Jake Brownson wrote:
> I'm trying to measure relative rotation within a sphere. I have an
> ACA302 (http://www.star-micronics.co.jp/eng/products/sensor/se01.htm).

If you want to become a good engineer, you're going to have to learn to
describe things carefully.  This is a mess.  My freshman physics professor
would have thrown me out of class for a description like this.  You have a
picture in your mind, but are forgetting there are more degrees of freedom
than you are fixing in your description.  Frankly I'm rather confused about
your setup.

> So, imagine holding a pole with an accel attached at the end, you can
> spin in place (horizontal rotation),

So the pole is being extended horizontally?  What the heck is "spin in
place" supposed to mean, rotation along the pole's axis, or just that the
center of rotation is as the center of the pole?

> and raise the pole up and down (vertical rotation),

Think back to freshman physics.  Raising something up or down describes a
displacement, not a rotation.  I can't even imagine how to get "vertical
rotation" (rotation about the Z axis?) out of this.

> Let's establish some terminology.

Good idea.

> The Z axis is pointing up from the accelerometer,

OK, I'm with you there.

> the X axis is pointing out from the middle of the sphere

That narrows it right down!  Can you show me a vector that does NOT point
out from the middle of the sphere.  *Think* about it.

> and the Y axis is normal to the plane made by Z and X.

That's a good thing, and I'll even assume that you mean that X, Y, and Z all
meet at right angles and that the coordinate system is right handed.

Why couldn't you have said "If you're looking at the sphere in front of you,
X is to the right, Y goes out the back, and Z is up.", if in fact that's
what you meant.

> I'm assuming that the person's rotations

What person?  This is the first mention of a person in all this.  How is the
person related to or connected to the sphere?  What does a person have to do
with anything at all?  And whatever happened to the pole?  What's it got to
do with anything?

> will be _relatively_ slow and
> smooth, so the vertical rotation can be measured by looking for an
> acceleration of 1G between the Z and X axes.

What the heck is "vertical rotation"?  It doesn't look like it's rotation
about the Z axis.  Since you want to measure it with changes in orientation
of the X and Z axes, I guess it's rotation about the Y axis, but I don't see
how "vertical rotation" specifies that any more than rotation about X
assuming it doesn't mean rotation about Z in the first place.

I think what you're trying to say is that you want to track slow rotations
(slow meaning centrifugal "accelleration" can be ignored?) by finding the
gravity vector.  Yes, that works except that it can't tell you angular
position about the vertical axis.

> The horizontal rotation will be a little more tricky...

I guess, whatever "horizontal rotation" means.

> theoretically I can do a numerical 'integration':

Theorectially, yes.  However the gain errors, offset, and hysteresis of real
accellerometers will cause runaway drift.  Your positional error will
increase with the square of time.  In practise this kind of inertial
navigation will probably only be useful for a few 100mS to a couple of
seconds or so, depending on the quality of your accellerometers and your
accuracy requirements.  I'm assuming you are using MEMS devices.  There are
gyros and accellerometers that can do useful inertial navigation for much
longer times, but these units cost in the 10s to 100s $K.

> Also
> I'm concerned that if the zero point for the accelerometer isn't
> calibrated _exactly_ the drift will add up very quickly.

Right.

> So is this idea insane?

For some thresholds of sanity.  How accurate does it need to be?  For how
long after starting from a known position?

> I'm aware of digital compass modules, and that is a possibility,
> however those need to be level to operate,

Why?  You should be able to measure the direction of external magnetic field
lines.  At least this will have a fixed angular error which will not
accumulate over time.  Whether the external magnetic field lines are all
parallel over the operating range of your device is another question.

> I also have a very low budget for this, and anything over $50
> might be a problem.

Then inertial navigation for anything more than a second or so to maybe 5-10
degrees error is probably out of the question, and I'm probably being
generous.

> By the way this is for a student project at Oregon Institute of
> Technology if anybody is curious.

It sounds like a good project you will learn a lot from.  Learning how to
perform inertial navigation with recalibration from as many external clues
as possible will be an excellent lesson, whether the final product severs a
useful purpose or not.

In general, I think you have the right idea.  Try to use gravity and the
magnetic field to provide a fixed external reference and try to fill in the
cracks with inertial navigation.  This won't be trivial, but an excellent
lesson.

What year are you in?  What course is this for?  What is your major?


******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products
-- 
http://www.piclist.com PIC/SX FAQ & list archive
View/change your membership options at
http://mailman.mit.edu/mailman/listinfo/piclist