Quantitative examinations for multi joint arm trajectory planning - using a robust calculation algorithm of the minimum commanded torque change trajectory

Citation
Y. Wada et al., Quantitative examinations for multi joint arm trajectory planning - using a robust calculation algorithm of the minimum commanded torque change trajectory, NEURAL NETW, 14(4-5), 2001, pp. 381-393
Citations number
16
Language
INGLESE
art.tipo
Article
Categorie Soggetti
AI Robotics and Automatic Control
Journal title
NEURAL NETWORKS
ISSN journal
0893-6080 → ACNP
Volume
14
Issue
4-5
Year of publication
2001
Pages
381 - 393
Database
ISI
SICI code
0893-6080(200105)14:4-5<381:QEFMJA>2.0.ZU;2-I
Abstract
In previous research, criteria based on optimal theories were examined to e xplain trajectory features in time and space in multi joint arm movement. F our criteria have been proposed. They were the minimum hand jerk criterion (by which a trajectory is planned in an extrinsic-kinematic space), the min imum angle jerk criterion (which is planned in an intrinsic-kinematic space ), the minimum torque change criterion (where control objects are joint lin ks; it is planned in an intrinsic-dynamic-mechanical space), and the minimu m commanded torque change criterion (which is planned in an intrinsic space considering the arm and muscle dynamics). Which of these is proper as a cr iterion for trajectory planning in the central nervous system has been inve stigated by comparing predicted trajectories based on these criteria with p reviously measured trajectories. Optimal trajectories based on the two form er criteria can be calculated analytically. In contrast, optimal trajectori es based on the minimum commanded torque change criterion are difficult to be calculated, even with numerical methods. In some cases, they can be comp uted by a Newton-like method or a steepest descent method combined with a p enalty method. However, for a realistic physical parameter range, the forme r becomes unstable quite often and the latter is unreliable about the optim ality of the obtained solution. In this paper, we propose a new method to stably calculate optimal trajecto ries 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 th e boundary conditions strictly, is expressed by using orthogonal polynomial s. The coefficients of the orthogonal polynomials are estimated by using a linear iterative calculation so as to satisfy the Euler-Poisson equations w ith a sufficiently high accuracy. In numerical experiments, we show that th e optimal solution can be computed in a wide work space and can also be obt ained in a short lime compared with the previous methods. Finally, we perform supplementary examinations of the experiments by Nakano , Imamizu, Osu, Uno, Gomi, Yoshioka et al. (1999). Estimation of dynamic jo int torques and trajectory formation from surface electromyography signals using a neural network model. Biological Cybernetics, 73, 291-300. Their ex periments showed that the measured trajectory is the closest to the minimum commanded torque change trajectory by statistical examination of many poin t-to-point trajectories over a wide range in a horizontal and sagittal work space. We recalculated the minimum commanded torque change trajectory usin g the proposed method, and performed the same examinations as previous inve stigations. As a result, it could be reconfirmed that the measured trajecto ry is closest to the minimum commanded torque change trajectory previously reported. (C) 2001 Elsevier Science Ltd. All rights reserved.