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爬壁机器人系统的Noether对称性和守恒量

傅景礼 陆晓丹 项春

傅景礼, 陆晓丹, 项春. 爬壁机器人系统的Noether对称性和守恒量. 力学学报, 2022, 54(6): 1680-1693 doi: 10.6052/0459-1879-22-084
引用本文: 傅景礼, 陆晓丹, 项春. 爬壁机器人系统的Noether对称性和守恒量. 力学学报, 2022, 54(6): 1680-1693 doi: 10.6052/0459-1879-22-084
Fu Jingli, Lu Xiaodan, Xiang Chun. Noether symmetries and conserved quantities of wall climbing robot system. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1680-1693 doi: 10.6052/0459-1879-22-084
Citation: Fu Jingli, Lu Xiaodan, Xiang Chun. Noether symmetries and conserved quantities of wall climbing robot system. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1680-1693 doi: 10.6052/0459-1879-22-084

爬壁机器人系统的Noether对称性和守恒量

doi: 10.6052/0459-1879-22-084
基金项目: 国家自然科学基金资助项目(11872335)
详细信息
    作者简介:

    傅景礼, 教授, 主要研究方向: 柔性机器人系统动力学. E-mail: sqfujingli@163.com

  • 中图分类号: 0320

NOETHER SYMMETRIES AND CONSERVED QUANTITIES OF WALL CLIMBING ROBOT SYSTEM

  • 摘要: 爬壁机器人的运动是一种模仿壁虎爬行的运动, 爬壁机器人的运动可分解为四肢带动身体的运动, 先前的研究都是基于牛顿力学的方法. 本文采用Lagrange 力学的方法建立爬壁机器人系统的运动方程, 并运用Lie群分析方法建立该系统的Noether对称性理论, 得出爬壁机器人的运动规律. 首先, 给出非完整爬壁机器人系统的动能、势能和Lagrange函数以及所受的非完整约束, 从而建立了非完整爬壁机器人系统的Lagrange方程; 其次, 引入关于时间和广义坐标的无限小变换, 提出了非完整爬壁机器人系统的Hamilton作用量和Hamilton作用量的基本变分公式; 第三, 给出爬壁机器人系统 Noether对称性变换和广义准对称变换的定义, 判据和存在的Noether守恒量, 并提出了非保守完整系统和非保守非完整爬壁机器人系统的Noether定理; 最后, 以圆锥面上爬壁机器人为例, 对给出的守恒量直接进行积分给出圆锥面上爬壁机器人整体运动的精确解和四肢运动的数值解, 发现了该爬壁机器人的运动规律, 很好地验证了非完整爬壁机器人系统的Noether对称性理论. 本文的研究为Lie群分析方法应用于其他复杂的机器人系统以及柔性机器人系统的对称性求解提出了一种新的对称性求解方法.

     

  • 图  1  斯坦福大学的StickyBotIII机器人

    Figure  1.  StickyBotIII robot at Stanford University

    图  2  爬壁机器人单腿简化图

    Figure  2.  Simplified view of a single leg of a wall-climbing robot

    图  3  圆锥曲面上的爬壁机器人

    Figure  3.  A wall-climbing robot on a conical surface

    图  4  壁虎的爬行运动

    Figure  4.  The creeping movement of a gecko

    图  5  四肢各关节运动规律

    Figure  5.  The motion rule of each joint of limbs

  • [1] Wang W, Ahn SH. Shape memory alloy-based soft gripper with variable stiffness for compliant and effective grasping. Soft Robotics, 2017, 4(4): 379-389 doi: 10.1089/soro.2016.0081
    [2] 方五益, 郭晛, 黎亮等. 柔性铰柔性杆机器人动力学建模、仿真和控制. 力学学报, 2020, 52(4): 965-974 (Fang Wuyi, Guo Jian, Li Liang, Zhang DG. Dynamic modeling, simulation and control of flexible articulated flexible link robot. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 965-974 (in Chinese)

