Stabilization of natural motions embedded in chaotic responses of a multilink robot; Applications of bifurcation theory

2023 Fiscal Year Final Research Report

• Project/Area Number: 21K04109
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 21040:Control and system engineering-related
• Research Institution: The University of Tokushima
• Principal Investigator: UETA Tetsushi 徳島大学, 情報センター, 教授 (00243733)
• Co-Investigator(Kenkyū-buntansha): 美井野 優 鳴門教育大学, 大学院学校教育研究科, 講師 (70845049) ; 伊藤 大輔 岐阜大学, 工学部, 助教 (90759250)
• Project Period (FY): 2021-04-01 – 2024-03-31
• Keywords: ロボット / 旋回運動 / 多様体 / 分岐 / ホモクリニック軌道 / カオス / サドル型平衡点

Outline of Final Research Achievements

We studied the homoclinic orbits of a two-link robot in which a friction loss and a constant torque at each joint are applied. The system becomes a four-dimensional autonomous system including many nonlinear functions. We calculated the bifurcation diagram which is which is able to explain the number of equilibrium points and their topological properties. We also identified all possible cases of the manifolds regarding equilibria and formulated the conditions of existence for a homoclinic orbit. Using numerical methods for solving variational equations, we computed several homoclinic orbits and investigated their relationship with the cylindrical periodic solutions. We developed analytical tools using Python and visualized the dynamical behavior of a two-link robot simulator.

Free Research Field

非線形力学系の解析

Academic Significance and Societal Importance of the Research Achievements

2リンクロボットではあっても，正弦関数・余弦関数が複雑に絡む方程式となり，その非線形力学系としての解析結果はあまり例をみない．また，この系に関するホモクリニック軌道の検討例もいくつかは存在するが，摩擦を考慮しない特殊な場合を対象としている．よって摩擦を鑑みた，より実モデルに近い系におけるホモクリニック軌道や，第二種周期解について解析を行った取組は他にはないと思われる．