Skip to main content
Log in

Adaptive practical predefined-time neural tracking control for multi-joint uncertain robotic manipulators with input saturation

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Predefined-time stability contributes to constraining the tracking time of robotic manipulators, but the stringent judgment conditions restrict its practical application. This paper studies an adaptive practical predefined-time neural control scheme for uncertain multi-joint robotic manipulators with input saturation. First, a practical predefined-time stability criterion is established to ensure the closed-loop stability of uncertain systems. Then, the unknown robotic dynamic model can be approximated by radial basis function neural networks. Meanwhile, the input saturation of the robotic manipulator is compensated by introducing an adaptive term. Based on the constructed stability criterion, the proposed controller is proved to guarantee that the tracking error of the system converges to a small neighborhood of the origin within a predefined time and is independent of the initial state. Finally, the effectiveness of the proposed control scheme is emphasized by numerical simulations and experiments of a two-joint and a nine-joint robotic manipulator, respectively.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Data availability

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

References

  1. Pan Y, Du P, Xue H, Lam HK (2020) Singularity-free fixed-time fuzzy control for robotic systems with user-defined performance. IEEE Trans Fuzzy Syst 29(8):2388–2398

    Google Scholar 

  2. Wang H, Liu S, Yang X (2020) Adaptive neural control for non-strict-feedback nonlinear systems with input delay. Inf Sci 514:605–616

    MathSciNet  MATH  Google Scholar 

  3. Sai H, Xu Z, Xu C, Wang X, Wang K, Zhu L (2022) Adaptive local approximation neural network control based on extraordinariness particle swarm optimization for robotic manipulators. J Mech Sci Technol 36(3):1469–1483

    Google Scholar 

  4. Haimo VT (1986) Finite time controllers. SIAM J Control Optim 24(4):760–770

    MathSciNet  MATH  Google Scholar 

  5. Shao K, Zheng J, Huang K, Wang H, Man Z, Fu M (2019) Finite-time control of a linear motor positioner using adaptive recursive terminal sliding mode. IEEE Trans Industr Electron 67(8):6659–6668

    Google Scholar 

  6. Zhihong M, O’day M, Yu X (1999) A robust adaptive terminal sliding mode control for rigid robotic manipulators. J Intell Robot Syst 24(1):23–41

  7. Yu X, Zhihong M (2002) Fast terminal sliding-mode control design for nonlinear dynamical systems. IEEE Trans Circuits Syst I Fundam Theory Appl 49(2):261–264

    MathSciNet  MATH  Google Scholar 

  8. Yang L, Yang J (2011) Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems. Int J Robust Nonlinear Control 21(16):1865–1879

    MathSciNet  MATH  Google Scholar 

  9. Polyakov A (2011) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57(8):2106–2110

    MathSciNet  MATH  Google Scholar 

  10. Zuo Z (2015) Non-singular fixed-time terminal sliding mode control of non-linear systems. IET Control Theory Appl 9(4):545–552

    MathSciNet  Google Scholar 

  11. Zuo Z (2015) Nonsingular fixed-time consensus tracking for second-order multi-agent networks. Automatica 54:305–309

    MathSciNet  MATH  Google Scholar 

  12. Zuo Z, Han QL, Ning B, Ge X, Zhang XM (2018) An overview of recent advances in fixed-time cooperative control of multiagent systems. IEEE Trans Industr Inf 14(6):2322–2334

    Google Scholar 

  13. Ning B, Han QL, Zuo Z, Ding L, Lu Q, Ge X (2022) Fixed-time and prescribed-time consensus control of multi-agent systems and its applications: a survey of recent trends and methodologies. IEEE Trans Ind Inf

  14. Su Y, Zheng C, Mercorelli P (2020) Robust approximate fixed-time tracking control for uncertain robot manipulators. Mech Syst Signal Process 135:106379

    Google Scholar 

  15. Sai H, Xu Z, Xia C, Sun X (2022) Approximate continuous fixed-time terminal sliding mode control with prescribed performance for uncertain robotic manipulators. Nonlinear Dyn 1–18

  16. Yang P, Su Y (2021) Proximate fixed-time prescribed performance tracking control of uncertain robot manipulators. IEEE/ASME Trans Mechatron

  17. Ba D, Li YX, Tong S (2019) Fixed-time adaptive neural tracking control for a class of uncertain nonstrict nonlinear systems. Neurocomputing 363:273–280

    Google Scholar 

  18. Wang F, Lai G (2020) Fixed-time control design for nonlinear uncertain systems via adaptive method. Syst Control Lett 140:104704