    Fang Wuyi, Guo Jian, Li Liang, Zhang DG. Dynamic modeling, simulation and control of flexible articulated flexible link robot, Chinese Journal of Theoretical and Applied Mechanics, 2020, 52 (4): 965-974(in Chinese)
    [3] Miriyev A, Stack K, Lipson H. Soft material for soft actuators. Nature Communications, 2017, 8(1): 1-8 doi: 10.1038/s41467-016-0009-6
    [4] Valentin TM, Dubois EM, Machnicki CE, et al. 3D printed self-adhesive Pegda-paa hydrogels as modular components for soft actuators and microfluidics. Polymer Chemistry, 2019, 10(16): 2015-2028 doi: 10.1039/C9PY00211A
    [5] Park J, Lee Y, Barbee MH, et al. A hierarchical nanoparticle-in-micropore architecture for enhanced mechanosensitivity and stretch ability in mechanochromic electronic skins. Advanced Materials, 2019, 31(25): 1-10
    [6] Cangialosi A, Yoon CK, Liu J, et al. DNA sequence-directed shape change of photopatterned hydrogels via high-degree swelling. Science, 2017, 357(6356): 1126-1130 doi: 10.1126/science.aan3925
    [7] Fei Y, Wang J, Pang W. A novel fabric-based versatile and stiffness-tunable soft gripper integrating soft pneumatic fingers and wrist. Soft Robotics, 2019, 6(1): 1-20 doi: 10.1089/soro.2018.0015
    [8] Autumn K, Liang YA, Hsieh ST, et al. Adhesive force of a single gecko foot-hair. Nature, 2000, 405: 681-685 doi: 10.1038/35015073
    [9] 程思敏, 陈韦宇, 丛培杰. 爬壁机器人的研究现状. 机电工程技术, 2019, 48(9): 6-10 (Cheng Simin, Chen Weiyu, Cong Peijie. Research status of wall climbing robot. Electromechanical Engineering Technology, 2019, 48(9): 6-10 (in Chinese) doi: 10.3969/j.issn.1009-9492.2019.09.003

    Cheng Simin, Chen Weiyu, Cong Peijie. Research status of wall climbing robot, Electromechanical Engineering Technology, 2019, 48 (9): 6-10(in Chinese) doi: 10.3969/j.issn.1009-9492.2019.09.003
    [10] 章旭君. 仿壁虎机器人的机构设计与仿真. [硕士论文]. 南京: 南京航空航天大学, 2005

    Zhang Xujun. Mechanism design and simulation of gecko like robot. [Master's Thesis]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2005 (in Chinese))
    [11] Qian ZY, Zhao YZ, Fu Z, et al. Design and realization of a non-actuated glass-curtain wall-cleaning robot prototype with dual suction cups. International Journal of Advance Manufacturing Technology, 2006, 30(2): 147-155
    [12] Sangbae K, Spenko M, Trujillo S, et al. Smooth vertical surface climbing with directional adhesion. IEEE Transaction on Robotic, 2008, 24(1): 65-74 doi: 10.1109/TRO.2007.909786
    [13] Cutkosky MR, Sangbae K. Design and fabrication of multimaterial structures for bioinspired robots. Philosophical Transactions of the Royal Society, 2009, 367(13): 1799-1813
    [14] Carlo M, Metin S. Gecko inspired surface climbing robots//IEEE Internation Conference on Robotics and Biomimetics. Shenyang, China. 2004: 618-619
    [15] Daltorio KA, Wei TE, Gorb SN, et al. Passive foot design and contact area analysis for climbing mini-whegs//Proceedings of the IEEE International Conference on Robotics and Automation. Roma, Italy. 2007: 1274-1279
    [16] Cepolina F, Michelini RC, Razzoli RP, et al. Gecko, a climbing robot for walls cleaning//Proceedings of the 1st International Workshop on Advances in Services Robotics. http://www.dimec.unige.it/PMAR/pages/down load/papers/zoppi11, 2003
    [17] Zhao A, Mei T, et al. Fabrication and characterization of tree-like nanorod arrays for bionic gecko foot-hairs//Proceedings of 7th IEEE international Conference on Nanotechnology. Hongkong, China. 2007: 259-262
    [18] 谈士力, 王建成, 苏建良等. 球面移动机器人机构研制. 机床与液压, 2003(2): 19-22 (Tan Shili, Wang Jiancheng, Su Jianliang, et al. Development of spherical mobile robot. Mechanism Machine Tools and Hydraulics, 2003(2): 19-22 (in Chinese) doi: 10.3969/j.issn.1001-3881.2003.02.008

