Combining Euler angles to get the correct orientation

RobM · 2013-12-08T19:08:14

I've been working on an issue for around 2 weeks now and I'm so close but yet so far from a solution. I've been trying to create an orientation matrix from my IMU sensor (gyro, accelerometer and magnetometer) and I've got yaw and pitch working but I'm having a problem with roll. In my current setup (I've tried all sorts of quaternion and matrix solutions), I'm computing the figure for yaw and this I can do regardless of how the sensor is tilted. It also returns the true yaw when the sensor is upside down, i.e. pitched by 180 degrees. So yaw gives me a 0-359 reading for which direction the sensor's +z axis is pointing in pretty much any orientation. I've also managed to get the pitch in degrees between 0-359 and if I create myself a matrix using MatrixRotationYawPitchRoll with zero roll, I can happily move the sensor around and yaw and pitch work perfectly. If I hold the sensor flat and roll it, half way down, my screen object tends to go a bit strange in order to get itself in the right orientation for it being upside down and facing the opposite direction yaw-wise. So just to clarify that, if I hold the sensor flat and z is pointing zero degrees north, if rotate it on that z axis 180 degrees, my avatar pitches over and ends up facing in the opposite direction but upside down as expected. If, from the original flat position again, I _roll_ it 180 degrees, my avatar [eventually] ends up upside down and facing me - as expected. Now as it looks as though pitch and yaw work correctly, I naively thought it was a simple case of adding roll and that would be it. That's obviously not the case. So the directx YawPitchRoll method apparently applies roll, then pitch, then yaw. I've read in several places that in order for this to work correctly, we need to do things like have pitch going from -90 to 90 only and I can understand that if you yaw'd around 180 degrees, the limited pitch movement combined with full yaw still gives you effectively 360 degrees of pitch. But what do I need to do for roll in this situation? I know order matters and I guess it doesn't matter which one you choose as long as you stick to it so the DX roll, pitch, yaw seems to be the one to go for, especially as there's already a method to create the matrix. So given the order is roll, pitch and yaw, which of these do I need to make full 0-360 and which need to be -90 to 90? Sensor-wise, it returns degrees per second around each axis which I use to smooth out the accelerometer vector. The accelerometer vector always points toward gravity (down) so if you rotate the sensor, the accelerometer vector returned is effectively the inverse of that. I use this vector to get my pitch angle and I also couple it with the magnetometer vector to get the yaw. Roll is slightly more tricky because you have to effectively remove pitch in order to get the roll. I've ordered a book on rotations and quaternions but until that arrives I wondered if any of you could give me a quick hand? I'm getting close to being out of ideas. Thanks

Math and Physics Programming

Started by RobM December 06, 2013 01:32 PM

9 comments, last by RobM 11 years, 2 months ago

RobM

Author

1,164

December 08, 2013 07:08 PM

When the sensor is at rest sitting on the table, the vector is pointing directly down.

That makes no sense. The acceleration should be pointing directly up when the device is resting on the table: The table is pushing the device up, which is what is being detected.

The acceleration is essentially gravity, so when the device is flat, gravity is 1G (normalized) and pointing directly down, hence -1. I actually flip it so it shows 1 as it made it easier to visualise (I show a line on the screen depicting the accelerometer vector).

I reread your previous post earlier - I've been playing about with quaternions today. I created 3 actually, one for each axis. I create one which is rotation about Y (or up) by the yaw, then I use the cross of yaw -90 (and up) to create one for the pitch and then create one for the roll. Using these and multiplying them together I can apply Euler angles for yaw, then pitch and then roll. Doing some test numbers gives correct results even using full 360 degree values.

So now I have this, and I can get the accurate tilt-compensated yaw, I just need to get the pitch and roll from the accelerometer and that should be it.

So your idea of using the gyro to get the quaternion and then nudging towards the accelerometer values, could you elaborate a bit on that?

Combining Euler angles to get the correct orientation

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