ImuCalibration

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Theory

Accelerometers and Magnetometers calibration is critical for AHRS performances and can be performed using no special hardware. For the magnetometer, it is even very important that the calibration be performed in the fully assembled vehicle, with all systems powered. This is the so-called hard-iron calibration and will allow us to compensate for any constant parasitic magnetic field generated by the vehicle. The calibration process consist in finding a set of neutrals and scale factors for each sensor, such as



The principle of the calibration is the following : An accelerometer, on a vehicle at rest measures a constant vector ( the opposite of gravity ) in the earth frame, expressed in the vehicle frame.


DCM is a rotation matrix that converts between earth frame and body frame. It will change when we change the orientation of the vehicle. Nevertheless, a rotation conserves the norm of a vector. We can thus obtain the following scalar equation that doesn't depend on the vehicle orientation :


We can then record an important number of measurements in different orientations and find the set of scale factor and neutral giving the norm closest to 9.81

calibration script

Booz comes with a python script to perform this operation ( sw/tools/calibration/calibrate.py ). Here is the way to use it

Switch to the "raw sensors" telemetry mode and launch "server" to record a log.

Move the quad in different orientations ( upright, inverted, on nose, on tail, on right side, on left side ) . You can also take some measurememts banking 45 degres.

Try to get an homogeneous distribution of your measurements. I find it better to let the quad rest while measuring.


You can then run the python script to get your calibration coefficients. e.g. for accelerometer calibration: sw/tools/calibration/calibrate.py -i <your_ac_id> -s ACCEL <path_to_data_file>

It first makes an initial guess using min and max, ie for each axis

neutral = 0.5 * (max + min)

sensitivity = 0.5*(max-min)

It then uses a datafit algorithm to optimise the initial guess


Screenshot of scilab version. CalibAccel.png

this is not clear, more ont later ->


Note for magnetometer: Because the magnetic field changes depending where on the globe you are, you will have to recalibrate your mag to fly somewhere else. When you move the quad to different positions for logging make sure you align it along the direction of the magnetic field which will result in the maximum values for each axis ( or you can look up the inclination and declination of the magnetic field where you live here).


Finding Signs

For supported IMUs, sign "should" ( will.. ) be hardcoded in the code. If using a new IMU or sign for yours are not in the code yet, here is the way to find them.

We're calibrating everything relative to the IMU frame - Booz has a parameter to define the orientation of the IMU with respect to the body of the vehicle that we'll use later, once you'll have decided of a good mechanical mounting.

Booz uses North East Down ( NED) frame, that is positive x is pointing to the front, positive y to the righ and positive z down.

Accelerometer:

An accelerometer measures the non gravitational acceleration, that is

 is pointing down, so  is pointing up. So stop moving, disregard earth rotation and you'll measure 
-When your IMU is level you should see x=0 y=0 z=-9.81
-When you pitch up -g is aligning with x, so you should see  x>0, y=0 and z<0
-When you bank left -g is aligning with y, so you should see x=0, y>0 and z<0


Magnetometer:

A magnetometer measures the magnetic vector, that is a vector pointing north and down

-When you align your IMU with the direction of north, you should see x>0, y=0, z>0
-when you pitch down the IMU, the magnetic vector is aligning with x, so x should increase and z should decrease to zero.
-if you yaw your IMU to the left, the magnetic vector is aligning with y, so y should be positive, x should decrease to zero and z stay positive

Gyrometer:

You need some turntable to calibrate the scale factors of your gyros. For signs, the definition of the frame give the following properties:

-when banking right,  should be positive
-When pitching up,  should be positive
-When yawing to the right,  should be positive

Verification:

Switch to AHRS telemetry mode and look for the fields that are prefixed with imu_

-bank righ should give positive phi 
-pitch up should give positive theta
-yaw right should give increasing psi
-the value you'll see after letting the IMU rest will end up being the "measure" ( that is accelerometer and mag ). If those are wrong the problem is in the calibration of your sensors
-the value you get while moving the IMU are influenced by the gyro. If what you see is the value you crazy when you move then stabilize to something good after you stop moving, the problem is in your gyros

Body to IMU rotation

coming soon !