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Adaptive synchronized tracking of heterogeneous spherical robots using distributed hierarchical sliding surfaces under a directed graph

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Abstract

This paper addresses an adaptive synchronized tracking problem of multiple spherical robots with heterogeneous nonlinearities and uncertain rolling resistances under directed networks. A dynamic leader is considered, and its information has been accessed by only a small fraction of follower robots. The main contribution of this paper is to present distributed hierarchical sliding surfaces in consideration of underactuated characteristics of spherical robots so that all followers track a dynamic leader and the swing-up angle of each follower tracks its swing-up balance angle in a fully distributed fashion. Based on these surfaces, we design an adaptive synchronized tracking algorithm with distributed estimators for estimating the leader signal’s velocity and the swing-up balance angular velocity, and the adaptive laws for estimating rolling resistances. The stability of the overall closed-loop system is analyzed in the Lyapunov sense. A simulation result is given to illustrate the effectiveness of the proposed methodology.

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References

  1. Armour, R.H., Vincent, J.F.V.: Rolling in nature and robotics: a review. J. Bion. Eng. 3(4), 195–208 (2006)

    Article  Google Scholar 

  2. Zhan, Q., Zengbo, L., Cai, Y.: A back-stepping based trajectory tracking controller for a non-chained nonholonomic spherical robot. Chin. J. Aeronaut. 21(5), 472–480 (2008)

    Article  Google Scholar 

  3. Cai, Y., Zhan, Q., Xi, X.: Path tracking control of a spherical mobile robot. Mech. Mach. Theory 51, 58–73 (2012)

    Article  Google Scholar 

  4. Zheng, M., Zhan, Q., Liu, J., Cai, Y.: Control of a spherical robot: path following based on nonholonomic kinematics and dynamics. Chin. J. Aeronaut. 24(3), 337–345 (2011)

    Article  Google Scholar 

  5. Yu, T., Sun, H., Jia, Q., Zhao, W.: Path following control of a spherical robot rolling on an inclined plane. Sens. Transducers 21, 42–47 (2013)

    Google Scholar 

  6. Wang, L., Zhao, B.: Dynamic modeling and control strategy for turning in place motion of a two-coaxial pendulums driven spherical inspector based on stick-slip principle. Mech. Mach. Theory 83, 69–80 (2015)

    Article  Google Scholar 

  7. Yue, M., Liu, B.: Adaptive control of an underactuated spherical robot with a dynamic stable equilibrium point using hierarchical sliding mode approach. Int. J. Adapt. Control Signal Process. 28(6), 523–535 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Yue, M., Liu, B., An, C., Sun, X.: Extended state observer-based adaptive hierarchical sliding mode control for longitudinal movement of a spherical robot. Nonlinear Dyn. 78(2), 1233–1244 (2014)

    Article  MathSciNet  Google Scholar 

  9. Cao, Y., Yu, W., Ren, W., Chen, G.: An overview of recent progress in the study of distributed multi-agent coordination. IEEE Trans. Ind. Inform. 9(1), 427–438 (2013)

    Article  Google Scholar 

  10. Peng, Z., Wang, D., Wang, H., Wang, W.: Distributed coordinated tracking of multiple autonomous underwater vehicles. Nonlinear Dyn. 78(2), 1261–1276 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ghommam, J., Mehrjerdi, H., Saad, M., Mnif, F.: Formation path following control of unicycle-type mobile robots. J. Robot. Auton. Syst. 58(5), 727–736 (2010)

    Article  Google Scholar 

  12. Ghommam, J., Mehrjerdi, H., Mnif, F., Saad, M.: Cascade design for formation control of nonholonomic systems in chanined form. J. Frankl. Inst. 348(6), 973–998 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Dong, W., Farrell, J.A.: Formation control of multiple underactuated surface vessels. IET Control Theory Appl. 2(12), 1077–1085 (2008)

    Article  MathSciNet  Google Scholar 

  14. Dong, W., Farrell, J.A.: Cooperative control of multiple nonholonomic mobile agents. IEEE Trans. Autom. Control 53(6), 1434–1448 (2008)

    Article  MathSciNet  Google Scholar 

  15. Xie, S., Chen, J., Luo, J., Li, H., Yao, J., Gu, J.: Dynamic analysis and control system of spherical robot for polar region scientific research. In: Proceeding of the IEEE international conference on robotics and biomimetics, pp 2540–2545 (2013)

  16. Michaud, F., Laplante, J.F., Larouche, H., Duquette, A., Caron, S., Letourneau, D., Masson, P.: Autonomous spherical mobile robot for child-development studies. IEEE Trans. Syst. Man Cybern. A Syst. Hum. 35(4), 471–480 (2005)

    Article  Google Scholar 

  17. Wang, W., Liu, X.D., Yi, J.Q.: Structure design of two types of sliding-mode controllers for a class of under-actuated mechanical systems. IET Control Theory Appl. 1(1), 163–172 (2007)

    Article  MathSciNet  Google Scholar 

  18. Qian, D., Liu, X., Yi, J.: Adaptive control based on hierarchical sliding mode for under-actuated systems. In: International conference on mechatronics and automation, pp. 1050–1055 (2012)

  19. Wang, C.L., Chiang, C.C., Yeh, Y.W.: Adaptive fuzzy hierarchical sliding-mode control for the trajectory tracking of uncertain underactuated nonlinear dynamic systems. IEEE Trans. Fuzzy Syst. 22(2), 286–299 (2014)

  20. Ren, W.: On consensus algorithms for double-integrator dynamics. IEEE Trans. Autom. Control 53, 1053–1059 (2008)

    Article  MathSciNet  Google Scholar 

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Acknowledgments

This research was supported by the MSIP (Ministry of Science, ICT and Future Planning), Korea, under the ITRC (Information Technology Research Center) support program (IITP-2015-H8501-15-1018) supervised by the IITP (Institute for Information & communications Technology Promotion), by the Human Resources Development (No. 20154030200860) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Trade, Industry and Energy, and by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2014R1A1A2055753).

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  1. School of Electrical and Electronics Engineering, Chung-Ang University, 84 Heukseok-Ro, Dongjak-Gu, Seoul, 156-756, Republic of Korea

    Yun Ho Choi & Sung Jin Yoo

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  1. Yun Ho Choi
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  2. Sung Jin Yoo
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Correspondence to Sung Jin Yoo.

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Choi, Y.H., Yoo, S.J. Adaptive synchronized tracking of heterogeneous spherical robots using distributed hierarchical sliding surfaces under a directed graph. Nonlinear Dyn 85, 913–922 (2016). https://doi.org/10.1007/s11071-016-2732-2

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  • DOI: https://doi.org/10.1007/s11071-016-2732-2

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