Analysis of bipedal walking models as a hybrid system from the viewpoint of the basin of attraction

2020 Fiscal Year Final Research Report

• Project/Area Number: 16K17638
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Institute of Physical and Chemical Research (2018-2020); Tohoku University (2016-2017)
• Principal Investigator: Obayashi Ippei 国立研究開発法人理化学研究所, 革新知能統合研究センター, 研究員 (30583455)
• Project Period (FY): 2016-04-01 – 2021-03-31
• Keywords: 力学系 / 二足歩行 / 数理モデル / 計算トポロジー

Outline of Final Research Achievements

I have researched mathematical models of bipedal walking and published two papers. These results are based on the analysis of a simple compass-type model of passive walking (walking motion using a hill without driving force). Although this model is simple, it contains the basic mechanism of walking, the "inverted pendulum model," and is important for understanding the dynamics of walking. Using the mathematical theory of dynamical systems, the formation mechanism of the basin of attraction, which is deeply related to the stability of walking, is clarified. For computational topology, I studied persistent homology. Persistent homology enables us to characterize the shape of data quantitatively. The method obtained in this research is helpful for data analysis by persistent homology.

Free Research Field

応用数学

Academic Significance and Societal Importance of the Research Achievements

二足歩行の安定性を理解することは理論的な興味関心にとどまらない．二足歩行ロボットを転倒させずに歩き続けさせるための理論的基盤となる．またヒトの二足歩行への展開としては怪我や病気で歩行に困難が生じた人々への支援などへの応用も期待される．本研究成果がそういった応用に直接つながるもではないが，より現実的な歩行モデルの解析やヒトやロボットから得られたデータの解析に本研究の成果が有効に活用できることができればロボット設計などの実利的な方向にもつながっていくことが期待される．
計算トポロジーの結果はデータ解析の新たなツールとして有用であると期待される．