Calculating gyroscope turn regardless of angle

[brownt]

Hi,

I am using an electronic gyroscope and accelerometer, and I want to calculate the degrees the device has turned regardless of any angle changes whilst it is turning. So for example with the Z gyroscope I can calculate a 90 degree turn accurately, but of course when I tilt the device, the Z gyroscope readings slow down relative to the angle. The steeper the angle the slower the readings. I guess tilt compensation is possible using trigonometry, but I have tried various things and I have not been able to get it right.

I want to be able to measure the degrees turned around a particular axis regardless of how the device is tilting during that turn.

I have also tried summing all the X, Y and Z values together, which might work but the gyroscope values change during any angle change, and that is added to the equation.

any ideas?

thanks

 

[c_mitra]

This is basically a matter of coordinate frame and how they transform once the object is subject to external forces.

The Z gyroscope axis is fixed on the device; If the device is rotated by 90 deg and you take a turn about the (old) Z axis, it will not be recorded by the device.

 

[brownt]

This is basically a matter of coordinate frame and how they transform once the object is subject to external forces.

The Z gyroscope axis is fixed on the device; If the device is rotated by 90 deg and you take a turn about the (old) Z axis, it will not be recorded by the device.

Yes that is understood. thanks. But how do I implement a coordinate frame?

 

[brownt]

This is basically a matter of coordinate frame and how they transform once the object is subject to external forces.

The Z gyroscope axis is fixed on the device; If the device is rotated by 90 deg and you take a turn about the (old) Z axis, it will not be recorded by the device.

What is the mathematical relationship between gyroscope output and angle.
When there is no angle the degrees per second around a gyroscope axis is at maximum, say 2000 dps. When the device is on a 45 degree pitch, what is now the gyroscope output, is it half. And is it linear through the angle change?

 

[FvM]

Consider cosine function.

 

[brownt]

thanks. I have considered cosine. That would give a gyroscope output of 0.707 at 45 degrees pitch. Is that correct though. The physical tests I have done show 0.5 gyro output at 45 degrees pitch.

 

[brownt]

thanks for that. The reason why cosine does not rule is because it does not work. My physical tests show that when the device is on a 45 degree pitch, the output from the gyroscope is halved, but the cosine of 45 degrees is 0.707. How do I use that to produce a doubling of the output.

 

[brownt]

I have looked at the paper and it is beyond my understanding. The only part of the technicalities I understood was the final equation. angle = sqrt(x * x + y * y + z * z). Perhaps if I take the cosine of that angle and divide it into the relevant gyroscope output it will compensate for the angle change?

 

[FvM]

I don't see a reason why cosine law shouldn't rule in this case.

A paper related to your original question www.mdpi.com/1424-8220/11/9/8536/pdf

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The reason why cosine does not rule is because it does not work.

That's not a reason. It's an observation apparently contradicting an assumption. To give a reason why the assumption is wrong, you have to derive the correct relation from physical law.

 

[c_mitra]

angle = sqrt(x * x + y * y + z * z)...

This cannot be an accurate formula: angle is dimensionless and the right-hand-side is L²

I do not understand what are these x, y and z quantities are ...

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A paper related to your original question www.mdpi.com/1424-8220/11/9/8536/pdf...

The paper appears to be correct (not because I too have published a paper in the same journal) but it is true that transformations using rotational axes (also use Euler angles) can be confusing.

But what the application notes say?