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Iterative convergence control method for planar underactuated manipulator based on support vector regression model

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Abstract

An iterative convergence control method (ICCM) based on the support vector regression (SVR) is proposed to realize the position–posture control of the planar four-link underactuated manipulator with a passive second link. Firstly, the particle swarm optimization (PSO) algorithm is used to obtain the target angles of all links according to the position–posture control objective. Then, two prediction models for the coupling relationship between the first link and the passive link, and the third link and the passive link are established based on the SVR, whose optimal parameters are selected by the chaos particle swarm optimization (CPSO) algorithm. By repeatedly controlling the first link or the third link to rotate an angle which is calculated by the trained SVR model, the passive link gradually converges to its target angle after several iterations. Next, the active links are controlled to rotate to their target angles with low speeds, and the passive link does not rotate due to friction. Finally, the experimental results verify the effectiveness and feasibility of the proposed method.

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References

  1. Mohammadi, A., Maggiore, M., Consolini, L.: Dynamic virtual holonomic constraints for stabilization of closed orbits in underactuated mechanical systems. Automatica 94, 112–124 (2018)

    Article  MathSciNet  Google Scholar 

  2. Wang, Y.W., Lai, X.Z., Zhang, P.: A new control method for planar four-link underactuated manipulator based on intelligence optimization. Nonlinear Dyn. 96(1), 573–583 (2019)

    Article  Google Scholar 

  3. Donaire, A., Mehra, R., Ortega, R.: Shaping the energy of mechanical systems without solving partial differential equations. IEEE Trans. Autom. Control 61(4), 1051–1056 (2016)

    Article  MathSciNet  Google Scholar 

  4. Liu, Y.N., Xin, X.: Global motion analysis of energy-based control for 3-link planar robot with a single actuator at the first joint. Nonlinear Dyn. 88(3), 1749–1768 (2017)

    Article  Google Scholar 

  5. Cruz-Villar, C.A., Alvarez-Gallegos, J., Villarreal-Cervantes, M.G.: Concurrent redesign of an underactuated robot manipulator. Mechatronics 19(2), 178–183 (2009)

    Article  Google Scholar 

  6. Ryalat, M., Laila, D.S.: A robust IDA-PBC approach for handling uncertainties in underactuated mechanical systems. IEEE Trans. Autom. Control 63(10), 3495–3502 (2018)

    Article  MathSciNet  Google Scholar 

  7. Mahindrakar, A.D., Banavar, R.N., Reyhanoglu, M.: Controllability and point-to-point control of 3-DOF planar horizontal underactuated manipulators. Int. J. Control 78(1), 1–13 (2005)

    Article  MathSciNet  Google Scholar 

  8. Pucci, D., Romano, F., Nori, F.: Collocated adaptive control of underactuated mechanical systems. IEEE Trans. Robot. 31(6), 1527–1536 (2015)

    Article  Google Scholar 

  9. Luca, A.D., Oriolo, G.: Trajectory planning and control for planar robots with passive last joint. Int. J. Robot. Res. 21(5–6), 575–590 (2002)

    Article  Google Scholar 

  10. Lai, X.Z., She, J.H., Cao, W.H.: Stabilization of underactuated planar acrobot based on motion-state constraints. Int. J. Non-Linear Mech. 77, 342–347 (2015)

    Article  Google Scholar 

  11. Lai, X.Z., Wang, Y.W., Wu, M., Cao, W.H.: Stable control strategy for planar three-link underactuated mechanical system. IEEE/ASME Trans. Mechatron. 21(3), 1345–1356 (2016)

    Article  Google Scholar 

  12. He, G.P., Wang, Z.L., Zhang, J.: Characteristics analysis and stabilization of a planar 2R underactuated manipulator. Robotica 34(3), 584–600 (2016)

    Article  Google Scholar 

  13. Liu, Q., Yu, Y., Xia, Q.: A new fuzzy method for the motion control of underactuated robots based on genetic algorithm. In: 16th IEEE International Conference on Fuzzy Systems, pp. 999–1003 (2008)