    Tan SL, Wang JC, Su JL, et al. Development of spherical mobile robot, mechanism Machine tools and hydraulics, 2003 (2): 19-2(in Chinese) doi: 10.3969/j.issn.1001-3881.2003.02.008
    [19] 王巍, 宗光华. 气动擦窗机器人的控制和环境检测. 液压与气动, 2001, 1: 4-7 (Wang Wei, Zong Guanghua. Control and environment detection of pneumatic window cleaning robot. Hydraulic and Pneumatic, 2001, 1: 4-7 (in Chinese) doi: 10.3969/j.issn.1000-4858.2001.01.006

    Wang W, Zong GH. Control and environment detection of pneumatic window cleaning robot, Hydraulic and pneumatic, 2001, 1: 4-7(in Chinese) doi: 10.3969/j.issn.1000-4858.2001.01.006
    [20] 李冰. 柔性仿壁虎机器人的研究. [硕士论文]. 合肥: 中国科学技术大学, 2011

    Li Bing. Research on flexible gecko like robot. [Master's Thesis]. Hefei: University of Science and Technology of China, 2011 (in Chinese)
    [21] Guo C, Cai L, Xie HR, et al. The divisional and hierarchical innervations of gecko's toes to motion and reception. Chinese Science Bulletin, 2009, 54(16): 2880-2887
    [22] Li HK, Dai ZD, Shi AJ, et al. Angular observation of joints of geckos moving on horizontal and vertical surfaces. Chinese Science Bulletin, 2009, 54(4): 592-598 doi: 10.1007/s11434-009-0077-7
    [23] Liu JF, Xu LS, Xu JJ, et al. Analysis and optimization of the wall-climbing robot with an adsorption system and adhesive belts. International Journal of Advanced Robotic Systems, 2020, 17(3): 1-14
    [24] Liu JF, Xu LS, Xu JJ, et al. Design, modeling and experimentation of a biomimetic wall-climbing robot for multiple surfaces. Journal of Bionic Engineering, 2020, 17(3): 523-538 doi: 10.1007/s42235-020-0042-3
    [25] 邵洁. 基于壁虎形态仿生的爬壁机器人技术研究. [博士论文]. 北京: 北京理工大学, 2014

    Shao Jie. Research on wall climbing robot technology based on gecko morphology bionics. [PhD thesis]. Beijing: Beijing University of Technology, 2014 (in Chinese)
    [26] Bluman GW, Anco SC. Symmethy and Integration Methods for Differential Equations. New York: Springer-Verlag, 2002
    [27] 梅凤翔. 李群李代数对约束力学系统的应用. 北京: 科学出版社, 1999

    Mei Fengxiang. Application of Lie Group Lie Algebra to Constrained Mechanical System. Beijing: Science Press, 1999 (in Chinese)
    [28] Noether E. Invariant variation problems. Transport Theory and Statistical Physics, 1971, 1(3): 186-207 doi: 10.1080/00411457108231446
    [29] Candotti E. On the inversion of Noether’s theorem in classical dynamical systems. American Journal of Physics, 1972, 40(3): 424-429 doi: 10.1119/1.1986566
    [30] Djukic DDS, Vujanovic BD. Noether's theory in classical nonconservative mechanic. Acta Mechanica, 1975, 23(1): 17-27
    [31] 李子平. 约束系统的变换性质. 物理学报, 1981, 30(12): 1659-1671 (Li Ziping. Transformation properties of constrained systems. Actaf Physica Sinica, 1981, 30(12): 1659-1671 (in Chinese) doi: 10.3321/j.issn:1000-3290.1981.12.012

