Skip to main content

A Novel Recurrent Neural Network for Robot Control

  • Chapter
  • First Online:
Robot Control and Calibration

Abstract

To date, neural networks with high learning ability have been widely used in natural language processing, process control and other fields. In this chapter, a new recurrent neural network (RNN) is proposed to deal with time-varying underdetermined linear systems with disturbances, thereby achieving better control results. The related background of the underdetermined linear system is described in Sect. 3.1. In Sect. 3.2, we introduce the problem description. The theoretical analysis is discussed in Sect. 3.3. The experimental results are presented in Sect. 3.4. Finally, the conclusions and future research work are given in Sect. 3.5.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 49.99
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. Wu, D., He, Q., Luo, X., Shang, M.S., He, Y., Wang, G.Y.: A posterior-neighborhood regularized latent factor model for highly accurate web service QoS prediction. IEEE Trans. Serv. Comput. 15(2), 793–805 (2022)

    Article  Google Scholar 

  2. Luo, X., Zhou, M.C., Wang, Z.D., Xia, Y.N., Zhu, Q.S.: An effective QoS estimating scheme via alternating direction method-based matrix factorization. IEEE Trans. Serv. Comput. 12(4), 503–518 (2019)

    Article  Google Scholar 

  3. Luo, X., Zhou, M.C., Xia, Y.N., Zhu, Q.S., Ammari, A.C., Alabdulwahab, A.: Generating highly accurate predictions for missing QoS-data via aggregating non-negative latent factor models. IEEE Trans. Neural Netw. Learn. Syst. 27(3), 524–537 (2016)

    Article  MathSciNet  Google Scholar 

  4. Donoho, D., Tsaig, Y., Drori, I., Starck, J.L.: Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit. IEEE Trans. Inf. Theory. 58(2), 1094–1121 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Wang, M., Xu, W., Tang, A.: A unique “nonnegative” solution to an underdetermined system: from vectors to matrices. IEEE Trans. Signal Process. 65(13), 3551–3582 (2017)

    MathSciNet  Google Scholar 

  6. Esmaeili, H., Mahdavi-Amiri, N., Spedicato, E.: Explicit ABS solution of a class of linear inequality systems and LP problems. Bull. Iranian Math. Soc. 30(2), 21–38 (2004)

    MathSciNet  MATH  Google Scholar 

  7. Morigi, S., Sgallari, F.: A regularizing L-curve Lanczos method for underdetermined linear systems. Appl. Math. Comput. 121(1), 55–73 (2001)

    MathSciNet  MATH  Google Scholar 

  8. Hu, L., Zhang, J., Pan, X.Y., Luo, X., Yuan, H.Q.: An effective link-based clustering algorithm for detecting overlapping protein complexes in protein-protein interaction networks. IEEE Trans. Netw. Sci. Eng. 8(4), 3275–3289 (2021)

    Article  Google Scholar 

  9. Hu, L., Yang, S.C., Luo, X., Yuan, H.Q., Zhou, M.C.: A distributed framework for large-scale protein-protein interaction data analysis and prediction using MapReduce. IEEE/CAA J. Autom. Sin. 9(1), 160–172 (2022)

    Article  Google Scholar 

  10. Hu, L., Yuan, X.H., Liu, X., Xiong, S.W., Luo, X.: Efficiently detecting protein complexes from protein interaction networks via alternating direction method of multipliers. IEEE/ACM Trans. Comput. Biol. Bioinform. 16(6), 1922–1935 (2019)

    Article  Google Scholar 

  11. Wang, Z., Liu, Y., Luo, X., Wang, J.J., Gao, C., Peng, D.Z., Chen, W.: Large-scale affine matrix rank minimization with a novel nonconvex regularizer. IEEE Tran. Neural Netw. Learn. Syst. 33(9), 4661–4675 (2022)

    Article  MathSciNet  Google Scholar 

  12. Jin, L., Hu, B.: RNN models for dynamic matrix inversion: a control-theoretical perspective. IEEE Trans. Industr. Inform. 14(1), 189–199 (2017)

