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Forward kinematics analysis of parallel manipulator using modified global Newton-Raphson method

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Abstract

In order to obtain direct solutions of parallel manipulator without divergence in real time, a modified global Newton-Raphson (MGNR) algorithm was proposed for forward kinematics analysis of six-degree-of-freedom (DOF) parallel manipulator. Based on geometrical frame of parallel manipulator, the highly nonlinear equations of kinematics were derived using analytical approach. The MGNR algorithm was developed for the nonlinear equations based on Tailor expansion and Newton-Raphson iteration. The procedure of MGNR algorithm was programmed in Matlab/Simulink and compiled to a real-time computer with Microsoft visual studio.NET for implementation. The performance of the MGNR algorithms for 6-DOF parallel manipulator was analyzed and confirmed. Applying the MGNR algorithm, the real generalized pose of moving platform is solved by using the set of given positions of actuators. The theoretical analysis and numerical results indicate that the presented method can achieve the numerical convergent solution in less than 1 ms with high accuracy (1×10−9 m in linear motion and 1×10−9 rad in angular motion), even the initial guess value is far from the root.

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References

  1. MERLET J P. Parallel manipulator [M]. Norwell, MA: Kluwer Academic Publishers, 2000: 6–12.

    Google Scholar 

  2. CHIN J H, SUN Y H, CHENG Y M. Force computation and continuous path tracking for hydraulic parallel manipulators [J]. Control Engineering Practice, 2008, 16(6): 697–709.

    Article  Google Scholar 

  3. HE Qing-hua, HE Xiang-yu, ZHU Jian-xin. Fault detection of excavator’s hydraulic system based on dynamic principal component analysis [J]. Journal of Central South University of Technology, 2008, 15(5): 700–705.

    Article  Google Scholar 

  4. BANDE P, SEIBT M, UHLMANN E, SAHA S K, RAO P V M. Kinematics analysis of Dodekapod [J]. Mechanism and Machine Theory, 2005, 40(6): 740–756.

    Article  MATH  Google Scholar 

  5. JAIME G A, JOSE M R M, GURSEL A. Kinematics and singularity analyses of a 4-DOF parallel manipulator using screw theory [J]. Mechanism and Machine Theory, 2006, 41(9): 1048–1061.

    Article  MATH  MathSciNet  Google Scholar 

  6. PETUYA V, GUTIERREZ J M, ALONSO A, ALTUZARRA O, HERNANDEZ A. A numerical procedure to solve non-linear kinematic problems in spatial mechanism [J]. International Journal for Numerical Methods in Engineering, 2008, 73(6): 825–843.

    Article  MATH  MathSciNet  Google Scholar 

  7. JIN Y, CHEN I M, YANG G L. Kinematic design of a 6-DOF parallel manipulator with decoupled translation and rotation [J]. IEEE Transactions on Robotics, 2006, 22(3): 545–551.

    Article  Google Scholar 

  8. BARON L, ANGELES J. The direct kinematics of parallel manipulator under join-sensor redundancy [J]. IEEE Transactions on Robotics and Automation, 2000, 16(1): 12–19.

    Article  Google Scholar 

  9. LEE T Y, SHIM J K. Improved dialytic elimination algorithms for the forward kinematics of the general Stewart-Gough platform [J]. Mechanism and Machine Theory, 2003, 38(6): 563–577.

    Article  MATH  Google Scholar 

  10. SELFRIDGE R G, MATTHEW G K. Forward analysis of some special Stewart platforms [J]. Journal of Robotic System, 2000, 17(10): 517–526.

    Article  MATH  Google Scholar 

  11. RAGHAVAN M. The Stewart platform of general geometry has 40 configurations [J]. ASME Journal of Mechanical Design, 1993, 115(2): 227–282.

    Article  Google Scholar 

  12. KAMRA R, KOHLI D, DHINGRA A K. Forward displacement analysis of a six-DOF parallel manipulator actuated by 3R3P and 4R2P chains [J]. Mechanism and Machine Theory, 2002, 37(6): 619–637.

    Article  MATH  Google Scholar 

  13. DIDRIT O, PETITOT M, WALTER E. Guaranteed solution of direct kinematic problems for general configuration of parallel manipulator [J]. IEEE Transactions on Robotics and Automation, 1998, 14(2): 259–265.

    Article  Google Scholar 

  14. MERLET J P. Solving the forward kinematics of a Gough-type parallel manipulator with interval analysis [J]. International Journal of Robotics Research, 2004, 23(3): 221–235.

    Article  Google Scholar 

  15. JI Ping, WU Hong-tao. A closed-form forward kinematics solution for the 6-6P Stewart platform [J]. IEEE Transactions on Robotics and Automation, 2001, 17(4): 522–526.

    Article  Google Scholar 

  16. QUARTERONI A, SACCO R, SALERI F. Numerical mathematics [M]. Berlin: Springer, 2000: 80-87.

    Google Scholar 

  17. KELLEY C T. Solving nonlinear equations with Newton’s method [M]. Philadelphia: SIAM, 2003: 158-165.

  18. PARIKH P J, LAM S S Y. A hybrid strategy to solve the forward kinematics problem in parallel manipulators [J]. IEEE Transactions on Robotics, 2005, 21(1): 18–25.

    Article  Google Scholar 

  19. ROCCO V, VINCENZO P C. Accurate and fast body pose estimation by three point position data [J]. Mechanism and Machine Theory, 2007, 42(9): 1170–1183.

    Article  MATH  Google Scholar 

  20. KIM H S, CHO Y M, LEE K. Robust nonlinear task space control for 6 DOF parallel manipulator [J]. Automatic, 2005, 41(9): 1591–1600.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, 150001, China

    Chi-fu Yang  (杨炽夫), Shu-tao Zheng  (郑淑涛), Jun Jin  (靳军), Si-bin Zhu  (朱思斌) & Jun-wei Han  (韩俊伟)

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  1. Chi-fu Yang  (杨炽夫)
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  2. Shu-tao Zheng  (郑淑涛)
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  3. Jun Jin  (靳军)
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  4. Si-bin Zhu  (朱思斌)
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  5. Jun-wei Han  (韩俊伟)
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Corresponding author

Correspondence to Chi-fu Yang  (杨炽夫).

Additional information

Foundation item: Project(HgdJG00401D04) supported by National 921 Manned Space Project Foundation of China; Project(SKLRS200803B) supported by the Self-Planned Task Foundation of State Key Laboratory of Robotics and System (HIT) of China; Project(CDAZ98502211) supported by China’s “World Class University (985)” Project Foundation; Project(50975055) supported by the National Natural Science Foundation of China

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Yang, Cf., Zheng, St., Jin, J. et al. Forward kinematics analysis of parallel manipulator using modified global Newton-Raphson method. J. Cent. South Univ. Technol. 17, 1264–1270 (2010). https://doi.org/10.1007/s11771-010-0630-1

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  • DOI: https://doi.org/10.1007/s11771-010-0630-1

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