Nonlinear analysis of an indirectly controlled limit cycle walker
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Towards controlling the frequency of limit cycle locomotion as well as adapting to rough terrain and performing specific tasks, a novel and indirect method has been recently introduced using an active wobbling mass attached to limit cycle walkers. One of the strongest advantages of the method is the easiness of its implementation, prompting its applicability to a wide variety of locomotion systems. To deeply understand the nonlinear dynamics for further enhancement of the methodology, we use a combined rimless wheel with an active wobbling mass as an example to perform nonlinear analysis in this paper. First, we introduce the simplified equation of motion and the gait frequency control method. Second, we obtain Arnold tongue, which represents region of entrained locomotion. In regions where the locomotion is not entrained, we explore chaotic and quasi-periodic gaits. To characterize bistability of two different locomotions that underlie hysteresis phenomena, basins of attraction for the two locomotions were computed. The present nonlinear analysis may help understanding the detailed mechanism of indirectly controlled limit cycle walkers.
KeywordsEntrainment effect Limit cycle walking Chaos stability Basin of attraction
This research was partially supported by Grant-in-Aid for Scientific Research (C) No. 16K06154, provided by the Japan Society for the Promotion of Science (JSPS).
- 1.Goswami A, Espiau B, Keramane A (1996) Limit cycle walking and their stability in a passive bipedal gait. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp 246-251Google Scholar
- 4.Li L, Asano F, Tokuda I (2017) High-speed and energy-efficient locomotion of a seed-like underactuated robot on level surface by utilizing asymmetric wobbling effects. In: Proceedings of the 2017 IEEE International Conference on Robotics and Biomimetics, pp 1014-1019Google Scholar
- 7.Shinya A, Yamashita T, Tsuchiya K (2015) Hysteresis in the gait transition of a quadruped investigated using simple body mechanical and oscillator network models. Phys Rev E 83(6):061909Google Scholar
- 9.Harata Y, Asano F, Taji K, Uno Y (2009) Efficient parametric excitation walking with delayed feedback control, efficient parametric excitation walking with delayed feedback control. In: Proceedings of the 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp 2934-2939Google Scholar
- 10.Liljebäck P, Pettersen KY, Stavdahl Ø, Gravdahl JT (2009) Stability analysis of snake robot locomotion based on Poincar maps. In: Proceedings of the 2009 IEEE/RSJ International Conference Intelligent Robots and Systems, pp 3623-3630Google Scholar