# 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

Research output: Contribution to journalArticle

6 Citations (Scopus)

### 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 92-103 12 Systems and Computers in Japan 36 2 https://doi.org/10.1002/Scj.20014 Published - 2005 Feb Yes

### Fingerprint

Euler-Poisson Equations
Poisson equation
Torque
Trajectories
Trajectory
Orthogonal Polynomials
Optimal Solution
Polynomials
Steepest descent method
Newton-like Method
Steepest Descent Method
Numerical Accuracy
Optimal Trajectory
Motion
High Accuracy
Numerical Experiment
Boundary conditions
Model
Angle
Necessary Conditions

### 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

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.

In: Systems and Computers in Japan, Vol. 36, No. 2, 02.2005, p. 92-103.

Research output: Contribution to journalArticle

Kaneko, Yuichi ; Nakano, Eri ; Osu, Rieko ; Wada, Yasuhiro ; Kawato, Mitsuo. / Trajectory formation based on the minimum commanded torque change model using the euler-poisson equation. In: Systems and Computers in Japan. 2005 ; Vol. 36, No. 2. pp. 92-103.
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