    Article  Google Scholar 

  13. Chen, K.: Robustness analysis of Wang neural network for online linear equation solving. Electron. Lett. 48(22), 1391–1392 (2012)

    Article  Google Scholar 

  14. Xiao, L., Liao, B., Li, S., Zhang, Z., Ding, L., Jin, L.: Design and analysis of FTZNN applied to the real-time solution of a nonstationary Lyapunov equation and tracking control of a wheeled mobile manipulator. IEEE Trans. Industr. Inform. 14(1), 98–105 (2018)

    Article  Google Scholar 

  15. Keramati, B.: An approach to the solution of linear system of equations by He’s homotopy perturbation method. Chaos Solitons Fract. 41(1), 152–156 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Cichocki, A., Ramirez-Angulo, J., Unbehauen, R.: Architectures for analog VLSI implementation of neural networks for solving linear equations with inequality constraints. Proc. IEEE Int. Sym. Circuits Syst., 1529–1532 (1992)

    Google Scholar 

  17. Wu, D., Luo, X., Shang, M., He, Y., Wang, G.Y., Zhou, M.C.: A deep latent factor model for high-dimensional and sparse matrices in recommender systems. IEEE Trans. Syst. Man Cybern. Syst. 51(7), 4285–4296 (2021)

    Article  Google Scholar 

  18. Liu, Z., Luo, X., Wang, Z., Liu, X.: Constraint-induced symmetric nonnegative matrix factorization for accurate community detection. Inf. Fusion. 89, 588–602 (2023)

    Article  Google Scholar 

  19. Wu, D., Shang, M.S., Luo, X., Wang, Z.D.: An L1-and-L2-norm-oriented latent factor model for recommender systems. IEEE Trans. Neural Netw. Learn. Syst. 33(10), 5775–5788 (2021)

    Article  Google Scholar 

  20. Hu, L., Pan, X., Tang, Z., Luo, X.: A fast Fuzzy clustering algorithm for complex networks via a generalized momentum method. IEEE Trans. Fuzzy Syst. 30(9), 3473–3485 (2022)

    Article  Google Scholar 

  21. Li, W., Luo, X., Yuan, H., Zhou, M.C.: A momentum-accelerated Hessian-vector-based latent factor analysis model. IEEE Trans. Serv. Comput. https://doi.org/10.1109/TSC.2022.3177316

  22. Xu, F., Li, Z., Shao, H., Guo, D.: New recurrent neural network for online solution of time-dependent underdetermined linear system with bound constraint. IEEE Trans. Industr. Inform. 15(4), 2167–2176 (2018)

    Article  Google Scholar 

  23. Peng, Q., Xia, Y., Zhou, M.C., Luo, X., Wang, S., Wang, Y., Wu, C., Pang, S., Lin, M.: Reliability-aware and deadline-constrained mobile service composition over opportunistic networks. IEEE Trans. Autom. Sci. Eng. 18(3), 1012–1025 (2021)

    Article  Google Scholar 

  24. Qin, W., Luo, X., Li, S., Zhou, M.: Parallel adaptive stochastic gradient descent algorithms for latent factor analysis of high-dimensional and incomplete industrial data. IEEE Trans. Autom. Sci. Eng. https://doi.org/10.1109/TASE.2023.3267609

  25. Jin, L., Zheng, X., Luo, X.: Neural dynamics for distributed collaborative control of manipulators with time delays. IEEE/CAA J. Autom. Sin. 9(5), 854–863 (2022)

    Article  Google Scholar 

  26. Jin, L., Liang, S., Luo, X., Zhou, M.: Distributed and time-delayed K-winner-take-all network for competitive coordination of multiple robots. IEEE Trans. Cybern. 53(1), 641–652 (2022)