    Li ZP. Transformation properties of constrained systems, Actaf physica Sinica, 1981, 30 (12): 1659-1671(in Chinese) doi: 10.3321/j.issn:1000-3290.1981.12.012
    [32] Djukic DS, Sreauss AM. Noether’s theory for nonconservative generalised mechanical systems. Journal of Physics A: General Physics, 1980, 13(2): 431-435
    [33] Djukic DS, Sutela T. Integrating factors and conservation laws for nonconservative dynamical systems. International Journal of Non-Linear Mechanics, 1984, 19(4): 331-339 doi: 10.1016/0020-7462(84)90061-1
    [34] Mei FX. Exchange relations in nonholonomic systems mechanics. Mechanics in Engineering, 1979, 1(3): 37-38
    [35] Mei FX. Stability of equilibrium for the autonomous Birkhoff system. Science Bulletin, 1993, 23(10): 816-819
    [36] Mei FX. One type of integrals for the equations of motion of higher order nonholonomic systems. Applied Mathematics and Mechanics, 1991, 12(8): 799-806 doi: 10.1007/BF02458170
    [37] Giachetta G. First integrals of nonholonomic systems and their generators. Journal of Physics A:General Physics, 2000, 33(30): 53-69
    [38] Cai PP, Fu JL, Guo YX. Noether symmetries of the nonconservative and nonholonomic systems on time scales. Science China: Physics, Mechanics & Astronomy, 2013, 56(5): 1-12
    [39] 梅凤翔. 关于Noether定理—分析力学札记之三十. 力学与实践, 2020, 42(1): 66-74 (Mei Fengxiang. About Noether's theorem−thirty notes on analytical mechanics. Mechanics and Practice, 2020, 42(1): 66-74 (in Chinese) doi: 10.6052/1000-0879-19-332

    Mei FX. About Noether's theorem -- thirty notes on analytical mechanics, Mechanics and practice, 2020, 42 (1): 66-74(in Chinese) doi: 10.6052/1000-0879-19-332
    [40] 李子平. 经典和量子约束系统及其对称性质. 北京: 北京工业大学出版社, 1993

    Li Ziping. Classical and Quantum Constrained Systems and Their Symmetry Properties. Beijing: Beijing University of Technology Press,1993 (in Chinese)
    [41] Fu JL, Chen BY, Fu H, et al. Velocity-dependent symmetries and non-Noether conserved quantities of electromechanical systems. Science China: Physics, Mechanics and Astronomy, 2011, 54(2): 288-295 doi: 10.1007/s11433-010-4173-0
    [42] 傅景礼, 陈立群, 陈本永. 非规范格子离散机电耦合动力系统的 Noether 理论. 中国科学(G辑), 2010, 40(2): 133-145 (Fu Jingli, Chen Liqun, Chen Benyong. Noether theory of irregular lattice discrete electromechanical coupling dynamic system. Chinese Science (Series G), 2010, 40(2): 133-145 (in Chinese)

    Fu JL, Chen LQ, Chen BY. Noether theory of irregular lattice discrete electromechanical coupling dynamic system, Chinese Science (Series G), 2010, 40 (2): 133-145(in Chinese)
    [43] 王周义. 大壁虎斜面运动力学脚趾外翻脱附力学及其仿生研究. [博士论文]. 南京: 南京航空航天大学, 2015

    Wang ZY. Kinematics of gecko's inclined plane, mechanics of toe valgus and desorption and its bionic research investigate. [PhD Thesis]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2015 (in Chinese)
    [44] 赵跃宇, 梅凤翔. 关于力学系统的对称性和守恒量. 力学进展, 1993, 23(3): 360-372 (Zhao Yueyu, Mei Fengxiang. On the symmetry and conserved quantity of mechanical system. Mechanical Progress, 1993, 23(3): 360-372 (in Chinese) doi: 10.3321/j.issn:1000-0992.1993.03.010

    Zhao YY, Mei FX. On the symmetry and conserved quantity of mechanical system, Mechanical Progress,1993, 23(3): 360-372(in Chinese) doi: 10.3321/j.issn:1000-0992.1993.03.010
    [45] 赵跃宇. 非保守力学系统的Lie对称性和守恒量. 力学学报, 1994, 26(3): 380-384 (Zhao Yueyu. Lie symmetries and conserved quantities of nonconservative mechanical systems. Chinese Journal of Theoretical and Applied Mechanics, 1994, 26(3): 380-384 (in Chinese)

    Zhao Yueyu. Lie symmetries and conserved quantities of nonconservative mechanical systems, Chinese Journal of Theoretical and Applied Mechanics, 1994,26 (3): 380-38446.(in Chinese)
    [46] Fu JL, Chen LQ, Yang XD. Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems. Chinese Physics B, 2003, 12(7): 695-699 doi: 10.1088/1009-1963/12/7/301
    [47] Fu JL, Chen LQ, Chen BY. Noether-type theory for discrete mechanico-electrical dynamical systems with nonregular lattices. Science China: Physics, Mechanics & Astronomy, 2010, 53(9): 1687-1698
    [48] 张毅. Caputo导数下分数阶Birkhoff系统的准对称性与分数阶Noether定理. 力学学报, 2017, 49(3): 693-702 (Zhang Yi. Quasi symmetry and fractional Noether theorem of fractional Birkhoff system under Caputo derivative. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 693-702 (in Chinese)

