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How to integrate a gyroscope?

  1. Jul 14, 2011 #1
    Hey guys,

    I recently did a project with combining and accelerometer and gyroscope together using the 6DOF IMU Razor and an Arduino and now i need to try something different but i need some help. How does one integrate a gyroscope output? I tried something like this below but i dont think its complete:

    Code (Text):
        xGyro  = analogRead((X_GYRO_APIN) - 403); //removing offset from raw ADC value
        xGyro *= (3.3 / 1023.0) / 0.00333; //now reads deg/sec
        tmpf = xGyro;
        tmpf *= interval / 1000.0f; //now reads deg
    How do i update my angle, hence integrating my gyro?

    Any help is much appreciated!
  2. jcsd
  3. Jul 14, 2011 #2
    Well, there are a lot of different numerical integration techniques. The simplest follows this pattern and is called "rectangular integration"...

    You need two things: your current velocity (degrees/sec in this case) and the time between your current sample and previous sample (in seconds of course). Then your angle is just the running sum of your previous angles and the current velocity divided by the time delta.

    angle = angle + velocity/deltat;
  4. Jul 14, 2011 #3
    Ok so, up to now ive found my deg/sec and ive also divided it by time so as to get my value in deg. How do i get my current and previous time sample though? And does "angle" represent the degrees value in this case? Like this:
    Code (Text):
        xGyro  = analogRead((X_GYRO_APIN) - 403); //removing offset from raw ADC value
        xGyro *= (3.3 / 1023.0) / 0.00333; //now reads deg/sec
        angle = xGyro*time;
        angle = angle + xGyro)/time
    And my time could be any sample time? (eg 100ms)?
    Last edited: Jul 14, 2011
  5. Jul 14, 2011 #4
    Your time between samples depends on how your system works. The easiest method is to have a system that sample at a constant rate... for example at 100Hz. In this case your time between samples would always be 0.01 seconds. This can be done in different ways, from using a periodic interrupt for a software based system or implementing the periodic sampling in hardware (where you software would then read out of buffered data).

    In other systems you may not be able to periodically sample. In this case you may have to time stamp the data and determine how long it has been between samples. A worse case here would be if you were using a Windows system. Every time you sample you may have to look at the system time and use it versus the system time of your previous sample to determine how long it has been between samples.

    In either case, the accuracy of your answer not only depends on the readings but also on your ability to determine the time between them.

    And actually I just realized I made a mistake in my earlier post. You actually want to multiply by time and not divide (you would divide if you were using frequency).

    So it should be: angle = angle + sample*sample_time


    If you think about it this way: velocity = change position / change in time

    So if you want to get change in position you need to multiply by change in time -> velocity * change in time = change position

    Now, if you sum up all your change in positions, you get your current position relative to where you started.
  6. Jul 14, 2011 #5
    you can try this way:

    Code (Text):
    double angle = 0.;  ///< your start (initial) angle in degree
    double time = 0.01; ///< [seconds] imagine that you get info every 10 milliseconds

    while(1) {
        xGyro  = analogRead((X_GYRO_APIN) - 403); //removing offset from raw ADC value
        xGyro *= (3.3 / 1023.0) / 0.00333; //now reads deg/sec
        angle += xGyro*time;
    this code is OK for one gyro integration. It will be more interesting when you start to integrate all three gyro together.
  7. Jul 14, 2011 #6
    i actually did do my integration like what you both just mentioned so its fine now, the only weird thing is that my graph looks funny now...im starting to think there's something wrong with my graph code and not my actual integral :/
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