    Article  Google Scholar 

  27. Luo, X., Zhou, M.C., Li, S., Xia, Y.N., You, Z.H., Zhu, Q.S., Leung, H.: An efficient second order approach to factorizing sparse matrices in recommender systems. IEEE Trans. Industr. Inform. 11(4), 946–956 (2015)

    Article  Google Scholar 

  28. Chen, D., Zhang, Y.: Robust zeroing neural-dynamics and its time-varying disturbances suppression model applied to mobile robot manipulators. IEEE Trans. Neural Netw. Learn. Syst. 29(9), 4385–4397 (2017)

    Article  Google Scholar 

  29. Pazos, F.A., Bhaya, A.: Control Lyapunov function design of neural networks that solve convex optimization and variational inequality problems. Neurocomputing. 72(16–18), 3863–3872 (2009)

    Article  Google Scholar 

  30. Zhao, K., Chen, L., Chen, C.L.P.: Event-based adaptive neural control of nonlinear systems with deferred constraint. IEEE Trans. Syst. Man Cybern. Syst. 52(10), 6273–6282 (2022)

    Article  Google Scholar 

  31. Jin, L., Zhang, Y., Li, S., Zhang, Y.: Noise-tolerant ZNN models for solving time-varying zero-finding problems: a control-theoretic approach. IEEE Trans. Autom. Control. 62(2), 992–997 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  32. Yan, J., Jin, L., Luo, X., Li, S.: Modified RNN for solving comprehensive Sylvester equation with TDOA application. IEEE Trans. Neural Netw. Learn. Syst. https://doi.org/10.1109/TNNLS.2023.3263565

  33. Yuan, Y., He, Q., Luo, X., Shang, M.S.: A multilayered-and-randomized latent factor model for high-dimensional and sparse matrices. IEEE Trans. Big Data. 8(3), 784–794 (2022)

    Article  Google Scholar 

  34. Wu, H., Luo, X., Zhou, M.C., Rawa, M.J., Sedraoui, K., Albeshri, A.: A PID-incorporated latent factorization of tensors approach to dynamically weighted directed network analysis. IEEE/CAA J. Autom. Sin. 9(3), 533–546 (2022)

    Article  Google Scholar 

  35. Luo, X., Wang, Z.D., Shang, M.S.: An instance-frequency-weighted regularization scheme for non-negative latent factor analysis on high-dimensional and sparse data. IEEE Trans. Syst. Man Cybern. Syst. 51(6), 3522–3532 (2021)

    Article  Google Scholar 

  36. Zhang, Y., Li, S.: A neural controller for image-based visual servoing of manipulators with physical constraints. IEEE Trans. Neural Netw. Learn. Syst. 29(11), 5419–5429 (2018)

    Article  MathSciNet  Google Scholar 

  37. Yang, C., Jiang, Y., Li, Z., He, W., Su, C.Y.: Neural control of bimanual robots with guaranteed global stability and motion precision. IEEE Trans. Industr. Inform. 13(3), 1162–1171 (2017)

    Google Scholar 

  38. Wu, D., Luo, X.: Robust latent factor analysis for precise representation of high-dimensional and sparse data. IEEE/CAA J. Autom. Sin. 8(4), 796–805 (2021)

    Article  MathSciNet  Google Scholar 

  39. Chen, M., Ma, G., Liu, W., Zeng, N., Luo, X.: An overview of data-driven battery health estimation technology for battery management system. Neurocomputing. 532, 152–169 (2023)

    Article  Google Scholar 

  40. Luo, X., Zhong, Y.R., Wang, Z.D., Li, M.Z.: An alternating-direction-method of multipliers incorporated approach to symmetric non-negative latent factor analysis. IEEE Trans. Neural Netw. Learn. Syst. https://doi.org/10.1109/TNNLS.2021.3125774

  41. Li, W., Wang, R., Luo, X., Zhou, M.: A second-order symmetric non-negative latent factor model for undirected weighted network representation. IEEE Trans. Netw. Sci. Eng. 10(2), 606–618 (2023)

