Artificial Life and Robotics

, Volume 23, Issue 4, pp 508–514 | Cite as

Nonlinear analysis of an indirectly controlled limit cycle walker

  • Longchuan LiEmail author
  • Isao Tokuda
  • Fumihiko Asano
Original Article


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.


Entrainment 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).


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Copyright information

© ISAROB 2018

Authors and Affiliations

  1. 1.Graduate School of Advanced Institute of Science and TechnologyJapan Advanced Institute of Science and TechnologyIshikawaJapan
  2. 2.Department of Mechanical EngineeringRitsumeikan UniversityShigaJapan
  3. 3.School of Information ScienceJapan Advanced Institute of Science and TechnologyIshikawaJapan

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