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Ton Van Den Bogert
06-01-1999, 01:45 AM
Necip Berme wrote to Biomch-L:

> I was expecting Albert King from Wayne State University to respond to the
> "accelerometer gravity correction" listing. As he has not, I am doing so to
> set the record straight. In 1970's one of Dr. King's doctoral students
> showed that nine accelerometers appropriately positioned on a rigid body
> are necessary and sufficient to separate the effect of gravity from the
> other acceleration information. Hence, it is possible to calculate the
> position of a rigid body from acceleration data.

Dr. Berme is correct and it is important for anyone using 3-D accelerometry
to know about this work. The full reference is:

N.K. Mital and A.I. King (1979) Computation of rigid-body rotation in
three-dimensional space from body-fixed linear acceleration measurements.
J. Appl. Mech. 46: 925-930.

Mital and King were able to solve the angular acceleration vector of a rigid body
from multiple accelerometer signals, and successfully eliminated the effect of
gravity on that result. Obtaining the attitude then required a double integration
in order to obtain Euler angles. This works for movements of short duration with
accurately known initial conditions (initial attitude and angular velocity). For
movements of longer duration, the end result will drift noticeably due to
inaccuracies in the initial conditions of the integration. It would be hard to
predict at which duration this becomes a problem. My feeling is that it is not
a practical method for most applications. Movement analysis in automobile crash
testing is probably a feasible application, and I think this is the area that Dr.
King works in.

Angular velocity can also be solved directly, using the centrifugal terms in
the accelerometer signals, but this tends to be noisy for typical movements
(my own observations). On the other hand, then only a single integration
is required to obtain Euler angles. Attitude (or Euler angles) can not
be solved directly from the accelerometer signals. Integration is always
required.

Once attitude is known, the gravity contribution to the translational
acceleration of the rigid body can then be calculated and a correction can
be made to obtain the true translational accelerations. With a further
double integration, position and velocity of the rigid body will be known.

There is an even earlier paper where a similar analysis was used, although
no integrations were carried out. Only angular velocity and angular
acceleration were needed. Reference:

T.R. Kane, W.C. Hayes and J.D. Priest (1974) Experimental determination
of forces exerted in tennis play. In: R.C. Nelson and C.A. Morehouse (eds.)
Biomechanics IV, University Park Press, Baltimore, pp. 284-290.

For the sake of completeness, here is a later development of that method.
The methodology is presented, but to my knowledge it has not been applied
again. Reference:

W.C. Hayes, J.D. Gran, M.L. Nagurka, J.M. Feldman and C. Oatis (1983) Leg motion
analysis during gait by multiaxial accelerometry: theoretical foundations and
preliminary validations. J. Biomech. Eng. 105:283-289.

Ton van den Bogert

--

A.J. (Ton) van den Bogert, PhD
Department of Biomedical Engineering
Cleveland Clinic Foundation
9500 Euclid Avenue (ND-20)
Cleveland, OH 44195, USA
Phone/Fax: (216) 444-5566/9198

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