# 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 language English Artificial Neural Networks - ICANN 2001 - International Conference, Proceedings Springer Verlag 977-984 8 2130 3540424865, 9783540446682 https://doi.org/10.1007/3-540-44668-0_135 Published - 2001 Yes International Conference on Artificial Neural Networks, ICANN 2001 - Vienna, AustriaDuration: 2001 Aug 21 → 2001 Aug 25

### Publication series

Name Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 2130 0302-9743 1611-3349

### Other

Other International Conference on Artificial Neural Networks, ICANN 2001 Austria Vienna 01/8/21 → 01/8/25

### Fingerprint

Euler-Poisson Equations
Poisson equation
Trajectories
Trajectory
Torque
Optimal Trajectory
Polynomials
Steepest descent method
Orthogonal Polynomials
High Accuracy
Angle
Newton-like Method
Numerical methods
Steepest Descent Method
Penalty Method
Workspace
Boundary conditions
Optimality
Strictly
Optimal Solution

### Keywords

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

### ASJC Scopus subject areas

• Computer Science(all)
• Theoretical Computer Science

### 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

Multi-joint arm trajectory formation based on the minimization principle using the euler-poisson equation. / Wada, Yasuhiro; Kaneko, Yuichi; Nakano, Eri; Osu, Rieko; Kawato, Mitsuo.

Artificial Neural Networks - ICANN 2001 - International Conference, Proceedings. Vol. 2130 Springer Verlag, 2001. p. 977-984 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2130).

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

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, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2130, Springer Verlag, pp. 977-984, International Conference on Artificial Neural Networks, ICANN 2001, Vienna, Austria, 01/8/21. https://doi.org/10.1007/3-540-44668-0_135
Wada Y, Kaneko Y, Nakano E, Osu R, Kawato M. 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. Springer Verlag. 2001. p. 977-984. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-44668-0_135
Wada, Yasuhiro ; Kaneko, Yuichi ; Nakano, Eri ; Osu, Rieko ; Kawato, Mitsuo. / Multi-joint arm trajectory formation based on the minimization principle using the euler-poisson equation. Artificial Neural Networks - ICANN 2001 - International Conference, Proceedings. Vol. 2130 Springer Verlag, 2001. pp. 977-984 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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