    MathSciNet  MATH  Google Scholar 

  19. Hu Y, Yan H, Zhang H, Wang M, Zeng L (2022) Robust adaptive fixed-time sliding-mode control for uncertain robotic systems with input saturation. IEEE Trans Cybern 53(4):2636–2646

    Google Scholar 

  20. Chen M, Wang H, Liu X (2021) Adaptive practical fixed-time tracking control with prescribed boundary constraints. IEEE Trans Circuits Syst I Regul Pap 68(4):1716–1726

    MathSciNet  Google Scholar 

  21. Sánchez-Torres JD, Gómez-Gutiérrez D, López E, Loukianov AG (2018) A class of predefined-time stable dynamical systems. IMA J Math Control Inf 35(Supplement_1):i1–i29

  22. Muñoz-Vázquez AJ, Sánchez-Torres JD, Gutiérrez-Alcalá S, Jiménez-Rodríguez E, Loukianov AG (2019) Predefined-time robust contour tracking of robotic manipulators. J Franklin Inst 356(5):2709–2722

    MathSciNet  MATH  Google Scholar 

  23. Munoz-Vazquez AJ, Sánchez-Torres JD, Jimenez-Rodriguez E, Loukianov AG (2019) Predefined-time robust stabilization of robotic manipulators. IEEE/ASME Trans Mechatron 24(3):1033–1040

    MATH  Google Scholar 

  24. Ni J, Liu L, Tang Y, Liu C (2019) Predefined-time consensus tracking of second-order multiagent systems. IEEE Trans Syst Man Cybern Syst 51(4):2550–2560

    Google Scholar 

  25. Sai H, Li Y, He S, Zhang E, Zhu M, Xu Z (2022) A nine-degree-of-freedom modular redundant robotic manipulator: development and experimentation. Proc Inst Mech Eng Part C J Mech Eng Sci 09544062221139968

  26. Xie Z, Jin L (2022) Hybrid control of orientation and position for redundant manipulators using neural network. IEEE Trans Syst Man Cybern Syst

  27. Muñoz-Vázquez AJ, Sánchez-Torres JD (2020) Predefined-time control of cooperative manipulators. Int J Robust Nonlinear Control 30(17):7295–7306

    MathSciNet  Google Scholar 

  28. Shuzhi SG, Hang CC, Woon L (1997) Adaptive neural network control of robot manipulators in task space. IEEE Trans Ind Electron 44(6):746–752

    Google Scholar 

  29. Aldana-López R, Gómez-Gutiérrez D, Jiménez-Rodríguez E, Sánchez-Torres JD, Defoort M (2019) Enhancing the settling time estimation of a class of fixed-time stable systems. Int J Robust Nonlinear Control 29(12):4135–4148

    MathSciNet  MATH  Google Scholar 

  30. Sánchez-Torres JD, Defoort M, Munoz-Vázquez AJA (2018) Second order sliding mode controller with predefined-time convergence. In: 15th International conference on electrical engineering, computing science and automatic control (CCE). IEEE 2018:1–4

  31. Wu C, Yan J, Shen J, Wu X, Xiao B (2021) Predefined-time attitude stabilization of receiver aircraft in aerial refueling. IEEE Trans Circuits Syst II Express Briefs 68(10):3321–3325

    Google Scholar 

  32. Wang Z, Liang B, Sun Y, Zhang T (2019) Adaptive fault-tolerant prescribed-time control for teleoperation systems with position error constraints. IEEE Trans Ind Inf 16(7):4889–4899

    Google Scholar 

  33. Liu B, Hou M, Wu C, Wang W, Wu Z, Huang B (2021) Predefined-time backstepping control for a nonlinear strict-feedback system. Int J Robust Nonlinear Control 31(8):3354–3372

    MathSciNet  Google Scholar 

  34. Sai H, Xu Z, He S, Zhang E, Zhu L (2022) Adaptive nonsingular fixed-time sliding mode control for uncertain robotic manipulators under actuator saturation. ISA Trans 123:46–60

    Google Scholar 

  35. Zhu G, Du J (2020) Robust adaptive neural practical fixed-time tracking control for uncertain Euler–Lagrange systems under input saturations. Neurocomputing 412:502–513

    Google Scholar 

  36. Jia S, Shan J (2019) Finite-time trajectory tracking control of space manipulator under actuator saturation. IEEE Trans Ind Electron 67(3):2086–2096

    Google Scholar 

  37. Jiménez-Rodríguez E, Loukianov AG, Sánchez-Torres JD (2017) A second order predefined-time control algorithm. In: 2017 14th international conference on electrical engineering, computing science and automatic control (CCE). IEEE, pp 1–6

  38. Zhang N, Wang S, Hou Y, Zhang L (2020) A robust predefined-time stable tracking control for uncertain robot manipulators. IEEE Access 8:188600–188610

