動的に級数展開係数を求めるＧＡによる非線形２点境界値問題の解法とその応用

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  • 横瀬 義雄
    呉工業高等専門学校 電気工学科
  • 泉 照之
    島根大学 総合理工学部 電子制御システム工学科

書誌事項

タイトル別名
  • Non-linear Two-Point Boundary Value Problem Obtaining the Expansion Coefficients by the Dynamic GA and Its Application
  • 動的に級数展開係数を求めるGAによる非線形2点境界値問題の解決とその応用
  • ドウテキ ニ キュウスウ テンカイ ケイスウ オ モトメル GA ニ ヨル ヒセンケイ 2テン キョウカイチ モンダイ ノ カイケツ ト ソノ オウヨウ

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抄録

The global warming and the environmental destruction are caused from the mass consumption of energy in a factory in which robotic manipulators are used. It is necessary to take the trajectory planning into considerations in order to save the consumption energy of the manipulator controlled with Point-to-Point (PTP) motion. An optimal trajectory that minimizes the consumption energy can be obtained by solving a two-point boundary value problem. The optimal trajectory can be analyzed easily if the system is linear. However, the dynamical equation of the multi-link manipulator with Coulomb friction has a strong non-linearity. Then the Genetic Algorithm (GA) is applied to obtain the solution of two-point boundary value problem with the strong non-linearity. The GA is the method for searching discrete solution space by genes. However, the trajectory function is continuous with respect to time. In this paper, the coefficients of the approximation functions are determined as the gene’s phenotype. This method has disadvantages that are long computation time and increase the possibility of lapsing into the local optimal solution. So, a new method is proposed in order to shorten the computation time and to lessen the possibility of lapsing into the local optimal solution. It is seen from application to the minimization of the consumption energy of a manipulator with Coulomb friction that a proposed method is effective.

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