Abstract
Since even a small disturbance may lead to the passive dynamic walker falling, former researches tried to enlarge the basin of attraction of the walking motion to resist disturbances. However, experience with real walking robots reveals that a new disturbance in one step will be added to the total disturbances accumulated from last steps, which results in falling due to a small accidental disturbance. Therefore, fast speed of convergence to the periodic walking motion is necessary to inhibit the accumulation of disturbances. In this paper, the internal features in the basin of attraction of the simplest walking model are investigated for the consideration that the performance for handling disturbances of a walking motion is determined by not only the size of basin of attraction, but also the internal features, such as the speed of convergence. The features of the basin of attraction are obtained by the cell mapping method with defining a convergent cell. The results show that it needs fewer steps for some stripe regions far away to converge than points close to the long period solution. Especially in some stripe regions, the convergence speed is very fast. There is no obvious relation between the size of the basin of attraction and the convergence speed, which motivates us to continue the research to find solutions for designing the walking model with high performance on both aspects.
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Recommended by Associate Editor Kyoungchul Kong
Kang An received his Ph.D. degree in control theory and control engineering from Tongji University in 2014. He is currently working at Shanghai Normal University. His research interests include intelligent robots, biped robots, dynamics and control.
Qijun Chen received the B.E. degree from Huazhong University of Science and Technology, the Master’s degree from Xi’an Jiaotong University, and the Ph.D. degree from Tongji University, Shanghai, China, in 1987, 1990 and 1999, respectively. He is currently a Professor with the Department of Electronic and Information Engineering, Tongji University. His research interests include motion control of robots, environmental perception and understanding of mobile robot, and intelligent systems.
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An, K., Fang, Z., Li, Y. et al. Internal features in basin of attraction of the simplest walking model. J Mech Sci Technol 29, 4913–4921 (2015). https://doi.org/10.1007/s12206-015-1039-4
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DOI: https://doi.org/10.1007/s12206-015-1039-4