  14. Bhave, M., Janardhanan, S., Dewan, L.: Configuration control of planar underactuated robotic manipulator using terminal sliding mode. IFAC-PapersOnLine 49(1), 148–153 (2016)

    Article  Google Scholar 

  15. Yoshikawa, T., Kobayashi, K., Watanabe, T.: Design of a desirable trajectory and convergent control for 3-DOF manipulator with a nonholonomic constraint. J. Robot. Soc. Jpn. 18(4), 584–589 (2000)

    Article  Google Scholar 

  16. Akbarimajd, A., Kia, S.: Narma-L2 controller for 2-DOF underactuated planar manipulator. In: 2010 11th International Conference on Control Automation Robotics and Vision, pp. 195–200 (2010)

  17. Duong, S.C., Kinjo, H., Uezato, E.: Intelligent control of a three-DOF planar underactuated manipulator. Artif. Life Robot. 14(2), 284–288 (2009)

    Article  Google Scholar 

  18. Seifried, R., Burkhardt, M., Iwamura, M.: Inversion based end-effector trajectory tracking of passive-joint manipulator. In: ASME Dynamic System and Control Conference Joint with the JSME 11th Motion and Vibration Conference, pp. 81–89 (2013)

  19. Bergerman, M., Lee, C., Xu, Y.: Experimental study of an underactuated manipulator. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 2, pp. 317–322 (1995)

  20. Sangwan, V., Kuebler, H., Agrawal, S.K.: Differentially flat design of underactuated planar robots: experimental results. In: 2008 IEEE International Conference on Robotics and Automation, pp. 2423–2428 (2008)

  21. Hasan, A.T.: Underactuated robot manipulator positioning control using artificial neural network inversion technique. Adv. Artif. Intell. 2012, 1–6 (2012)

    Article  Google Scholar 

  22. Al-Assadi, H.M.A.A., Yaakob, M.A.F., Ramli, M.: Learning algorithm predicts passive joint positioning for 3R underactuated robot. Procedia Eng. 41, 1316–1322 (2012)

    Article  Google Scholar 

  23. Sariyildiz, E., Ucak, K., Oke, G.: Support vector regression based inverse kinematic modeling for a 7-DOF redundant robot arm. In: 2012 International Symposium on Innovations in Intelligent Systems and Applications, pp. 1–5 (2012)

  24. Sariyildiz, E., Ucak, K., Oke, G.: A trajectory tracking application of redundant planar robot arm via support vector machines. In: International Conference on Adaptive and Intelligent Systems, pp. 192–202 (2011)

  25. Sariyildiz, E., Ucak, K., Ohnishi, K.: Intelligent systems based solutions for the kinematics problem of the industrial robot arms. In: 2013 9th Asian Control Conference, pp. 1–6 (2013)

  26. Mistry, K., Zhang, L., Neoh, S.C., Lim, C.P., Fielding, B.: A micro-GA embedded PSO feature selection approach to intelligent facial emotion recognition. IEEE Trans. Cybern. 2(8), 1496–1509 (2016)

    Google Scholar 

  27. Lee, C.S., Wang, M.H., Wang, C.S.: PSO-based fuzzy markup language for student learning performance evaluation and educational application. IEEE Trans. Fuzzy Syst. 25(6), 2618–2633 (2018)

    Article  Google Scholar 

  28. Lin, C.J., Lin, P.T.: Particle swarm optimization based feedforward controller for a XY PZT positioning stage. Mechatronics 22(5), 614–628 (2012)

    Article  Google Scholar 

  29. Hu, C., Jain, G., Zhang, P.: Data-driven method based on particle swarm optimization and k-nearest neighbor regression for estimating capacity of lithiumion battery. Appl. Energy 129, 49–55 (2014)

    Article  Google Scholar 

  30. Elish, M.O.: A comparative study of fault density prediction in aspect-oriented systems using MLP, RBF, KNN, RT, DENFIS and SVR models. Artif. Intell. Rev. 42(4), 695–703 (2014)

