Nonlinear Dynamics

, Volume 84, Issue 4, pp 2285–2304 | Cite as

Adaptive speed controller using swing leg motion for 3-D limit-cycle-based bipedal gait

  • Taisuke KobayashiEmail author
  • Tadayoshi Aoyama
  • Yasuhisa Hasegawa
  • Kosuke Sekiyama
  • Toshio Fukuda
Original Paper


In this paper, we propose an adaptive speed controller (ASC) for a limit-cycle-based gait classified as a three-dimensional (3-D) bipedal gait. The limit-cycle-based gait of bipedal robots is excellent for energy efficiency. However, the forward and sideward moving speeds of these robots are difficult to control since they are autonomous systems and their behavior depends upon the initial states of every step. Therefore, in this study, we design a swing leg motion to appropriately adjust the initial states of every step. First, the forward speed is controlled by injecting the momentum of the swing leg, which shifts an energy equilibrium point from the original point to the reference point where the reference forward speed is achieved. Second, the sideward speed is controlled by asymmetric touchdown positions on the right and the left legs, which separate the limit cycle into two different limit cycles for each leg, and this separation leads to the sideward motion. The proposed ASC can be easily applied to an arbitrary limit-cycle-based gait because it is independent of the dynamics of the gait model. The performance of the proposed ASC was validated in terms of the residual error, step response, and disturbance rejection capabilities in numerical simulations for two examples of walking. The proposed ASC also achieved a highly energy-efficient gait, which was consistent with the analytical results. Further, the proposed ASC could adapt a robot to various environments that contained up and down slopes or an obstacle.


3-D bipedal gait Limit cycle Adaptive speed controller Swing leg motion Passive dynamic autonomous control 

Supplementary material

Supplementary material 1 (mp4 9095 KB)


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Taisuke Kobayashi
    • 1
    Email author
  • Tadayoshi Aoyama
    • 2
  • Yasuhisa Hasegawa
    • 1
  • Kosuke Sekiyama
    • 1
  • Toshio Fukuda
    • 3
  1. 1.Department of Micro-Nano Systems EngineeringNagoya UniversityNagoyaJapan
  2. 2.Department of System CyberneticsHiroshima UniversityHigashi-HiroshimaJapan
  3. 3.Faculty of Science and EngineeringMeijo UniversityNagoyaJapan

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