  1. Huimin Lu
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Correspondence to Huimin Lu.

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Lu, H., Yao, W. & Chen, L. Distributed Multi-robot Circumnavigation with Dynamic Spacing and Time Delay. J Intell Robot Syst 99, 165–182 (2020). https://doi.org/10.1007/s10846-019-01111-0

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