    Zhang Y. Quasi symmetry and fractional Noether theorem of fractional Birkhoff system under Caputo derivative, Chinese journal of Theoretical and Applied Mechanics, 2017, 49 (3): 693-702(in Chinese)
    [49] 梅凤翔. 约束力学系统的对称性与守恒量. 北京: 北京理工大学出版社, 2004

    Mei Fengxiang. Symmetry and Conserved Quantities of Constrained Mechanical Systems. Beijing: Beijing Institute of Technology Press, 2004 (in Chinese)
    [50] Song CJ, Zhang Y. Noether symmetry and conserved quantity for fractional Birkhoffian mechanics and its applications. Fractional Calculus & Applied Analysis, 2018, 21(2): 509-526
    [51] Cai PP, Fu JL, Guo YX. Lie symmetries and conserved quantities of the constraint mechanical systems on time scales. Reports on Mathematical Physics, 2017, 79(3): 279-296 doi: 10.1016/S0034-4877(17)30045-9
    [52] Fu JL, Fu LP, Chen BY, et al. Lie symmetries and their inverse problems of nonholonomic Hamilton systems with fractional derivatives. Physics Letters A, 2016, 380(1): 15-21
    [53] Zhang Y, Zhai XH. Perturbation to Lie symmetry and adiabatic invariants for Birkhoffian systems on time scales. Communication in Nonlinear Science and Numerical Simulation, 2019, 75: 251-261 doi: 10.1016/j.cnsns.2019.04.005
    [54] Fu JL, Chen BY, Chen LQ. Noether symmetries of discrete nonholonomic dynamical systems. Physics Letters A, 2009, 373(4): 409-412 doi: 10.1016/j.physleta.2008.11.039
    [55] 傅景礼, 陈立群, 陈本永. 非规范格子离散非保守系统的 Noether 理论. 中国科学(G 辑), 2009, 39(9): 1320-1329 (Fu Jingli, Chen Liqun, Chen Benyong. Noether's theory of discrete nonconservative systems with non canonical lattices. Chinese Science (Series G), 2009, 39(9): 1320-1329 (in Chinese)

    Fu JL, Chen LQ, Chen BY. Noether's theory of discrete nonconservative systems with non canonical lattices, Chinese Science (Series G), 2009, 39 (9): 1320-1329(in Chinese)
    [56] Zhang HB. Lie symmetries and conserved quantities of nonholonomic mechanical systems with unilateral Vacco constraints. Chinese Physics, 2002, 11(1): 1-4 doi: 10.1088/1009-1963/11/1/301
    [57] 梅凤翔. 非完整系统力学基础. 北京: 北京工业学院出版社, 1985
    [58] Fu JL, Zhang LJ, Khalique CM, and Guo ML. Motion equations and non-Noether symmetries of Lagrangian systems with the conformable fractional derivatives. Thermal Science, 2021, 25(2B): 1365-1372
    [59] Feng K, Qin MZ. Symplectic Geometric Algorithms for Hamiltonian Systems. New York: Springer, 2010
    [60] Zhao GL, Chen LQ, Fu JL. Mei symmetries and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices. Chinese Physics B, 2013, 22(3): 54-60
    [61] Zhao L, Fu JL, Chen BY. A new type of conserved quantity of Mei symmetry for the motion of mechanico-electrical coupling dynamical systems. Chinese Physics B, 2011, 20(4): 1-4
    [62] 谢传峰, 王琪. 理论力学, 第2版. 北京: 高等教育出版社, 2015

    Xie Chuanfeng, Wang Qi. Theoretical Mechanics (2nd Edition). Beijing: Higher Education Press, 2015 (in Chinese)
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出版历程
  • 收稿日期:  2022-02-24
  • 录用日期:  2022-04-13
  • 网络出版日期:  2022-04-14
  • 刊出日期:  2022-06-18

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