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Cooperative learning control of uncertain nonholonomic wheeled mobile robots with state constraints

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Abstract

This article investigates the cooperative tracking control of multiple homogeneous uncertain nonholonomic wheeled mobile robots with state constraints. Transforming each mobile robot system into a chained form, a cooperative learning control scheme based on the adaptive neural network is proposed. Firstly, a virtual control law is designed for the kinematic model of the constrained chain system combined with the barrier Lyapunov function (BLF). Then, radial basis function neural networks (RBF NNs) are exploited to deal with the unknown nonlinear dynamics in the mobile robot system, a robust term is introduced to compensate for the NN approximation errors and the external disturbance, and the Moore–Penrose inverse is adopted to avoid the violation of state constraints. Communication network is used to realize the online sharing of NN weights of each mobile robot individuals, such that locally accurate identification of the unknown nonlinear dynamics with common optimal weights can be obtained. As a result, the learned knowledge can be reused in the cooperative learning control tasks and the trained network model has better generalization capabilities than the normal decentralized learning control. Finally, numerical simulation verifies the effectiveness of the control scheme.

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References

  1. Shao J, Xie G, Wang L (2007) Leader-following formation control of multiple mobile vehicles. IET Control Theory Appl 1(2):545–552. https://doi.org/10.1049/iet-cta:20050371

    Article  Google Scholar 

  2. Defoort M, Floquet T, Kokosy A, Perruquetti W (2008) Sliding-mode formation control for cooperative autonomous mobile robots. IEEE Trans Ind Electron 55(11):3944–3953. https://doi.org/10.1109/TIE.2008.2002717

    Article  Google Scholar 

  3. Balch T, Arkin RC (1998) Behavior-based formation control for multirobot teams. IEEE Trans Robot Autom 14(6):926–939. https://doi.org/10.1109/70.736776

    Article  Google Scholar 

  4. Ghommam J, Mehrjerdi H, Saad M, Mnif F (2010) Formation path following control of unicycle-type mobile robots. Robot Auton Syst 58(5):727–736. https://doi.org/10.1016/j.robot.2009.10.007

    Article  Google Scholar 

  5. Cao K-C, Jiang B, Yue D (2017) Cooperative path following control of multiple nonholonomic mobile robots. ISA Trans 71:161–169. https://doi.org/10.1016/j.isatra.2017.06.028

    Article  Google Scholar 

  6. Han SI (2018) Prescribed consensus and formation error constrained finite-time sliding mode control for multi-agent mobile robot systems. IET Control Theory Appl 12(2):282–290. https://doi.org/10.1049/iet-cta.2017.0351

    Article  MathSciNet  Google Scholar 

  7. Desai JP, Ostrowski JP, Kumar V (2001) Modeling and control of formations of nonholonomic mobile robots. IEEE Trans Robot Autom 17(6):905–908. https://doi.org/10.1109/70.976023

    Article  Google Scholar 

  8. Consolini L, Morbidi F, Prattichizzo D, Tosques M (2008) Leader-follower formation control of nonholonomic mobile robots with input constraints. Automatica 44(5):1343–1349. https://doi.org/10.1016/j.automatica.2007.09.019

    Article  MathSciNet  MATH  Google Scholar 

  9. Peng Z, Yang S, Wen G, Rahmani A (2014) Distributed consensus-based robust adaptive formation control for nonholonomic mobile robots with partial known dynamics. Math Probl Eng. https://doi.org/10.1155/2014/670497

    Article  MathSciNet  MATH  Google Scholar 

  10. Peng Z, Wen G, Rahmani A, Yu Y (2015) Distributed consensus-based formation control for multiple nonholonomic mobile robots with a specified reference trajectory. Int J Syst Sci 46(8):1447–1457. https://doi.org/10.1080/00207721.2013.822609

    Article  MathSciNet  MATH  Google Scholar 

  11. Peng Z, Yang S, Wen G, Rahmani A, Yu Y (2016) Adaptive distributed formation control for multiple nonholonomic wheeled mobile robots. Neurocomput 173:1485–1494. https://doi.org/10.1016/j.neucom.2015.09.022

    Article  Google Scholar 

  12. Dierks T, Jagannathan S (2009) Neural network control of mobile robot formations using RISE feedback. IEEE Trans Syst Man, Cybern, Part B: Cybern 39(2):332–347. https://doi.org/10.1109/TSMCB.2008.2005122