    Article  MathSciNet  Google Scholar 

  42. Ferreira, L.V., Kaszkurewicz, E., Bhaya, A.: Solving systems of linear equations via gradient systems with discontinuous righthand sides: application to LS-SVM. IEEE Trans. Neural Netw. 16(2), 501–505 (2005)

    Article  Google Scholar 

  43. 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. Industr. Inform. 14(3), 921–930 (2018)

    Article  Google Scholar 

  44. Luo, X., Zhou, M., Li, S., Shang, M.: An inherently non-negative latent factor model for high-dimensional and sparse matrices from industrial applications. IEEE Trans. Industr. Inform. 14(5), 2011–2022 (2018)

    Article  Google Scholar 

  45. Qin, W.J., Wang, H.L., Zhang, F., Wang, J.J., Luo, X., Huang, T.W.: Low-rank high-order tensor completion with applications in visual data. IEEE Trans. Image Process. 31, 2433–2448 (2022)

    Article  Google Scholar 

  46. Song, Y., Zhu, Z.Y., Li, M., Yang, G.S., Luo, X.: Non-negative latent factor analysis incorporated and feature-weighted fuzzy double c-means clustering for incomplete data. IEEE Trans. Fuzzy Syst. 30(10), 4165–4176 (2022)

    Article  Google Scholar 

  47. Li, W.L., He, Q., Luo, X., Wang, Z.D.: Assimilating second-order information for building non-negative latent factor analysis-based recommenders. IEEE Trans. Syst. Man Cybern. Syst. 52(1), 485–497 (2021)

    Article  Google Scholar 

  48. Luo, X., Yuan, Y., Zhou, M.C., Liu, Z.G., Shang, M.S.: Non-negative latent factor model based on β-divergence for recommender systems. IEEE Trans. Syst. Man Cybern. Syst. 51(8), 4612–4623 (2021)

    Article  Google Scholar 

  49. Zhang, Y., Wang, Y., Jin, L., Mu, B., Zheng, H.: Different ZFs leading to various ZNN models illustrated via online solution of time-varying underdetermined systems of linear equations with robotic application. Lect. Notes Comput. Sci. 7952, 481–488 (2013)

    Article  Google Scholar 

  50. Guo, D., Li, K., Liao, B.: Bi-criteria minimization with MWVNINAM type for motion planning and control of redundant robot manipulators. Robotica. 36(5), 655–675 (2018)

    Article  Google Scholar 

  51. Hu, L., Yan, S.C., Luo, X., Zhou, M.C.: An algorithm of inductively identifying clusters from attributed graphs. IEEE Trans. Big Data. 8(2), 523–534 (2022)

    Google Scholar 

  52. Luo, X., Wu, H., Yuan, H.Q., Zhou, M.C.: Temporal pattern-aware QoS prediction via biased non-negative latent factorization of tensors. IEEE Trans. Cybern. 50(5), 1798–1809 (2020)

    Article  Google Scholar 

  53. Song, Y., Li, M., Luo, X., Yang, G.S., Wang, C.J.: Improved symmetric and nonnegative matrix factorization models for undirected, sparse and large-scaled networks: a triple factorization-based approach. IEEE Trans. Industr. Inform. 16(5), 3006–3017 (2020)

    Article  Google Scholar 

  54. Shi, X.Y., He, Q., Luo, X., Bai, Y.N., Shang, M.S.: Large-scale and scalable latent factor analysis via distributed alternative stochastic gradient descent for recommender systems. IEEE Trans. Big Data. 8(2), 420–431 (2022)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Luo, X., Li, Z., Jin, L., Li, S. (2023). A Novel Recurrent Neural Network for Robot Control. In: Robot Control and Calibration. SpringerBriefs in Computer Science. Springer, Singapore. https://doi.org/10.1007/978-981-99-5766-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-981-99-5766-8_3

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-99-5765-1

  • Online ISBN: 978-981-99-5766-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics