### 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 |
---|---|

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 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Systems and Computers in Japan*,

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

**Trajectory formation based on the minimum commanded torque change model using the euler-poisson equation.** / Kaneko, Yuichi; Nakano, Eri; Osu, Rieko; Wada, Yasuhiro; Kawato, Mitsuo.

Research output: Contribution to journal › Article

*Systems and Computers in Japan*, vol. 36, no. 2, pp. 92-103. https://doi.org/10.1002/Scj.20014

}

TY - JOUR

T1 - Trajectory formation based on the minimum commanded torque change model using the euler-poisson equation

AU - Kaneko, Yuichi

AU - Nakano, Eri

AU - Osu, Rieko

AU - Wada, Yasuhiro

AU - Kawato, Mitsuo

PY - 2005/2

Y1 - 2005/2

N2 - 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.

AB - 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.

KW - Euler-Poisson equation

KW - Minimum commanded torque change criterion

KW - Optimization

KW - System of orthogonal polynomials

KW - Trajectory generation

UR - http://www.scopus.com/inward/record.url?scp=14544278804&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=14544278804&partnerID=8YFLogxK

U2 - 10.1002/Scj.20014

DO - 10.1002/Scj.20014

M3 - Article

AN - SCOPUS:14544278804

VL - 36

SP - 92

EP - 103

JO - Systems and Computers in Japan

JF - Systems and Computers in Japan

SN - 0882-1666

IS - 2

ER -