### Abstract

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 language | English |
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Pages (from-to) | 92-103 |

Number of pages | 12 |

Journal | Systems and Computers in Japan |

Volume | 36 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2005 Feb 1 |

Externally published | Yes |

### Keywords

- 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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## Cite this

*Systems and Computers in Japan*,

*36*(2), 92-103. https://doi.org/10.1002/Scj.20014