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Lie group analysis method for wall climbing robot systems

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Abstract

The motion of wall climbing robot can be regarded as the motion of gecko like crawling. Its motion can be decomposed into the motion of limbs driving the body. Previous studies were based on the method of Newton mechanics. In this paper, Lagrange mechanics method and Lie group analysis method are used to solve the problems of wall climbing robot system. Firstly, the kinetic energy, potential energy, Lagrange function and nonholonomic constraints of the nonholonomic wall climbing robot system are given, and the Lagrange equations of the nonholonomic wall climbing robot system are established. Secondly, basding on the invariance of differential equations under infinitesimal transformation on time and generalized coordinates, the Lie symmetry determination equations, restriction equations and additional restriction equations of the wall climbing robot system are obtained, and the Lie symmetry theorems and the conserved quantities are also given for the system. Thirdly, the Lie symmetry properties and a series of the conserved quantities of the wall climbing robot on the conical surface are obtained. Furthermore, we considering initial conditions and utilizing the conserved quantities, the exact solutions of the whole body motion and the numerical solution of the limb motion of the wall climbing robot on the conical surface are given. This work has established Lie symmetry theory of nonholonomic wall climbing robot system, and obtained the motion law of the wall climbing robot system on the conical surface with the technique of Lie group analysis. This is a complex and pioneering work, and 101 important equations have been derived; and this technique can be applied to other complex robot and flexible robot systems.

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References

  1. W Wang and S H Ahn Soft Robotics 4 379 (2017)

    Article  Google Scholar 

  2. W Y Fang, X Guo, L Li and D G Zhang Acta Mechanica Sinica 52 965 (2020) (in Chinese)

    Google Scholar 

  3. A Miriyev, K Stack and H Lipson Nature Communications 8 1 (2017)

    Article  Google Scholar 

  4. T M Valentin, E M Dubois, C E Machnicki, D Bhaskar, F R Cui and L Y Wong Polymer Chemistry 10 2015 (2019)

    Article  Google Scholar 

  5. J Park et al Advanced Materials 31 1808148 (2019)

    Article  Google Scholar 

  6. A Cangialosi, C K Yoon, J Liu, Q Huang, J Guo, T D Nguyen, D H Gracias and R Schulman Science 357 1126 (2017

    Article  Google Scholar 

  7. Y Q Fei, J B Wang and W Pang Soft Robotics 6 1 (2019)

    Article  Google Scholar 

  8. K Autumn, Y A Liang, S T Hsieh, W Zesch, W P Chan, T W Kenny et al Nature 405 681 (2000)

    Article  Google Scholar 

  9. S M Cheng, W Y Chen and P J Cong Mechanical and Electrical Engineering Technology 48 6 (2019) (in Chinese)

    Google Scholar 

  10. X J Zhang Mechanism design and simulation of imitating gecko robot Nan Jing: Nanjing University of Science and Technology [Master's Thesis] (2005) (in Chinese)

  11. Z Y Qian, Y Z Zhao and Z Fu Q X Cao International Journal of Advance Manufacturing Technology 30 147 (2006)

    Article  Google Scholar 

  12. K Sangbae, M Spenko, S Trujillo, B Heyneman, D Sanlos and M R Cutkosky IEEE Transaction on Robotic 24 65 (2008)

    Article  Google Scholar 

  13. M R Cutkosky and K Sangbae Philosophical Transactions of the Royal Society 367 1799 (2009)

    Google Scholar 

  14. C Menon, M Murphy, M Sitti IEEE International Conference on Robotics and Biomimetics. Shenyang, China 618 (2004)

  15. K A Daltorio, T E Wei, S N Gorb, R E Ritzmann, R D Quinn Proceedings of the IEEE International Conference on Robotics and Automation Roma, Italy 1274 (2007)

  16. F Cepolina, R C Michelini, R P Razzoli Proceedings of the 1st International Workshop on Advances in Services Robotics (2003) http://www.dimec.unige.it/PMAR/pages/download/papers/zoppi11

  17. A W Zhao, T Mei, X H Lin, N Lin Proceedings of 7th IEEE International Conference on Nanotechnology. Hongkong 259 (2007)

