Friday, August 30, 2013

Arduino: simple compass with HMC5883L + Library


One of the most popular I2C-compatible magnetometer is the Honeywell HMC5883L. These sensors’ solid-state construction with very low cross-axis sensitivity is designed to measure both the direction and 
the magnitude of Earth’s magnetic fields, from milli-gauss to 8  gauss. 
In this tutorial I'll try to: 
  1. Introduce how a magnetometer works
  2. Explain how to retrieve the heading from the magnetometer data
  3. Provide the little library I wrote for Arduino IDE

How does a magnetometer work?

An electronic magnetometer like the HMC5883L is based on the Anisotropic Magnetoresistance phenomenon. Mastering the physics that descibe the phenomenon is not an easy task, since this is a huge field whose depths we cannot hope to begin to plumb in these few words. 
Basically, the a magnetic field interacts with the path of the current flowing through a ferrous material, according to the Lorentz Law hence the resistance of the material seems to change to the observer. You can imagine as if the bar of ferrous material (e.g InSb) grows longer, raising its electric resistance. Therefore measuring the change in the resistance we can estimate the magnetical field! The Equation that rules the phenomenon is in the image below. For a further investigation of the matter, especially on the electronics a magnetometer is based upon, you could read this.

From the raw data to the north! 

Supercomputer models of Earth's magnetic field from

In a compass, the magnetic field you measure is the earth's one. It is tangential to the surface of the planet and it flows from north to south. The HMC5883L has three different axis to calculate the headings, as you may not know the tilt of your device (i.e. our quadcopter) when you need the data! Anyway for this example we will assume that the sensor is flat on a table, so we don't have to worry about its tilt. Therefore we'll use only X and Y axes data.

We'll assume Hz =0

Hence the angle between the Y axis and the magnetic north will be, according to the quandrant:

Direction (y>0) = 90 - [arctan(x/y)] * 180 / π
Direction (y<0) = 270 - [arctan(x/y)] * 180 / π
Direction (y=0, x<0) = 180.0
Direction (y=0, x>0) = 0.0

First of all we have to scale the raw data according to the scale we chose.
The valid gauss values are: 0.88, 1.3, 1.9, 2.5, 4.0, 4.7, 5.6, 8.1. Of course for a geo-compass we just need 1.3 Ga, that leads us to a 0.92 [mG/LSb] of resolution and a gain of 1090 [LSb/Gauss]. The code I provide with this post is based on the code found here, but at the time this post is written, the original code won't work. There are some huge bugs as floating point number comparison that will not allow you to change the scale factor of the sensor, and some queer bugs on error handling (basically that code doesn't check for error at all, as you can easily prove executing it: it will always display an error setting the scale, and setting the measurement mode. More oddly this latter error display the same message because the error variable is not reset after its use). Of course even my library will have some bugs too, and it's not complete at all, but it's a good start to familiarize with the sensor itself.

Here is the code with a lots of comments:

On the image below you can see how the heading measured with an iPhone 4 is quite close to the one we read from Arduino. There are many margin of improvement. First, we ought compensate the potential tilt of the device using the accelerometer data from the ADXL345, for example using the info on my previous post! Moreover, my breadboard has an aluminium ground plane at its bottom, which can obviously make harder for the structure to sense the magnetic field and/or could drift it and create an offset.

Tuesday, August 27, 2013

Arduino IMU: Pitch & Roll from an ADXL345


The ADXL345 accelerometer measures the X,Y,Z components of the device's acceleration but in order to use this information we need to manipulate the data to a more convenient format. First of all, even if it's not mandatory, I prefer to scale the raw data from the sensor in a International System measure (g). There is this simple equation that binds the two kind of measurements:

Moreover, since I want to use the IMU for the construction of a quadcopter, I will need the estimation of pitch and roll. As you can easily imagine, there's no way to determine the yaw just trough the accelerometer's data. Indeed, if you imagine an airplane laying on the flat surface of the airport with the Z-axis perpendicular to its wing-plane, there are no change in the gravity (static acceleration) if you rotate it. But you can calculate its tilt!  That's what we're gonna do.

With a little bit of math you can see how pitch and roll can be estimated with just the three x,y and z "native" accelerometer's outputs. Indeed: 

Where φ is the roll angle and θ is the pitch angle. On Arduino you can use atan2() to semplify your integrity check (denominator must not be zero of course) which eliminate the ambiguity of the angle depending on the quadrant.

Roll & Pitch estimation

In this tutorial I'll use the same configuration as the last post but the ADXL345 is mounted on a GY80 made-in-china IMU I bought to bring on my test without spend a lot. It mounts 4 different sensors, of which I'll write on my next post.

In the snippet above I've inserted just the code relative to the post's arguments, if you want the whole code leave a comment with a valid email. The serial output is shown in the image below.