Symmetry Based Searching Process for Initial Conditions of Passive Running

doi:10.1007/s12204-011-1203-7

摘要/Abstract

摘要： Symmetrical passive running of a simple spring model is commonly used to predict the locomotion of real animals and develop the design strategies for legged systems. If the initial conditions for running can be found automatically, we can expand the ranges of the model parameters freely. To achieve this objective, we derive an efficient searching procedure based on analysis of the symmetries. Using this process, the desired initial states of the passive running are obtained. Existence of the results reveals that the leg symmetries can be used to generate the symmetrical running. Moreover, the leg forces are associated with the running pattern, implying that we should choose suitable motion for the given model characteristics.

关键词: symmetrical running, initial conditions, scissor algorithm, motion

Abstract: Symmetrical passive running of a simple spring model is commonly used to predict the locomotion of real animals and develop the design strategies for legged systems. If the initial conditions for running can be found automatically, we can expand the ranges of the model parameters freely. To achieve this objective, we derive an efficient searching procedure based on analysis of the symmetries. Using this process, the desired initial states of the passive running are obtained. Existence of the results reveals that the leg symmetries can be used to generate the symmetrical running. Moreover, the leg forces are associated with the running pattern, implying that we should choose suitable motion for the given model characteristics.

Key words: symmetrical running, initial conditions, scissor algorithm, motion

中图分类号:

TP 242.6

DENG Qi (邓奇), WANG Shi-gang* (王石刚), MO Jin-qiu (莫锦秋), LIANG Qing-hua (梁庆华). Symmetry Based Searching Process for Initial Conditions of Passive Running[J]. 上海交通大学学报（英文版）, 2013, 18(6): 673-678.

DENG Qi (邓奇), WANG Shi-gang* (王石刚), MO Jin-qiu (莫锦秋), LIANG Qing-hua (梁庆华). Symmetry Based Searching Process for Initial Conditions of Passive Running[J]. Journal of shanghai Jiaotong University (Science), 2013, 18(6): 673-678.

参考文献

[1] Seyfarth A, Geyer H, Guenthera M, et al. A movement criterion for running [J]. Journal of Biomechanics,2002, 35(5): 649-655.
[2] Nanua P, Waldron K J. Energy comparison between trot, bound, and gallop using a simple model [J].Journal of Biomechanical Engineering, 1995, 117(4):466-474.
[3] Herr H M, Huang G T, Mcmahon T A. A model of scale effects in mammalian quadrupedal running [J].Journal of Experimental Biology, 2002, 205: 959-967.
[4] Berkemeier M D. Modeling the dynamics of quadrupedal running [J]. The International Journal of Robotics Research, 1998, 17(9): 971-985.
[5] Zou Hong, Schmiedeler J P. The effect of asymmetrical body-mass distribution on the stability and dynamics of quadruped bounding [J]. IEEE Transactions on Robotics, 2006, 22(4): 711-723.
[6] Chatzakos P, Papadopoulos E. Bio-inspired design of electrically-driven bounding quadrupeds via parametric analysis [J]. Mechanism and Machine Theory,2009, 44(3): 559-579.
[7] Chen Jia-pin, Cheng Jun-shi, Xi Yu-geng. Virtual model control of a quadruped walking robot [J]. Journal of Shanghai Jiaotong University, 2001, 35(12):1771-1775 (in Chinese).
[8] Ma Jian-xu, Ma Pei-sun, Yang Bao-zhong, et al.Buffering of new walking mechanism in quadruped walking robot [J]. Journal of Shanghai Jiaotong University,1999, 33(7): 847-850 (in Chinese).
[9] Francois C, Samson C. A new approach to the control of the planar one-legged hopper [J]. The International Journal of Robotics Research, 1998, 17(11):1150-1166.
[10] M'Sirdi N K, Manamanni N, Ghanami D E. Control approach for legged robots with fast gaits [J]. Journal of Intelligent and Robotic Systems, 2000, 27(4):321-343.
[11] Krasny D P, Orin D E. Generating high-speed dynamic running gaits in a quadruped robot using an evolutionary search [J]. IEEE Transactions on Systems,Man, and Cybernetics. Part B: Cybernetics,2004, 34(4): 1685-1696.
[12] Poulakakis I, Papadopoulos E, Buehler M. On the stability of the passive dynamics of quadrupedal running with a bounding gait [J]. The International Journal of Robotics Research, 2006, 25(7): 669-687.
[13] Koditschek D E, Buehler M. Analysis of a simplified hopping robot [J]. The International Journal of Robotics Research, 1991, 10(6): 587-605.
[14] Hyon S H, Jiang X, Emura T, et al. Passive running of planar 1/2/4-legged robots [C]// IEEE/RSJ International Conference on Intelligent Robots and Systems.Sendai, Japan: IEEE, 2004: 3532-3539.
[15] Raibert M H. Running with symmetry [J]. The International Journal of Robotics Research, 1986, 5(4):3-19.
[16] Hildebrand M. Motions of the running cheetah and horse [J]. Journal of Mammalogy, 1959, 40(4): 481-495.
[17] Poulakakis I, Papadopoulos E, Buehler M. On the stable passive dynamics of quadrupedal running[C]// IEEE International Conference on Robotics & Automation. Taipei, China: IEEE, 2003: 1368-1373.
[18] Hyon S H, Emura T. Quasi-periodic gaits of passive one-legged hopper [C]// IEEE/RSJ International Conference on Intelligent Robots and Systems. Lausanne,Switzerland: IEEE, 2002: 2625-2630.
[19] Gray J. Animal locomotion [M]. London: Weidenfeld & Nicolson Press, 1968.
[20] Tian Wei-jun, Cong Qian, Jin Jing-fu. Joint angles and ground reaction forces of German shepherd dog[J]. Journal of Jilin University: Engineering and Technology Edition, 2009, 39(sup1): 227-231 (in Chinese).
[21] Walter R M, Carrier D R. Ground forces applied by galloping dogs [J]. Journal of Experimental Biology,2007, 210: 208-216.
[22] Farley C T, Taylor C R. A mechanical trigger for the trot-gallop transition in horses [J]. Science, 1991,253(5017): 306-308.
[23] Maes L D, Herbin M, Hackert R, et al. Steady locomotion in dogs: Temporal and associated spatial coordination patterns and the effect of speed [J]. Journal of Experimental Biology, 2008, 211: 138-149.