    Article  MATH  Google Scholar 

  13. Li Z, Yuan W, Chen Y, Ke F, Chu X, Chen CLP (2018) Neural-dynamic optimization-based model predictive control for tracking and formation of nonholonomic multirobot systems. IEEE Trans Neural Netw Learn Syst 29(12):6113–6122. https://doi.org/10.1109/TNNLS.2018.2818127

    Article  Google Scholar 

  14. Dong W, Farrell JA (2009) Decentralized cooperative control of multiple nonholonomic dynamic systems with uncertainty. Automatica 45(3):706–710. https://doi.org/10.1016/j.automatica.2008.09.015

    Article  MathSciNet  MATH  Google Scholar 

  15. Wu H-M, Karkoub M, Hwang C-L (2015) Mixed fuzzy sliding-mode tracking with backstepping formation control for multi-nonholonomic mobile robots subject to uncertainties: category (3), (5). J Intell Robot Syst: Theory Appl 79(1):73–86. https://doi.org/10.1007/s10846-014-0131-9

    Article  Google Scholar 

  16. Cheng Y, Jia R, Du H, Wen G, Zhu W (2018) Robust finite-time consensus formation control for multiple nonholonomic wheeled mobile robots via output feedback. Int J Robust Nonlinear Control 28(6):2082–2096. https://doi.org/10.1002/rnc.4002

    Article  MathSciNet  MATH  Google Scholar 

  17. Do KD, Pan J (2007) Nonlinear formation control of unicycle-type mobile robots. Robot Auton Syst 55(3):191–204. https://doi.org/10.1016/j.robot.2006.09.001

    Article  Google Scholar 

  18. Wang G, Wang C, Du Q, Li L, Dong W (2016) Distributed cooperative control of multiple nonholonomic mobile robots. J Intell Robot Syst: Theory Appl 83(3–4):525–541. https://doi.org/10.1007/s10846-015-0316-x

    Article  Google Scholar 

  19. Dierks T, Jagannathan S Control of nonholonomic mobile robot formations: Backstepping kinematics into dynamics. In: 16th IEEE International Conference on Control Applications, CCA 2007. Part of IEEE Multi-conference on Systems and Control, October 1, 2007 - October 3, 2007, Singapore, 2007. Proceedings of the IEEE International Conference on Control Applications. Institute of Electrical and Electronics Engineers Inc., pp 94-99. https://doi.org/10.1109/CCA.2007.4389212

  20. Dierks T, Jagannathan S (2009) Asymptotic adaptive neural network tracking control of nonholonomic mobile robot formations. J Intell Robot Syst: Theory Appl 56(1–2):153–176. https://doi.org/10.1007/s10846-009-9336-8

    Article  MATH  Google Scholar 

  21. Peng Z, Wen G, Yang S, Rahmani A (2016) Distributed consensus-based formation control for nonholonomic wheeled mobile robots using adaptive neural network. Nonlinear Dyn 86(1):605–622. https://doi.org/10.1007/s11071-016-2910-2

    Article  MathSciNet  MATH  Google Scholar 

  22. Shojaei K (2017) Neural adaptive output feedback formation control of type (m, s) wheeled mobile robots. IET Control Theory Appl 11(4):504–515. https://doi.org/10.1049/iet-cta.2016.0952

    Article  MathSciNet  Google Scholar 

  23. Wang C, Hill DJ (2006) Learning from neural control. IEEE Trans Neural Netw 17(1):130–146. https://doi.org/10.1109/TNN.2005.860843

    Article  Google Scholar 

  24. Wu Y, Wang C (2014) Adaptive neural control and learning of affine nonlinear systems. Neural Comput Appl 25(2):309–319. https://doi.org/10.1007/s00521-013-1488-6

    Article  Google Scholar 

  25. Dai S-L, Wang C, Wang M (2014) Dynamic learning from adaptive neural network control of a class of nonaffine nonlinear systems. IEEE Trans Neural Netw Learn Syst 25(1):111–123. https://doi.org/10.1109/TNNLS.2013.2257843

    Article  Google Scholar 

  26. Wang M, Wang C, Shi P, Liu X (2016) Dynamic learning from neural control for strict-feedback systems with guaranteed predefined performance. IEEE Trans Neural Netw Learn Syst 27(12):2564–2576. https://doi.org/10.1109/TNNLS.2015.2496622

    Article  MathSciNet  Google Scholar 

  27. Chen W, Hua S, Zhang H (2015) Consensus-based distributed cooperative learning from closed-loop neural control systems. IEEE Trans Neural Netw Learn Syst 26(2):331–345. https://doi.org/10.1109/TNNLS.2014.2315535

