Measuring tilt angle with CMMotionManager

Question

Suppose you are holding an iphone/ipad vertically in front of you with the screen facing you, in portrait orientation. You tilt the device to one side, keeping the screen facing you. How do you measure that static tilt angle using CMMotionManager? It seems a simple question which should have a simple answer, yet I cannot find any method that does not disappear into quaternions and rotation matrices.

Can anyone point me to a worked example?

Answer 1

It is kind of a late answer but you can found a working example on github and the blog article that comes with it.

To summarize the article mentioned above, you can use quaternions to avoid the gimbal lock problem that you are probably facing when holding the iPhone vertically.

Here is the coding part that compute the tilt (or yaw) :

CMQuaternion quat = self.motionManager.deviceMotion.attitude.quaternion;
double yaw = asin(2*(quat.x*quat.z - quat.w*quat.y));

// use the yaw value
// ...

You can even add a simple Kalman filter to ease the yaw :

CMQuaternion quat = self.motionManager.deviceMotion.attitude.quaternion;
double yaw = asin(2*(quat.x*quat.z - quat.w*quat.y));

if (self.motionLastYaw == 0) {
    self.motionLastYaw = yaw;
}

// kalman filtering
static float q = 0.1;   // process noise
static float r = 0.1;   // sensor noise
static float p = 0.1;   // estimated error
static float k = 0.5;   // kalman filter gain

float x = self.motionLastYaw;
p = p + q;
k = p / (p + r);
x = x + k*(yaw - x);
p = (1 - k)*p;
self.motionLastYaw = x;

// use the x value as the "updated and smooth" yaw
// ...

Answer 2

Here is an example that rotates a UIView self.horizon to keep it level with the horizon as you tilt the device.

- (void)startDeviceMotionUpdates 
{
    CMMotionManager* coreMotionManager = [[CMMotionManager alloc] init];
    NSOperationQueue* motionQueue = [[NSOperationQueue alloc] init]
    CGFloat updateInterval = 1/60.0;
    CMAttitudeReferenceFrame frame = CMAttitudeReferenceFrameXArbitraryCorrectedZVertical;
    [coreMotionManager setDeviceMotionUpdateInterval:updateInterval];
    [coreMotionManager startDeviceMotionUpdatesUsingReferenceFrame:frame
                            toQueue:motionQueue
                            withHandler:
     ^(CMDeviceMotion* motion, NSError* error){
         CGFloat angle =  atan2( motion.gravity.x, motion.gravity.y );
         CGAffineTransform transform = CGAffineTransformMakeRotation(angle);
         self.horizon.transform = transform;
     }];
}

This is a little oversimplified - you should be sure to have only one instance of CMMotionManager in your app so you want to pre-initialise this and access it via a property.

Answer 3

Look at gravity:

self.deviceQueue = [[NSOperationQueue alloc] init];
self.motionManager = [[CMMotionManager alloc] init];
self.motionManager.deviceMotionUpdateInterval = 5.0 / 60.0;

// UIDevice *device = [UIDevice currentDevice];

[self.motionManager startDeviceMotionUpdatesUsingReferenceFrame:CMAttitudeReferenceFrameXArbitraryZVertical
                                                        toQueue:self.deviceQueue
                                                    withHandler:^(CMDeviceMotion *motion, NSError *error)
{
    [[NSOperationQueue mainQueue] addOperationWithBlock:^{
        CGFloat x = motion.gravity.x;
        CGFloat y = motion.gravity.y;
        CGFloat z = motion.gravity.z;
    }];
}];

With this reference frame (CMAttitudeReferenceFrameXArbitraryZVertical), if z is near zero, you're holding it on a plane perpendicular with the ground (e.g. as if you were holding it against a wall) and as you rotate it on that plane, x and y values change. Vertical is where x is near zero and y is near -1.

---

Looking at this post, I notice that if you want to convert this vector into angles, you can use the following algorithms.

If you want to calculate how many degrees from vertical the device is rotated (where positive is clockwise, negative is counter-clockwise), you can calculate this as:

// how much is it rotated around the z axis

CGFloat angle = atan2(y, x) + M_PI_2;           // in radians
CGFloat angleDegrees = angle * 180.0f / M_PI;   // in degrees

You can use this to figure out how much to rotate the view via the Quartz 2D transform property:

self.view.layer.transform = CATransform3DRotate(CATransform3DIdentity, -rotateRadians, 0, 0, 1);

(Personally, I update the rotation angle in the startDeviceMotionUpdates method, and update this transform in a CADisplayLink, which decouples the screen updates from the angle updates.)

You can see how far you've tilted it backward/forward via:

// how far it it tilted forward and backward

CGFloat r = sqrtf(x*x + y*y + z*z);
CGFloat tiltForwardBackward = acosf(z/r) * 180.0f / M_PI - 90.0f;

Answer 4

Since iOS8 CoreMotion also returns you a CMAttitude object, which contains pitch, roll and yaw properties, as well as the quaternion. Using this will mean you don't have to do the manual maths to convert acceleration to orientation.