Multi-joint arm trajectory formation based on the minimization principle using the euler-poisson equation

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In previous research, criteria based on optimal theories were examined to explain trajectory features in time and space in multi joint arm movements. Four criteria have been proposed. They were the minimum hand jerk criterion, the minimum angle jerk criterion, the minimum torque change criterion, and the minimum commanded torque change criterion. Optimal trajectories based on the two former criteria can be calculated analytically. In contrast, optimal trajectories based on the minimum commanded torque change criterion are difficult to be calculated even with numerical methods. In some cases, they can be computed by a Newton-like method or a steepest descent method combined with a penalty method. However, for a realistic physical parameter range, a former becomes unstable quite often, and the latter is unreliable about the optimality of the obtained solution. In this paper, we propose a new method to stably calculate optimal trajectories based on the minimum commanded torque change criterion. The method can obtain trajectories satisfying Euler-Poisson equations with a sufficiently high accuracy. In the method, a joint angle trajectory, which satisfies the boundary conditions strictly, is expressed by using orthogonal polynomials. The coefficients of the orthogonal polynomials are estimated by using a linear iterative calculation so as to satisfy the Euler-Poisson equations with a sufficiently high accuracy. In numerical experiments, we show that the optimal solution can be computed in a wide work space and can also be obtained in a short time compared with the previous methods.

Original languageEnglish
Title of host publicationArtificial Neural Networks - ICANN 2001 - International Conference, Proceedings
PublisherSpringer Verlag
Pages977-984
Number of pages8
Volume2130
ISBN (Print)3540424865, 9783540446682
DOIs
Publication statusPublished - 2001
Externally publishedYes
EventInternational Conference on Artificial Neural Networks, ICANN 2001 - Vienna, Austria
Duration: 2001 Aug 212001 Aug 25

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2130
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

OtherInternational Conference on Artificial Neural Networks, ICANN 2001
CountryAustria
CityVienna
Period01/8/2101/8/25

Keywords

  • Computational neuroscience
  • Euler-Poisson equation
  • Minimization principle
  • Motor control
  • Trajectory formation

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

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  • Cite this

    Wada, Y., Kaneko, Y., Nakano, E., Osu, R., & Kawato, M. (2001). Multi-joint arm trajectory formation based on the minimization principle using the euler-poisson equation. In Artificial Neural Networks - ICANN 2001 - International Conference, Proceedings (Vol. 2130, pp. 977-984). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2130). Springer Verlag. https://doi.org/10.1007/3-540-44668-0_135