Advertisement

Redundancy Resolution with Periodic Input Disturbance

  • Yinyan Zhang
  • Shuai LiEmail author
  • Xuefeng Zhou
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 265)

Abstract

Input disturbances and physical constraints are important issues in the kinematic control of redundant manipulators. In this chapter, we present a novel recurrent neural network to simultaneously address the periodic input disturbance, joint angle constraint, and joint velocity constraint, and optimize a general quadratic performance index. The presented recurrent neural network applies to both regulation and tracking tasks. Theoretical analysis shows that, with the presented neural network, the end-effector tracking and regulation errors asymptotically converge to zero in the presence of both input disturbance and the two constraints. Simulation examples and comparisons with an existing controller are also presented to validate the effectiveness and superiority of the presented controller.

References

  1. 1.
    Li, S., Zhang, Y., Jin, L.: Kinematic control of redundant manipulators using neural networks. IEEE Trans. Neural Netw. Learn. Syst. 28(10), 2243–2254 (2017)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Klein, C.A., Huang, C.-H.: Review of pseudoinverse control for use with kinematically redundant manipulators. IEEE Trans. Syst. Man Cybern. SMC-13(2), 245–250 (1983)CrossRefGoogle Scholar
  3. 3.
    Liao, B., Liu, W.: Pseudoinverse-type bi-criteria minimization scheme for redundancy resolution of robot manipulators. Robotica 33(10), 2100–2113 (2015)CrossRefGoogle Scholar
  4. 4.
    Flacco, F., Luca, A.: Discrete-time redundancy resolution at the velocity level with acceleration/torque optimization properties. Robot. Auton. Syst. 70, 191–201 (2015)CrossRefGoogle Scholar
  5. 5.
    Klein, C.A., Kee, K.B.: The nature of drift in pseudoinverse control of kinematically redundant manipulators. IEEE Trans. Robot. Autom. 5(2), 231–234 (1989)CrossRefGoogle Scholar
  6. 6.
    Zhang, Y., Wang, J., Xia, Y.: A dual neural network for redundancy resolution of kinematically redundant manipulators subject to joint limits and joint velocity limits. IEEE Trans. Neural Netw. 14(3), 658–667 (2003)CrossRefGoogle Scholar
  7. 7.
    Huang, S., Peng, Y., Wei, W., Xiang, J.: Clamping weighted least-norm method for the manipulator kinematic control with constraints. Int. J. Control 89(11), 2240–2249 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Cheng, F.T., Chen, T.H., Sun, Y.Y.: Resolving manipulator redundancy under inequality constraints. IEEE Trans. Robot. Autom. 10(1), 65–71 (1994)CrossRefGoogle Scholar
  9. 9.
    Patchaikani, P.K., Behera, L., Prasad, G.: A single network adaptive critic-based redundancy resolution scheme for robot manipulators. IEEE Trans. Ind. Electron. 59(8), 3241–3253 (2012)CrossRefGoogle Scholar
  10. 10.
    He, W., Huang, B., Dong, Y., Li, Z., Su, C.: Adaptive neural network control for robotic manipulators with unknown deadzone. IEEE Trans. Cybern. 48(9), 2670–2682 (2018)CrossRefGoogle Scholar
  11. 11.
    Li, D., Liu, Y., Tong, S., Chen, C.L.P., Li, D.: Neural networks-based adaptive control for nonlinear state constrained systems with input delay. IEEE Trans. Cybern. 49(4), 1249–1258 (2019)CrossRefGoogle Scholar
  12. 12.
    Guo, D., Yan, L., Nie, Z.: Design, analysis, and representation of novel five-step dtzd algorithm for time-varying nonlinear optimization. IEEE Trans. Neural Netw. Learn. Syst. 29(9), 4248–4260 (2018)CrossRefGoogle Scholar
