Equilibrium-point control hypothesis examined by measured arm stiffness during multijoint movement

Science

Volumn 272, Issue 5258, 1996, Pages 117-120

  Gomi, Hiroaki ^a   Kawato, Mitsuo ^b  

^a Kashino Diverse Brain Research Laboratory of NTT Communication Science Laboratories   (Japan)

^b ADVANCED TELECOMMUNICATIONS RESEARCH INSTITUTE INTERNATIONAL   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ADULT; ARM MOVEMENT; ARTICLE; FEMALE; HUMAN; HUMAN EXPERIMENT; HYPOTHESIS; JOINT FUNCTION; JOINT STIFFNESS; MALE; MOTOR CONTROL; MOTOR COORDINATION; MUSCLE FUNCTION; NORMAL HUMAN; PRIORITY JOURNAL; VELOCITY;

EID: 0030010484     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.272.5258.117     Document Type: Article

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32. ext by the PFM. In the analysis, they were, respectively, measured as the difference between the perturbed trajectory and the control trajectory (the average of perturbed trajectories) and its first and second derivatives Offsets in all quantities relative to the control trajectory at the start of a perturbation were eliminated. The force perturbation was derived as the difference between the perturbed and the control external torque patterns. D and R denote viscosity and stiff ness matrices, respectively. If we apply a least-squared error estimation method to this vanational equation, then the time-variant 2 × 2 matrices for the acceleration coefficient (inertia), velocity coefficient (viscosity), and position coefficient (stiffness) can be estimated, but for the inertial matrix 36 (4 components × 9 times), independent parameters must be estimated. Because the left sides of both Eqs 1 and 2 can be linearized with respect to the physical parameters of the links, only three independent parameters are sufficient to specify them Those are uniquely determined from the physical characteristics of the links. These three parameters were preestimated with the use of all the data sets measured for each person, then viscosity and stiffness were estimated at each perturbation time (18).
33. d - θ) (6) For the case of single joint movement, it was demonstrated that with this new version a simple trajectory can control relatively fast movement (6). However, we found that even with this new version, a simple straight equilibrium-point trajectory cannot control multijoint movements (10) [N Schweighofer, thesis, University of Southern California (1995)]. This is reasonable because the viscosity force is always one order of magnitude smaller than the elastic force in our experiments. The third possible criticism is that for some reason our measured stiffness values are different from those used under the equilibrium-point control hypothesis. For example, stiffness value estimations depend on the perturbations used. In our exploratory experiments, we found that the measured stiffness values became smaller for larger amplitude perturbations and for lower temporal frequency (12, 13) Because the equilibrium-point trajectory seems to be larger in amplitude and lower in temporal frequency than the currently used perturbation patterns, our stiffness estimation may be an overestimation. Consequently, our main conclusion here still holds.
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38. We thank M. Honda and K. Ishii of NTT and Y. Tohkura of ATR for their continuing encouragement; F. Pollick and S. Schaal for improving the manuscript; and N. Imamura and E. Nagaoka of KOBELCO and T. Yoshioka of CSK Corp for their technical support. Supported by Human Frontier Science Program grants to M.K.