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 languageEnglish
Pages (from-to)92-103
Number of pages12
JournalSystems and Computers in Japan
Volume36
Issue number2
DOIs
Publication statusPublished - 2005 Feb
Externally publishedYes

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.
@article{8fba12aaa9f8414c84f9399ee708aa9a,
title = "Trajectory formation based on the minimum commanded torque change model using the euler-poisson equation",
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.",
keywords = "Euler-Poisson equation, Minimum commanded torque change criterion, Optimization, System of orthogonal polynomials, Trajectory generation",
author = "Yuichi Kaneko and Eri Nakano and Rieko Osu and Yasuhiro Wada and Mitsuo Kawato",
year = "2005",
month = "2",
doi = "10.1002/Scj.20014",
language = "English",
volume = "36",
pages = "92--103",
journal = "Systems and Computers in Japan",
issn = "0882-1666",
publisher = "John Wiley and Sons Inc.",
number = "2",

}

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 -