  13. 13.
    Yang, C., Li, Z., Cui, R., Xu, B.: Neural network-based motion control of underactuated wheeled inverted pendulum models. IEEE Trans. Neural Netw. Learn. Syst. 25(11), 2004–2016 (2014)CrossRefGoogle Scholar
  14. 14.
    Jin, L., Li, S., Hu, B., Liu, M., Yu, J.: Noise-suppressing neural algorithm for solving time-varying system of linear equations: a control-based approach. IEEE Trans. Ind. Inform. 15(1), 236–246 (2019)CrossRefGoogle Scholar
  15. 15.
    Jin, L., Li, S., Hu, B., Liu, M.: A survey on projection neural networks and their applications. Appl. Soft Comput. 76, 533–544 (2019)CrossRefGoogle Scholar
  16. 16.
    Xiao, L., Li, K., Tan, Z., Zhang, Z., Liao, B., Chen, K., Jin, L., Li, S.: Nonlinear gradient neural network for solving system of linear equations. Inf. Process. Lett. 142, 35–40 (2019)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Xiang, Q., Liao, B., Xiao, L., Lin, L., Li, S.: Discrete-time noise-tolerant Zhang neural network for dynamic matrix pseudoinversion. Soft Comput. 23(3), 755–766 (2019)zbMATHCrossRefGoogle Scholar
  18. 18.
    Xiao, L., Li, S., Yang, J., Zhang, Z.: A new recurrent neural network with noise-tolerance and finite-time convergence for dynamic quadratic minimization. Neurocomputing 285, 125–132 (2018)CrossRefGoogle Scholar
  19. 19.
    Xiao, L., Liao, B., Li, S., Chen, K.: Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations. Neural Netw. 98, 102–113 (2018)CrossRefGoogle Scholar
  20. 20.
    Xiao, L., Zhang, Z., Zhang, Z., Li, W., Li, S.: Design, verification and robotic application of a novel recurrent neural network for computing dynamic Sylvester equation. Neural Netw. 105, 185–196 (2018)CrossRefGoogle Scholar
  21. 21.
    Zhang, Z., Lu, Y., Zheng, L., Li, S., Yu, Z., Li, Y.: A new varying-parameter convergent-differential neural-network for solving time-varying convex QP problem constrained by linear-equality. IEEE Trans. Autom. Control 63(12), 4110–4125 (2018)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Jin, L., Li, S.: Nonconvex function activated zeroing neural network models for dynamic quadratic programming subject to equality and inequality constraints. Neurocomputing 267, 107–113 (2017)CrossRefGoogle Scholar
  23. 23.
    Jin, L., Li, S., Liao, B., Zhang, Z.: Zeroing neural networks: a survey. Neurocomputing 267, 597–604 (2017)CrossRefGoogle Scholar
  24. 24.
    Mao, M., Li, J., Jin, L., Li, S., Zhang, Y.: Enhanced discrete-time Zhang neural network for time-variant matrix inversion in the presence of bias noises. Neurocomputing 207, 220–230 (2016)CrossRefGoogle Scholar
  25. 25.
    Jin, L., Zhang, Y., Li, S.: Integration-enhanced Zhang neural network for real-time-varying matrix inversion in the presence of various kinds of noises. IEEE Trans. Neural Netw. Learn. Syst. 27(12), 2615–2627 (2016)CrossRefGoogle Scholar
  26. 26.
    Li, S., Li, Y.: Nonlinearly activated neural network for solving time-varying complex sylvester equation. IEEE Trans. Cybern. 44(8), 1397–1407 (2014)CrossRefGoogle Scholar
  27. 27.
    Li, S., Li, Y., Wang, Z.: A class of finite-time dual neural networks for solving quadratic programming problems and its k-winners-take-all application. Neural Netw. 39, 27–39 (2013)zbMATHCrossRefGoogle Scholar
  28. 28.
    Hopfield, J.J., Tank, D.W.: Neural’ computation of decisions in optimization problems. Biol. Cybern. 52(3), 141–152 (1985)zbMATHGoogle Scholar
  29. 29.
    Zhang, Y., Chen, S., Li, S., Zhang, Z.: Adaptive projection neural network for kinematic control of redundant manipulators with unknown physical parameters. IEEE Trans. Ind. Electron. 65(6), 4909–4920 (2017)CrossRefGoogle Scholar
  30. 30.
    Xia, Y., Feng, G., Wang, J.: A primal-dual neural network for online resolving constrained kinematic redundancy in robot motion control. IEEE Trans. Syst. Man Cybern. B Cybern. 35(1), 54–64 (2005)CrossRefGoogle Scholar
  31. 31.
    Zhang, Y., Wang, J., Xu, Y.: A dual neural network for bi-criteria kinematic control of redundant manipulators. IEEE Trans. Robot. Autom. 18(6), 923–931 (2002)CrossRefGoogle Scholar
  32. 32.
    Zhang, Y., Wang, J.: Obstacle avoidance for kinematically redundant manipulators using a dual neural network. IEEE Trans. Syst. Man Cybern. B Cybern. 34(1), 752–759 (2004)CrossRefGoogle Scholar
  33. 33.
    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)CrossRefGoogle Scholar
  34. 34.
    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)CrossRefGoogle Scholar
  35. 35.
    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)Google Scholar
  36. 36.
    Guo, D., Zhang, Y.: Acceleration-level inequality-based MAN scheme for obstacle avoidance of redundant robot manipulators. IEEE Trans. Ind. Electron. 61(12), 6903–6914 (2014)CrossRefGoogle Scholar
  37. 37.
    Zhang, Z., et al.: A varying-parameter convergent-differential neural network for solving joint-angular-drift problems of redundant robot manipulators. IEEE/ASME Trans. Mechatron. 23(2), 679–689 (2018)CrossRefGoogle Scholar
  38. 38.
    Xiao, L., et al.: 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. Ind. Inform. 14(1), 98–105 (2018)CrossRefGoogle Scholar
  39. 39.
    Zhang, Z., Beck, A., Magnenat-Thalmann, N.: Human-like behavior generation based on head-arms model for robot tracking external targets and body parts. IEEE Trans. Cybern. 45(8), 1390–1400 (2015)CrossRefGoogle Scholar
  40. 40.
    Chen, D., Zhang, Y.: A hybrid multi-objective scheme applied to redundant robot manipulators. IEEE Trans. Autom. Sci. Eng. 14(3), 1337–1350 (2017)CrossRefGoogle Scholar
  41. 41.
    Li, S., Chen, S., Liu, B., Li, Y., Liang, Y.: Decentralized kinematic control of a class of collaborative redundant manipulators via recurrent neural networks. Neurocomputing 91, 1–10 (2012)CrossRefGoogle Scholar
  42. 42.
    Li, S., He, J., Li, Y., Rafique, U.: Distributed recurrent neural networks for cooperative control of manipulators: a game-theoretic perspective. IEEE Trans. Neural Netw. Learn. Syst. 28(2), 415–426 (2017)MathSciNetCrossRefGoogle Scholar
  43. 43.
    Jin, L., Zhang, Y.: G2-type SRMPC scheme for synchronous manipulation of two redundant robot arms. IEEE Trans. Cybern. 45(2), 153–164 (2015)MathSciNetCrossRefGoogle Scholar
  44. 44.
    Hou, Z.G., Cheng, L., Tan, M.: Multicriteria optimization for coordination of redundant robots using a dual neural network. IEEE Trans. Syst. Man Cybern. B Cybern. 40(4) 1075–1087 (2010)Google Scholar
  45. 45.
    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)CrossRefGoogle Scholar
  46. 46.
    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)MathSciNetCrossRefGoogle Scholar
  47. 47.
    Jin, L., Li, S.: Distributed task allocation of multiple robots: a control perspective. IEEE Trans. Syst. Man Cybern. Syst. 48(5), 693–701 (2018)CrossRefGoogle Scholar
  48. 48.
    Wang, Z., et al.: Neural network learning adaptive robust control of an industrial linear motor-driven stage with disturbance rejection ability. IEEE Trans. Ind. Inform. 13(5), 2172–2183 (2017)CrossRefGoogle Scholar
  49. 49.
    Chen, W., Yang, J., Guo, L., Li, S.: Disturbance-observer-based control and related methods-an overview. IEEE Trans. Ind. Electron. 63(2), 1083–1095 (2016)CrossRefGoogle Scholar
  50. 50.
    Liu, F., Li, Y., Cao, Y., She, J., Wu, M.: A two-layer active disturbance rejection controller design for load frequency control of interconnected power system. IEEE Trans. Power Electorn. 31(4), 3320–3321 (2016)CrossRefGoogle Scholar
  51. 51.
    Fedele, G., Ferrise, A.: On the uncertainty on the phase of a stable linear system in the periodic disturbance cancellation problem. IEEE Trans. Autom. Control 61(9), 2720–2726 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  52. 52.
    Muramatsu, H., Katsura, S.: An Adaptive periodic-disturbance observer for periodic-disturbance suppression. IEEE Trans. Ind. Inform. 14(10), 4446–4456 (2018)CrossRefGoogle Scholar
  53. 53.
    Li, S., Zhou, M., Luo, X.: Modified primal-dual neural networks for motion control of redundant manipulators with dynamic rejection of harmonic noises. IEEE Trans. Neural Netw. Learn. Syst. 29(10), 4791–4801 (2018)MathSciNetCrossRefGoogle Scholar
  54. 54.
    Spong, M.W., Hutchinson, S., Vidyasagar, M.: Robot Modeling and Control. Wiley, New York (2006)Google Scholar
  55. 55.
    Guo, D., Zhang, Y.: A new inequality-based obstacle-avoidance MVN scheme and its application to redundant robot manipulators. IEEE Trans. Syst. Man Cybern. C Appl. Rev. 42(6), 1326–1340 (2012)CrossRefGoogle Scholar
  56. 56.
    Zhang, Z., Zheng, L., Yu, J., Li, Y., Yu, Z.: Three recurrent neural networks and three numerical methods for solving a repetitive motion planning scheme of redundant robot manipulators. IEEE/ASME Trans. Mechatron. 22(3), 1423–1434 (2017)CrossRefGoogle Scholar
  57. 57.
    Assal, S.F.M.: Learning from hint for the conservative motion of the constrained industrial redundant manipulators. Neural Comput. App. 23(6), 1649–6660 (2013)CrossRefGoogle Scholar
  58. 58.
    Kong, Y., Lu, H., Xue, Y., Xia, H.: Terminal neural computing: finite-time convergence and its applications. Neurocomputing 217, 133–141 (2016)CrossRefGoogle Scholar
  59. 59.
    Dosiek, L., Pillay, P.: Cogging torque reduction in permanent magnet machines. IEEE Trans. Ind. Appl. 43(6), 1565–1571 (2007)CrossRefGoogle Scholar
  60. 60.
    Zhang, Y., Ge, S.S.: Design and analysis of a general recurrent neural network model for time-varying matrix inversion. IEEE Trans. Neural Netw. 16(6), 1477–1490 (2005)CrossRefGoogle Scholar
  61. 61.
    Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, New York (2004)zbMATHCrossRefGoogle Scholar
  62. 62.
    Gao, X.B.: Exponential stability of globally projected dynamic systems. IEEE Trans. Neural Netw. 14(2), 426–431 (2003)Google Scholar
  63. 63.
    Oppenheim, A.V., Willsky, A.S.: Signals & Systems. Prentice-Hall, Englewood Cliffs (1997)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.College of Cyber SecurityJinan UniversityGuangzhouChina
  2. 2.School of Information Science and EngineeringLanzhou UniversityLanzhouChina
  3. 3.Guangdong Institute of Intelligent ManufacturingGuangdong Academy of ScienceGuangzhouChina

Personalised recommendations