    Article  Google Scholar 

  31. Ahanda, J.J.B.M., Mbede, J.B., Melingui, A.: Robust adaptive control for robot manipulators: support vector regression-based command filtered adaptive backstepping approach. Robotica 36(4), 516–534 (2018)

    Article  Google Scholar 

  32. Sun, Z., Zhao, J., Shi, Z.: Soft sensing of magnetic bearing system based on support vector regression and extended Kalman filter. Mechatronics 24(3), 186–197 (2014)

    Article  Google Scholar 

  33. Smola, A.J., Schlkopf, B.: A tutorial on support vector regression. Stat. Comput. 14(3), 199–222 (2004)

    Article  MathSciNet  Google Scholar 

  34. Deng, M., Inoue, A., Zhu, Q.M.: An integrated study procedure on real-time estimation of time-varying multi-joint human arm viscoelasticity. Trans. Inst. Meas. Control 33(8), 919–941 (2011)

    Article  Google Scholar 

  35. Deng, M., Kawashima, T.: Adaptive nonlinear sensorless control for an uncertain miniature pneumatic curling rubber actuator using passivity and robust right coprime factorization. IEEE Trans. Control Syst. Technol. 24(1), 318–324 (2016)

    Article  Google Scholar 

  36. Fujita, K., Deng, M., Wakimoto, S.: A miniature pneumatic bending rubber actuator controlled by using the PSO-SVR-based motion estimation method with the generalized Gaussian kernel. Actuators 6(1), 6 (2017)

    Article  Google Scholar 

  37. Kazem, A., Sharifi, E., Hussain, F.K.: Support vector regression with chaos-based firefly algorithm for stock market price forecasting. Appl. Soft Comput. 13(2), 947–958 (2013)

    Article  Google Scholar 

  38. Chen, J.H., Yau, H.T., Hung, T.H.: Design and implementation of FPGA-based Taguchi-chaos-PSO sun tracking systems. Mechatronics 25, 55–64 (2015)

    Article  Google Scholar 

  39. Martinez, R., Alvarez, J., Orlov, Y.: Hybrid sliding-mode-based control of underactuated systems with dry friction. IEEE Trans. Ind. Electron. 55(11), 3998–4003 (2008)

    Article  Google Scholar 

  40. Shen, X., Gong, X., Cai, Y.: Normalization and integration of large-scale metabolomics data using support vector regression. Metabolomics 12(5), 1–12 (2016)

    Article  Google Scholar 

  41. Kohavi, R.: A study of cross-validation and bootstrap for accuracy estimation and model selection. In: International Joint Conference on Artificial Intelligence, pp. 1137–1143 (1995)

  42. Van Den Bergh, F., Engelbrecht, A.P.: A study of particle swarm optimization particle trajectories. Inf. Sci. 176(8), 937–971 (2006)

    Article  MathSciNet  Google Scholar 

  43. Ratnaweera, A., Halgamuge, S.K., Watson, H.C.: Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Trans. Evol. Comput. 8(3), 240–255 (2004)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation for Young Scientists of China under Grant 61903344, the National Natural Science Foundation of China under Grant 61773353, the Hubei Provincial Natural Science Foundation of China under Grant 2015CFA010 and the 111 project under Grant B17040.

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Authors and Affiliations

  1. School of Automation, China University of Geosciences, Wuhan, 430074, Hubei, China

    Ya-Wu Wang, Hui-Qing Yang & Pan Zhang

  2. Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan, 430074, Hubei, China

    Ya-Wu Wang, Hui-Qing Yang & Pan Zhang

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  1. Ya-Wu Wang
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  2. Hui-Qing Yang
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Correspondence to Ya-Wu Wang.

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Wang, YW., Yang, HQ. & Zhang, P. Iterative convergence control method for planar underactuated manipulator based on support vector regression model. Nonlinear Dyn 102, 2711–2724 (2020). https://doi.org/10.1007/s11071-020-06108-1

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