    Google Scholar 

  39. Wu Y, Li G, Zuo Z, Liu X, Xu P (2020) Practical fixed-time position tracking control of permanent magnet DC torque motor systems. IEEE/ASME Trans Mechatron 26(1):563–573

    Google Scholar 

  40. Bateman H (1953) Higher transcendental functions [volumes i-iii]. vol. 1. McGraw-Hill Book Company

  41. Jin X (2018) Adaptive fixed-time control for MIMO nonlinear systems with asymmetric output constraints using universal barrier functions. IEEE Trans Autom Control 64(7):3046–3053

    MathSciNet  MATH  Google Scholar 

  42. Qian C, Lin W (2001) Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Syst Control Lett 42(3):185–200

    MathSciNet  MATH  Google Scholar 

  43. Sciavicco L, Siciliano B (2001) Modelling and control of robot manipulators. Springer

  44. Jing C, Xu H, Niu X (2019) Adaptive sliding mode disturbance rejection control with prescribed performance for robotic manipulators. ISA Trans 91:41–51

    Google Scholar 

  45. Sai H, Xu Z, Han T, Wang X, Li H (2022) Observer-based free-will arbitrary time sliding mode control for uncertain robotic manipulators. J Vib Control 10775463221138327

  46. Ge SS, Hang CC, Lee TH, Zhang T (2013) Stable adaptive neural network control, vol 13. Springer

  47. Wen C, Zhou J, Liu Z, Su H (2011) Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance. IEEE Trans Autom Control 56(7):1672–1678

    MathSciNet  MATH  Google Scholar 

  48. Sai H, Xu Z, Xu C, Wang X, Wang K, Zhu L (2022) Adaptive local approximation neural network control based on extraordinariness particle swarm optimization for robotic manipulators. J Mech Sci Technol 36(3):1469–1483

    Google Scholar 

  49. Chang W, Li Y, Tong S (2018) Adaptive fuzzy backstepping tracking control for flexible robotic manipulator. IEEE/CAA J Autom Sin 8(12):1923–1930

    MathSciNet  Google Scholar 

  50. Chen B, Liu X, Liu K, Lin C (2009) Direct adaptive fuzzy control of nonlinear strict-feedback systems. Automatica 45(6):1530–1535

    MathSciNet  MATH  Google Scholar 

  51. Zhang L, Wang Y, Hou Y, Li H (2019) Fixed-time sliding mode control for uncertain robot manipulators. IEEE Access 7:149750–149763

    Google Scholar 

  52. Jin L, Zhang F, Liu M, Xu SSD (2022) Finite-time model predictive tracking control of position and orientation for redundant manipulators. IEEE Trans Ind Electron

  53. Li R, Qiao H (2019) A survey of methods and strategies for high-precision robotic grasping and assembly tasks-some new trends. IEEE/ASME Trans Mechatron 24(6):2718–2732

    Google Scholar 

  54. Sun W, Diao S, Su SF, Sun ZY (2021) Fixed-time adaptive neural network control for nonlinear systems with input saturation. IEEE Trans Neural Netw Learn Syst

  55. Van M (2019) An enhanced tracking control of marine surface vessels based on adaptive integral sliding mode control and disturbance observer. ISA Trans 90:30–40

    Google Scholar 

  56. Santos JC, Gouttefarde M, Chemori A (2022) A nonlinear model predictive control for the position tracking of cable-driven parallel robots. IEEE Trans Robot 38(4):2597–2616

    Google Scholar 

  57. Wu Y, Wang Y (2020) Asymptotic tracking control of uncertain nonholonomic wheeled mobile robot with actuator saturation and external disturbances. Neural Comput Appl 32:8735–8745

    Google Scholar 

  58. Wang Y, Zhu K, Chen B, Jin M (2020) Model-free continuous nonsingular fast terminal sliding mode control for cable-driven manipulators. ISA Trans 98:483–495

    Google Scholar 

  59. Kong L, He W, Yang W, Li Q, Kaynak O (2020) Fuzzy approximation-based finite-time control for a robot with actuator saturation under time-varying constraints of work space. IEEE Trans Cybern 51(10):4873–4884

    Google Scholar 

Download references

Acknowledgements

This work is partially supported by the National Natural Science Foundation of China (11972343).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhenbang Xu.

Ethics declarations

Conflict of interest

The authors declare no potential conflict of interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file 1 (mp4 17929 KB)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sai, H., Xu, Z. & Zhang, E. Adaptive practical predefined-time neural tracking control for multi-joint uncertain robotic manipulators with input saturation. Neural Comput & Applic 35, 20423–20440 (2023). https://doi.org/10.1007/s00521-023-08797-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-023-08797-2

Keywords

Navigation