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J Neurophysiol 81: 2140-2155, 1999;
0022-3077/99 $5.00
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The Journal of Neurophysiology Vol. 81 No. 5 May 1999, pp. 2140-2155
Copyright ©1999 by the American Physiological Society

Quantitative Examinations of Internal Representations for Arm Trajectory Planning: Minimum Commanded Torque Change Model

Eri Nakano,1,2 Hiroshi Imamizu,3 Rieko Osu,3 Yoji Uno,4 Hiroaki Gomi,5 Toshinori Yoshioka,3 and Mitsuo Kawato1,3

 1ATR Human Information Processing Research Laboratories, Kyoto 619-0288;  2Graduate School of Science and Technology, Kobe University, Hyogo 657-0013;  3Kawato Dynamic Brain Project, ERATO, Japan Science and Technology Corporation, Kyoto 619-0288;  4Department of Information and Computer Sciences, Toyohashi University of Technology, Aichi 441-8540; and  5NTT Communication Science Laboratories, Nippon Telegraph and Telephone Corporation, Kanagawa 243-0198, Japan

Nakano, Eri, Hiroshi Imamizu, Rieko Osu, Yoji Uno, Hiroaki Gomi, Toshinori Yoshioka, and Mitsuo Kawato. Quantitative Examinations of Internal Representations for Arm Trajectory Planning: Minimum Commanded Torque Change Model. J. Neurophysiol. 81: 2140-2155, 1999.Quantitative examinations of internal representations for arm trajectory planning: minimum commanded torque change model. A number of invariant features of multijoint planar reaching movements have been observed in measured hand trajectories. These features include roughly straight hand paths and bell-shaped speed profiles where the trajectory curvatures between transverse and radial movements have been found to be different. For quantitative and statistical investigations, we obtained a large amount of trajectory data within a wide range of the workspace in the horizontal and sagittal planes (400 trajectories for each subject). A pair of movements within the horizontal and sagittal planes was set to be equivalent in the elbow and shoulder flexion/extension. The trajectory curvatures of the corresponding pair in these planes were almost the same. Moreover, these curvatures can be accurately reproduced with a linear regression from the summation of rotations in the elbow and shoulder joints. This means that trajectory curvatures systematically depend on the movement location and direction represented in the intrinsic body coordinates. We then examined the following four candidates as planning spaces and the four corresponding computational models for trajectory planning. The candidates were as follows: the minimum hand jerk model in an extrinsic-kinematic space, the minimum angle jerk model in an intrinsic-kinematic space, the minimum torque change model in an intrinsic-dynamic-mechanical space, and the minimum commanded torque change model in an intrinsic-dynamic-neural space. The minimum commanded torque change model, which is proposed here as a computable version of the minimum motor command change model, reproduced actual trajectories best for curvature, position, velocity, acceleration, and torque. The model's prediction that the longer the duration of the movement the larger the trajectory curvature was also confirmed. Movements passing through via-points in the horizontal plane were also measured, and they converged to those predicted by the minimum commanded torque change model with training. Our results indicated that the brain may plan, and learn to plan, the optimal trajectory in the intrinsic coordinates considering arm and muscle dynamics and using representations for motor commands controlling muscle tensions.




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