    Article  MathSciNet  Google Scholar 

  28. Yang H, Guo M, Xia Y, Cheng L (2018) Trajectory tracking for wheeled mobile robots via model predictive control with softening constraints. IET Control Theory Appl 12(2):206–214. https://doi.org/10.1049/iet-cta.2017.0395

    Article  MathSciNet  Google Scholar 

  29. Zamani MR, Rahmani Z, Rezaie B (2020) A novel model predictive control strategy for constrained and unconstrained systems in presence of disturbance. IMA J Math Control Inf 37(1):208–225. https://doi.org/10.1093/imamci/dny046

    Article  MathSciNet  MATH  Google Scholar 

  30. Wu Y, Huang R, Li X, Liu S (2019) Adaptive neural network control of uncertain robotic manipulators with external disturbance and time-varying output constraints. Neurocomput 323:108–116. https://doi.org/10.1016/j.neucom.2018.09.072

    Article  Google Scholar 

  31. He W, Huang H, Ge SS (2017) Adaptive neural network control of a robotic manipulator with time-varying output constraints. IEEE Trans Cybern 47(10):3136–3147. https://doi.org/10.1109/TCYB.2017.2711961

    Article  Google Scholar 

  32. Tee KP, Ge SS, Tay EH (2009) Barrier Lyapunov Functions for the control of output-constrained nonlinear systems. Automatica 45(4):918–927. https://doi.org/10.1016/j.automatica.2008.11.017

    Article  MathSciNet  MATH  Google Scholar 

  33. He W, Chen Y, Yin Z (2016) Adaptive neural network control of an uncertain robot with full-state constraints. IEEE Transactions on Cybernetics 46(3):620–629. https://doi.org/10.1109/TCYB.2015.2411285

    Article  Google Scholar 

  34. A. J. Laub (2004) Matrix Analysis for Scientists and Engineers. Soc Ind Appl Math

  35. Agaev R, Chebotarev P (2006) The matrix of maximum out forests of a digraph and its applications. Autom Remote Control 61(9):1424–1450

    MATH  Google Scholar 

  36. Panteley E, Loria A, Teel A (2001) Relaxed persistency of excitation for uniform asymptotic stability. IEEE Trans Autom Control 46(12):1874–1886. https://doi.org/10.1109/9.975471

    Article  MathSciNet  MATH  Google Scholar 

  37. Chen W, Wen C, Hua S, Sun C (2014) Distributed cooperative adaptive identification and control for a group of continuous-time systems with a cooperative PE condition via consensus. IEEE Trans Autom Control 59(1):91–106. https://doi.org/10.1109/TAC.2013.2278135

    Article  MathSciNet  MATH  Google Scholar 

  38. Shojaei K, Shahri AM (2012) Adaptive robust time-varying control of uncertain non-holonomic robotic systems. IET Control Theory Appl 6(1):90–102. https://doi.org/10.1049/iet-cta.2010.0655

    Article  MathSciNet  Google Scholar 

  39. Murray RM, Sastry SS (1993) Non-holonomic motion planning: steering using sinusoids. IEEE Trans Autom Control 38(5):700–716

    Article  Google Scholar 

  40. Zhao Z, He W, Ge SS (2014) Adaptive neural network control of a fully actuated marine surface vessel with multiple output constraints. IEEE Trans Control Syst Technol 22(4):1536–1543. https://doi.org/10.1109/TCST.2013.2281211

    Article  Google Scholar 

  41. Jiang Z-P (2000) Lyapunov design of global state and output feedback trackers for non-holonomic control systems. Int J Control 73(9):744–761. https://doi.org/10.1080/00207170050029250

    Article  MathSciNet  MATH  Google Scholar 

  42. Sirouspour MR, Salcudean SE (2001) Nonlinear control of hydraulic robots. IEEE Trans Robot Autom 17(2):173–182. https://doi.org/10.1109/70.928562

    Article  Google Scholar 

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Acknowledgements

This work is supported by Science and Technology Planning Project of Guangdong Province, China [2015B010133 002, 2017B090910011].

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  1. School of Automation Science and Engineering, Institute of South China University of Technology, Guangzhou, China

    Yuxiang Wu, Yu Wang, Haoran Fang & Fuxi Wan

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  1. Yuxiang Wu
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Wu, Y., Wang, Y., Fang, H. et al. Cooperative learning control of uncertain nonholonomic wheeled mobile robots with state constraints. Neural Comput & Applic 33, 17551–17568 (2021). https://doi.org/10.1007/s00521-021-06342-7

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