iOS CoreMotion CMAttitude relative to north pole

Question

I'm currently using CoreMotion's DeviceMotion to get the orientation (roll, pitch, yaw) of the iPhone. Now I would like to have these values relative to the geographic north pole; so I need a CMAttitude reference object containing the roll, pitch and yaw values, which would be reported, if the back of the iPhone would face to the north pole (3D). The CLLocationManager only returns the magnetic heading (x, y, z) in Tesla.

Do you have an idea of how to convert those values to roll, pitch and yaw?

Thanks in advance,

Alexander

Answer 1

iOS 5 provides the designated method. Look for CMAttitudeReferenceFrameXTrueNorthZVertical in the developer documentation.

Answer 2

Pseudo code:

1. start device motion updates
2. start a camera preview in the background ;)
3. capture the current gravity reading from the device as a CMAcceleration... once you have gravity store it in a local variable.
4. Then you have to take the 2 vectors and get the angle in between them, in this case the device gravity of (0,0,-1) and the real gravity vector...
5. we then turn theta into thetaPrime... a transform that matches the CoreMotion reference orientation
6. Setup a timer to animate....
7. during animation get the inverse of the rotationMatrix of motionManager's deviceMotion property.
8. Apply the Transformations in the correct order to reflect the device's current attitude (yaw,pitch,roll in eulerian mode or the devices quaternion rotation... 3 different ways to say the same thing basically)

Here is the code:

- (void) initMotionCapture
{
    firstGravityReading = NO;
    referenceAttitude = nil;

    if (motionManager == nil)
    {
        self.motionManager = [CMMotionManager new];
    }
    motionManager.deviceMotionUpdateInterval = 0.01;
    self.gravityTimer = [NSTimer scheduledTimerWithTimeInterval:1/60.0 target:self selector:@selector(getFirstGravityReading) userInfo:nil repeats:YES];
}


- (void) getFirstGravityReading
{
    CMAcceleration currentGravity; 

    CMDeviceMotion *dm = motionManager.deviceMotion;
    referenceAttitude = dm.attitude;
    currentGravity = dm.gravity;

    [motionManager startDeviceMotionUpdates];

    if (currentGravity.x !=0 && currentGravity.y !=0 && currentGravity.z !=0)
    {
        NSLog(@"Gravity = (%f,%f,%f)", currentGravity.x, currentGravity.y, currentGravity.z);

        firstGravityReading = YES;
        [gravityTimer invalidate];
        self.gravityTimer = nil;
        [self setupCompass];
    }
}

- (void) setupCompass
{
    //Draw your cube... I am using a quartz 3D perspective hack!
    CATransform3D initialTransform = perspectiveTransformedLayer.sublayerTransform;
    initialTransform.m34 = 1.0/-10000;


    //HERE IS WHAT YOU GUYS NEED... the vector equations!
    NSLog(@"Gravity = (%f,%f,%f)", currentGravity.x, currentGravity.y, currentGravity.z);

    //we have current gravity vector and our device gravity vector of (0, 0, -1)
    // get the dot product
    float dotProduct = currentGravity.x*0 + currentGravity.y*0 + currentGravity.z*-1;
    float innerMagnitudeProduct = currentGravity.x*currentGravity.x + currentGravity.y + currentGravity.y + currentGravity.z*currentGravity.z;
    float magnitudeCurrentGravity = sqrt(innerMagnitudeProduct);
    float magnitudeDeviceVector = 1; //since (0,0,-1) computes to: 0*0 + 0*0 + -1*-1 = 1

    thetaOffset = acos(dotProduct/(magnitudeCurrentGravity*magnitudeDeviceVector));
    NSLog(@"theta(degrees) = %f", thetaOffset*180.0/M_PI);

    //Now we have the device angle to the gravity vector (0,0,-1)
    //We must transform these coordinates to match our 
    //device's attitude by transforming to theta prime
    float theta_deg = thetaOffset*180.0/M_PI;
    float thetaPrime_deg = -theta_deg + 90; // ThetaPrime = -Theta + 90 <==> y=mx+b

    NSLog(@"thetaPrime(degrees) = %f", thetaOffset*180.0/M_PI);

    deviceOffsetRotation = CATransform3DMakeRotation((thetaPrime_deg) * M_PI / 180.0, 1, 0, 0);
    initialTransform = CATransform3DConcat(deviceOffsetRotation, initialTransform);

    perspectiveTransformedLayer.sublayerTransform = initialTransform;

    self.animationTimer = [NSTimer scheduledTimerWithTimeInterval:1/60.0 target:self selector:@selector(tick) userInfo:nil repeats:YES];

}

- (void) tick
{
    CMRotationMatrix rotation;

    CMDeviceMotion *deviceMotion = motionManager.deviceMotion;
    CMAttitude *attitude = deviceMotion.attitude;

    if (referenceAttitude != nil)
    {
        [attitude multiplyByInverseOfAttitude:referenceAttitude];
    }
    rotation = attitude.rotationMatrix;

    CATransform3D rotationalTransform = perspectiveTransformedLayer.sublayerTransform;

    //inverse (or called the transpose) of the attitude.rotationalMatrix
    rotationalTransform.m11 = rotation.m11;
    rotationalTransform.m12 = rotation.m21;
    rotationalTransform.m13 = rotation.m31;

    rotationalTransform.m21 = rotation.m12;
    rotationalTransform.m22 = rotation.m22;
    rotationalTransform.m23 = rotation.m32;

    rotationalTransform.m31 = rotation.m13;
    rotationalTransform.m32 = rotation.m23;
    rotationalTransform.m33 = rotation.m33;

    rotationalTransform = CATransform3DConcat(deviceOffsetRotation, rotationalTransform);
    rotationalTransform = CATransform3DConcat(rotationalTransform, CATransform3DMakeScale(1.0, -1.0, 1.0));


    perspectiveTransformedLayer.sublayerTransform = rotationalTransform;
}

Answer 3

You would need to calibrate your yaw value to the magnetic heading now and then to make sure you are on the right track. Check out this explanation on how to compensate the shaky compass: Compensating compass lag with the gyroscope on iPhone 4

Answer 4

The Tesla values are magnetic field strength, a measure of how much magnetic "pull" is felt in each of the three axes. Only by combining this information with accelerometer data, and doing a bunch of fancy math, can you get an actual heading (which way the device is "pointing" relative to magnetic north). Then add in information from the GPS and do more math, to get the true heading (relative to the geographic north pole).

Long story short, you probably don't want to do the math yourself. Luckily iOS provides both magneticHeading and trueHeading in its CLHeading object, available from the CLLocationManager heading property.

To get pitch and roll, which describe how the device is tilted, also involves doing math on these same raw data from the magnetometer and accelerometer. Sorry I don't know of any iOS API for pitch and roll.