Skip to main content

Computer Simulations of Applying Zhang Inequation Equivalency and Solver of Neurodynamics to Redundant Manipulators at Acceleration Level

  • Conference paper
  • First Online:
Neural Information Processing (ICONIP 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14447))

Included in the following conference series:

  • 651 Accesses

Abstract

An equation can be transformed into an equivalent equation at a different level, which is termed equation equivalence or even generalized to be equation equivalency. In recent years, Zhang equivalency, more specifically, Zhang equation equivalency, i.e., a new equation equivalency originated from Zhang neurodynamics, has been proposed and investigated. Referring to Zhang equivalency and doing a careful investigation, we similarly find that an inequation can also be transformed into an equivalent inequation at a different level. The novel inequation equivalency named Zhang inequation equivalency (ZIE) is investigated in this paper. Then, ZIE is applied to acceleration-level redundant manipulator motion control. The configuration adjustment and cyclic motion generation of two types of redundant manipulators are investigated and simulated. Comparative experimental results verify the validity of the proposed ZIE. In fact, ZIE can also be applied in different actual projects according to practical requirements.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Zhang, Y., Yang, M., Qiu, B., Li, J., Zhu, M.: From mathematical equivalence such as Ma equivalence to generalized Zhang equivalency including gradient equivalency. Theor. Comput. Sci. 817, 44–54 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  2. Zhang, Y., Yang, M., Huang, H., Xiao, M., Hu, H.: New discrete-solution model for solving future different-level linear inequality and equality with robot manipulator control. IEEE Trans. Ind. Inform. 15(4), 1975–1984 (2019)

    Article  Google Scholar 

  3. Li, J., Mao, M., Zhang, Y., Qiu, B.: Different-level algorithms for control of robotic systems. Appl. Math. Model. 77, 922–933 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  4. Zhang, Y., Li, Z., Yang, M., Ming, L., Guo, J.: Jerk-level Zhang Neurodynamics equivalency of bound constraints, equation constraints, and objective indices for cyclic motion of robot-arm systems. IEEE Trans. Neural Netw. Learn. Syst. 34(6), 3005–3018 (2021)

    Article  MathSciNet  Google Scholar 

  5. Tang, Z., Tan, N., Zhang, Y.: Velocity-layer Zhang equivalency for time-varying joint limits avoidance of redundant robot manipulator. IET Control Theor. Appl. 16(18), 1909–1921 (2022)

    Article  MathSciNet  Google Scholar 

  6. Zhang, Y., Chou, Y., Chen, J., Zhang, Z., Xiao, L.: Presentation, error analysis and numerical experiments on a group of 1-step-ahead numerical differentiation formulas. J. Comput. Appl. Math. 239(1), 406–414 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  7. Jin, L., Li, S., Luo, X., Li, Y., Qin, B.: Neural dynamics for cooperative control of redundant robot manipulators. IEEE Trans. Ind. Inform. 14(9), 3812–3821 (2018)

    Article  Google Scholar 

  8. Zhang, Y., He, L., Hu, C., Guo, J.: General four-step discrete-time zeroing and derivative dynamics applied to time-varying nonlinear optimization. J. Comput. Appl. Math. 347, 314–329 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhang, Y., Li, S., Kadry, S., Liao, B.: Recurrent neural network for kinematic control of redundant manipulators with periodic input disturbance and physical constraints. IEEE Trans. Cybern. 49(12), 4194–4205 (2019)

    Article  Google Scholar 

  10. Xiao, L., Zhang, Z., Li, S.: Solving time-varying system of nonlinear equations by finite-time recurrent neural networks with application to motion tracking of robot manipulators. IEEE Trans. Syst. Man Cybern. Syst. 49(11), 2210–2220 (2019)

    Article  Google Scholar 

  11. Guo, D., Xu, F., Li, Z., Nie, Z., Shao, H.: Design, verification, and application of new discrete-time recurrent neural network for dynamic nonlinear equations solving. IEEE Trans. Ind. Inform. 14(9), 3936–3945 (2018)

    Article  Google Scholar 

  12. Xiao, L., Li, K., Duan, M.: Computing time-varying quadratic optimization with finite-time convergence and noise tolerance: a unified framework for zeroing neural network. IEEE Trans. Neural Netw. Learn. Syst. 30(11), 3360–3369 (2019)

    Article  MathSciNet  Google Scholar 

  13. Zhang, Y., Ge, S.S., Lee, T.H.: A unified quadratic-programming-based dynamical system approach to joint torque optimization of physically constrained redundant manipulators. IEEE Trans. Syst. Man Cybern. B, Cybern. 34(5), 2126–2132 (2004)

    Google Scholar 

  14. Oppenheim, A.V., Willsky, A.S., Nawab, S.H.: Signals and Systems. Prentice Hall, New Jersey (1998)

    Google Scholar 

  15. Zhang, Y., Li, S., Gui, J., Luo, X.: Velocity-level control with compliance to acceleration-level constraints: a novel scheme for manipulator redundancy resolution. IEEE Trans. Ind. Inform. 14(3), 921–930 (2018)

    Article  Google Scholar 

  16. Jin, L., Li, S.: Distributed task allocation of multiple robots: a control perspective. IEEE Trans. Syst. Man Cybern. Syst. 48(5), 693–701 (2018)

    Article  Google Scholar 

  17. Zhang, Y., Zhang, Z.: Repetitive motion planning and control of redundant robot manipulators. Spinger-Verlag, Berlin (2013). https://doi.org/10.1007/978-3-642-37518-7

    Book  MATH  Google Scholar 

  18. Mathews, J.H., Fink, K.D., Nawab, S.H.: Numerical Methods Using MATLAB, 4th edn. Prentice Hall, New Jersey (2004)

    Google Scholar 

  19. Jin, L., Li, S., La, H.M., Luo, X.: Manipulability optimization of redundant manipulators using dynamic neural networks. IEEE Trans. Ind. Electron. 64(6), 4710–4720 (2017)

    Article  Google Scholar 

  20. Zhang, Z., Zhang, Y.: Acceleration-level cyclic-motion generation of constrained redundant robots tracking different paths. IEEE Trans. Syst. Man Cybern. B, Cybern. 42(4), 1257–1269 (2012)

    Google Scholar 

Download references

Acknowledgements

This work is aided by the National Natural Science Foundation of China under Grant 61976230, the Project Supported by Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme under Grant 2018, and also the Key-Area Research and Development Program of Guangzhou under Grant 202007030004.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yunong Zhang .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Lu, J., Yang, M., Tan, N., Hu, H., Zhang, Y. (2024). Computer Simulations of Applying Zhang Inequation Equivalency and Solver of Neurodynamics to Redundant Manipulators at Acceleration Level. In: Luo, B., Cheng, L., Wu, ZG., Li, H., Li, C. (eds) Neural Information Processing. ICONIP 2023. Lecture Notes in Computer Science, vol 14447. Springer, Singapore. https://doi.org/10.1007/978-981-99-8079-6_19

Download citation

  • DOI: https://doi.org/10.1007/978-981-99-8079-6_19

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-99-8078-9

  • Online ISBN: 978-981-99-8079-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics