Adaptive Kinematic Control of Redundant Manipulators

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


Redundancy resolution is of great importance in the control of manipulators. Among the existing results for handling this issue, the quadratic program approaches, which are capable of optimizing performance indices subject to physical constraints, are widely used. However, the existing quadratic program approaches require exactly knowing all the physical parameters of manipulators, the condition of which may not hold in some practical applications. This fact motivates us to consider the application of adaptive control techniques for simultaneous parameter identification and neural control. However, the inherent nonlinearity and non-smoothness of the neural model prohibits direct applications of adaptive control to this model and there has been no existing result on adaptive control of robotic arms using projection neural network (PNN) approaches with parameter convergence. Different from conventional treatments in joint angle space, we investigate the problem from the joint speed space and decouple the nonlinear part of the Jacobian matrix from the structural parameters that need to be learnt. Based on the new representation, we establish the first adaptive PNN with online learning for the redundancy resolution of manipulators with unknown physical parameters, which tackles the dilemmas in existing methods. The presented method is capable of simultaneously optimizing performance indices subject to physical constraints and handling parameter uncertainty. Theoretical results are presented to guarantee the performance of the presented neural network. Besides, simulations based on a PUMA 560 manipulator with unknown physical parameters together with the comparison with an existing PNN substantiate the efficacy and superiority of the presented neural network, and verify the theoretical results.


  1. 1.
    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
  2. 2.
    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
  3. 3.
    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
  4. 4.
    Xu, W., Zhang, J., Liang, B., Li, B.: Singularity analysis and avoidance for robot manipulators with nonspherical wrists. IEEE Trans. Ind. Electron. 63(1), 277–290 (2016)CrossRefGoogle Scholar
  5. 5.
    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
  6. 6.
    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
  7. 7.
    Liao, B., Liu, W.: Pseudoinverse-type bi-criteria minimization scheme for redundancy resolution of robot manipulators. Robotica 33(10), 2100–2113 (2015)CrossRefGoogle Scholar
  8. 8.
    Ding, H., Tso, S.K.: Redundancy resolution of robotic manipulators with neural computation. IEEE Trans. Ind. Electron. 46(1), 230–233 (1999)CrossRefGoogle Scholar
  9. 9.
    Klein, C.A., Huang, C.H.: Review of pseudoinverse control for use with kinematically redundant manipulators. IEEE Trans. Syst., Man, Cybern. (2), 245–250 (1983)CrossRefGoogle Scholar
  10. 10.
    Cherubini, A., Passama, R., Crosnier, A., Lasnier, A., Fraisse, P.: Collaborative manufacturing with physical human-robot interaction. Robot. Cim-Int. Manuf. 31, 1–13 (2016)CrossRefGoogle Scholar
  11. 11.
    Xiao, L., Zhang, Y.: Acceleration-level repetitive motion planning and its experimental verification on a six-link planar robot manipulator. IEEE Trans. Control Syst. Techno. 21(3), 906–914 (2013)CrossRefGoogle Scholar
  12. 12.
    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
  13. 13.
    Cheng, F.-T., Sheu, R.-J., Chen, T.-H.: The improved compact QP method for resolving manipulator redundancy. IEEE Trans. Syst., Man, Cybern. 25, 1521–1530 (1995)CrossRefGoogle Scholar
  14. 14.
    Zhang, Z., Li, Z., Zhang, Y., Luo, Y., Li, Y.: Neural-dynamic-method-based dual-arm CMG scheme with time-varying constraints applied to humanoid robots. IEEE Trans. Neural Netw. Learn. Syst. 26(12), 3251–3262 (2015)MathSciNetCrossRefGoogle Scholar
  15. 15.
    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
  16. 16.
    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)CrossRefGoogle Scholar
  17. 17.
    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
  18. 18.
    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
  19. 19.
    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
  20. 20.
    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
  21. 21.
    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
  22. 22.
    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
  23. 23.
    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
  24. 24.
    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
  25. 25.
    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
  26. 26.
    Jin, L., Li, S., Liao, B., Zhang, Z.: Zeroing neural networks: a survey. Neurocomputing 267, 597–604 (2017)CrossRefGoogle Scholar
  27. 27.
    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
  28. 28.
    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
  29. 29.
    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
  30. 30.
    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
  31. 31.
    Li, M., Li, Y., Ge, S.S., Lee, T.H.: Adaptive control of robotic manipulators with unified motion constraints. IEEE Trans. Syst., Man, Cybern. Syst. 47(1), 184–194 (2017)CrossRefGoogle Scholar
  32. 32.
    Wang, H.: Adaptive control of robot manipulators with uncertain kinematics and dynamics. IEEE Trans. Autom. Control 62(2), 948–954 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  33. 33.
    Aghili, F.: Adaptive control of manipulators forming closed kinematic chain with inaccurate kinematic model. IEEE/ASME Trans. Mechatron. 18(5), 1544–1554 (2013)CrossRefGoogle Scholar
  34. 34.
    Cheah, C.C., Hirano, M., Kawamura, S., Arimoto, S.: Approximate Jacobian control for robots with uncertain kinematics and dynamics. IEEE Trans. Robot. Autom. 19(4), 192–702 (2003)Google Scholar
  35. 35.
    Shimizu, M., Kakuya, H., Yoon, W.-K., Kitagaki, K., Kosuge, K.: Analytical inverse kinematic computation for 7-DOF redundant manipulators with joint limits and its application to redundancy resolution. IEEE Trans. Robot. 24(5), 1131–1141 (2008)CrossRefGoogle Scholar
  36. 36.
    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
  37. 37.
    Wang, H., Shi, P., Li, H., Zhou, Q.: Adaptive neural tracking control for a class of nonlinear systems with dynamic uncertainties. IEEE Trans. Cybern. 47(10), 3075–3087 (2017)CrossRefGoogle Scholar
  38. 38.
    Na, J., Chen, Q., Ren, X., Guo, Y.: Adaptive prescribed performance motion control of servo mechanisms with friction compensation. IEEE Trans. Ind. Electron. 61(1), 486–494 (2014)CrossRefGoogle Scholar
  39. 39.
    Li, Z., Huang, Z., He, W., Su, C.-Y.: Adaptive impedance control for an upper limb robotic exoskeleton using biological signals. IEEE Trans. Ind. Electron. 64(2), 1664–1674 (2017)CrossRefGoogle Scholar
  40. 40.
    Jaramillo-Lopez, F., Kenne, G., Lamnabhi-Lagarrigue, F.: Adaptive control for a class of uncertain nonlinear systems: application to photovoltaic control systems. IEEE Trans. Autom. Control 62(1), 393–398 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  41. 41.
    Spong, M.W., Hutchinson, S., Vidyasagar, M.: Robot Modeling and Control. Wiley, New York (2006)Google Scholar
  42. 42.
    Fang, J., Zhao, J., Mei, T., Chen, J.: Online optimization scheme with dual-mode controller for redundancy-resolution with torque constraints. Robot. Cim-Int. Manuf. 40, 44–54 (2016)CrossRefGoogle Scholar
  43. 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. Ind. Inform. 14(3), 921–930 (2018)CrossRefGoogle Scholar
  44. 44.
    Li, S., Zhang, Y., Jin, L.: Kinematic control of redundant manipulators using neural networks. IEEE Trans. Neurl Netw. Learn. Syst. 28(10), 2243–2254 (2017)MathSciNetCrossRefGoogle Scholar
  45. 45.
    Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, England (2004)zbMATHCrossRefGoogle Scholar
  46. 46.
    Xia, Y., Feng, G.: On convergence rate of projection neural networks. IEEE Trans. Autom. Control 49(1), 91–96 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  47. 47.
    OptiTrack Motion Capture Systems (2017). Available: [Online]
  48. 48.
    Salehian, S.S.M., Khoramshahi, M., Billard, A.: A dynamical system approach for softly catching a flying object: theory and experiment. IEEE Trans. Robot. 32(2), 462–471 (2016)CrossRefGoogle Scholar
  49. 49.
    Davis, E., Pounds, P.E.I.: Direct sensing of thrust and velocity for a quadrotor rotor array. IEEE Robot. Autom. Lett. 2(3), 1360–1366 (2017)CrossRefGoogle Scholar
  50. 50.
    Wang, A., Mu, B., Shi, Y.: Consensus control for a multi-agent system with integral-type event-triggering condition and asynchronous periodic detection. IEEE Trans. Ind. Electron. 64(7), 5629–5639 (2017)CrossRefGoogle Scholar
  51. 51.
    Bartelds, T., Capra, A., Hamaza, S., Stramigioli, S., Fumagalli, M.: Compliant aerial manipulators: toward a new generation of aerial robotic workers. IEEE Robot. Autom. Lett 1(1), 477–483 (2016)CrossRefGoogle Scholar
  52. 52.
    Ajoudani, A., Tsagarakis, N.G., Bicchim, A.: Tele-impedance: towards transferring human impedance regulation skills to robots. In: Proceedings of IEEE International Conference Robotics Automation, pp. 382–388 (2012)Google Scholar
  53. 53.
    Papini, G.P.R., Fontana, M., Bergamasco, M.: Desktop haptic interface for simulation of hand-tremor. IEEE Trans. Haptics 9(1), 33–42 (2016)CrossRefGoogle Scholar
  54. 54.
    Du, G., Zhang, P.: Online serial manipulator calibration based on multisensory process via extended kalman and particle filters. IEEE Trans. Ind. Electron. 61(12), 6852–6859 (2014)CrossRefGoogle Scholar
  55. 55.
    Han, J.: From PID to active disturbance rejection control. IEEE Trans. Ind. Electron. 56(3), 900–906 (2009)CrossRefGoogle Scholar
  56. 56.
    Levant, A.: Robust exact differentiation via sliding mode technique. Automatica 34(3), 379–384 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  57. 57.
    Dixon, W.E.: Adaptive regulation of amplitude limited robot manipulators with uncertain kinematics and dynamics. IEEE Trans. Autom. Control 52(3), 488–493 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  58. 58.
    Cheah, C.C., Liu, C., Slotine, J.J.E.: Adaptive jacobian tracking control of robots with uncertainties in kinematic, dynamic and actuator models. IEEE Trans. Autom. Control 51(6), 1024–1029 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  59. 59.
    Wang, H., Xie, Y.: Passivity based adaptive Jacobian tracking for free-floating space manipulators without using spacecraft acceleration. Automatica 45, 1510–1517 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  60. 60.
    Bellman, R.: Introduction to Matrix Analysis. Society for Industrial and Applied Mathematics, Philadelphia (1997)zbMATHGoogle Scholar
  61. 61.
    Khalil, H.K.: Nonlinear Systems. Prentice-Hall, New Jersey (2002)zbMATHGoogle Scholar
  62. 62.
    Gao, X.: Exponential stability of globally projected dynamic systems. IEEE Trans. Neural Netw. 14(2), 426–431 (2003)CrossRefGoogle Scholar
  63. 63.
    Adetola, V., Guay, M.: Finite-time parameter estimation in adaptive control of nonlinear systems. IEEE Trans. Autom. Control 53(3), 807–811 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  64. 64.
    Mishkov, R., Darmonsk, S.: Nonlinear adaptive control system design with asymptotically stable parameter estimation error. Int. J. Control 91(1), 181–203 (2018)MathSciNetzbMATHCrossRefGoogle Scholar
  65. 65.
    Bai, E.W., Sastry, S.S.: Persistency of excitation, sufficient richness and parameter convergence in discrete time adaptive control. Syst. Control Lett. 6, 153–163 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  66. 66.
    Dixon, W.E., Dawson, D.M., Zhang, F., Zergeroglu, E.: Global exponential tracking control of a mobile robot system via a PE condition. IEEE Trans. Syst., Man, Cybern. B, Cybern. 30(1), 129–142 (2000)CrossRefGoogle Scholar
  67. 67.
    Modares, H., Lewis, F.L., Naghibi-Sistani, M.B.: Integral reinforcement learning and experience replay for adaptive optimal control of partially-unknown constrained-input continuous-time systems. Automatica 50(1), 193–202 (2014)MathSciNetzbMATHCrossRefGoogle 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

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