Trajectory formation based on the minimum commanded torque change model using the euler-poisson equation

Yuichi Kaneko*, Eri Nakano, Rieko Osu, Yasuhiro Wada, Mitsuo Kawato

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


A minimum commanded torque change criterion based on the optimization principle is proposed as a model that accounts for human voluntary motion. It is shown that the trajectory of human arm motion can be well reproduced by the model. In the point-to-point movement, the calculation of the torque based on the minimum commanded torque change criterion requires a highly nonlinear calculation, and it is difficult to determine the optimal trajectory. As solution methods, a Newton-like method and a steepest descent method have been proposed. However, an optimal solution cannot be obtained by these methods, for several reasons. This paper proposes a method in which the trajectory of the joint angle is analytically represented by a system of orthogonal polynomials, and the coefficients of the orthogonal polynomials are estimated by a linear iterative calculation so that the parameters satisfy the EulerPoisson equation, as a necessary condition for the optimal solution. As a result of numerical experiments, it is shown that a solution satisfying the Euler-Poisson equation with high numerical accuracy is obtained in a short time, regardless of the parameters such as those of the boundary conditions.

Original languageEnglish
Pages (from-to)92-103
Number of pages12
JournalSystems and Computers in Japan
Issue number2
Publication statusPublished - 2005 Feb
Externally publishedYes


  • Euler-Poisson equation
  • Minimum commanded torque change criterion
  • Optimization
  • System of orthogonal polynomials
  • Trajectory generation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Hardware and Architecture
  • Computational Theory and Mathematics


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