  18. S L Tan, J C Wang and J L Su Machine Tools and Hydraulics 2 19 (2003) (in Chinese)

    Google Scholar 

  19. W Wang and G H Zong Hydraulics and Pneumatics 1 4 (2001) (in Chinese)

    Google Scholar 

  20. B Li Research on flexible gecko-like robot He Fei:University of Science and Technology of China [Master's Thesis] ( 2011) (in Chinese)

  21. C Guo, L Cai, H R Xie, Z Y Wang, Z D Dai and J R Sun Chinese Science Bulletin 54 2880 (2009)

    Google Scholar 

  22. H K Li, Z D Dai, A J Shi, H Zhang and J R Sun Chinese Science Bulletin 54 592 (2009)

    Article  Google Scholar 

  23. J F Liu, L S Xu, J J Xu, L Liu and X Liang International Journal of Advanced Robotic Systems 17 1 (2020)

    Google Scholar 

  24. J F Liu, L S Xu, J J Xu, T Li, S Chen, H Xu et al Journal of Bionic Engineering 17 523 (2020)

    Article  Google Scholar 

  25. J Shao Research on wall climbing robot technology based on gecko shape bionics. Beijing: Beijing Institute of Technology [PhD Thesis] (2014) (in Chinese)

  26. G W Bluman SC Anco Symmetry and integration methods for differential equations (New York: Springer-Verlag) (2002)

    Google Scholar 

  27. F X Mei The application of Lie groups and Lie algebras to constrained mechanical systems (Beijing: Science Press) (1999) (in Chinese)

    Google Scholar 

  28. P J Olver Application of Lie group to Differentia (New York: Springer Verlag) (1986)

    Book  Google Scholar 

  29. F Schwarz Computer Physics Communications 27 179 (1982)

    Article  Google Scholar 

  30. Z P Li Classical and quantum constrained systems and their symmetry properties (Beijing: Beijing University of Technology Press) (1993)

    Google Scholar 

  31. J L Fu, B Y Chen, H Fu, G L Zhao and R W Liu Mechanics and Astronomy 54 288 (2011)

    Article  Google Scholar 

  32. Z Y Wang Gecko oblique movement mechanics toe valgus detachment mechanics and its bionic research Nanjing: Nanjing University of Aeronautics and Astronautics [PhD thesis] (2015) (in Chinese)

  33. J L Fu, L Q Chen and X D Yang Chinese Physics B 12 695 (2003)

    Article  Google Scholar 

  34. J L Fu, L Q Chen and B Y Chen Mechanics & Astronomy 53 1687 (2010)

    Article  Google Scholar 

  35. F X Me The symmetry and conserved quantity of the constraint mechanical system (Beijing: Beijing Institute of Technology Press) (2004)(in Chinese)

    Google Scholar 

  36. P P Cai, J L Fu and Y X Guo Report on Mathematical Physics 79 279 (2017)

    Article  Google Scholar 

  37. J L Fu, L P Fu, B Y Chen and Y Sun Physics Letters A 380 15 (2016)

    Article  MathSciNet  Google Scholar 

  38. F X Mei The symmetry and conserved quantity of the constraint mechanical system (Beijing: Beijing Institute of Technology Press) (2004)(in Chinese)

    Google Scholar 

  39. S Cao and J L Fu Nonlinear Dynamics 92 1947 (2018)

    Article  Google Scholar 

  40. C F Xie and Q Wang Theoretical mechanics, 2nd edn. (Beijing: Higher Education Press) (2015) (in Chinese)

    Google Scholar 

Download references

Funding

This Project was partially supported by the National Natural Science Foundation of China (Grant No. 11872335) and State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences.

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Authors and Affiliations

  1. College of Mechanical and Automotive Engineering, Zhejiang University of Water Resources and Electric Power, Hangzhou, 310018, China

    Jing-Li Fu & Chun Xiang

  2. School of Science, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Jing-Li Fu & Xiao-Dan Lu

  3. College of Physics, Liaoning University, Shenyang, 110036, China

    Yong-Xin Guo

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  1. Jing-Li Fu
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  2. Xiao-Dan Lu
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  3. Chun Xiang
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  4. Yong-Xin Guo
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Correspondence to Jing-Li Fu.

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Fu, JL., Lu, XD., Xiang, C. et al. Lie group analysis method for wall climbing robot systems. Indian J Phys 96, 4231–4243 (2022). https://doi.org/10.1007/s12648-022-02306-2

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  • DOI: https://doi.org/10.1007/s12648-022-02306-2

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