This time I will discuss the gyro sensor (again). What it measures. How to cope with offset and drift. And how to use it.

Gyro sensors are among the most widely used sensors in robots. They are often used in self balancing robots for keeping upright. They are also used  in autonomous robots for keeping track of orientation. But also game controllers might use them to detect angular motion. A gyro sensor measures the angular velocity. In other words they measure how fast the sensor is rotating. This is most often expressed as degrees per second or radians per second. Some gyro sensors measure the angular velocity over one axis, others take measurements over two or three axes.

One should be aware that a  rotating object always rotates over just one axis. This axis however can have any orientation. Compare this to speed. An object can move in just one direction at any given time. This direction however can be any direction in a three dimensional space. Most often we do express the speed of an object over three perpendicular axes. A landing plane might fly at a speed of 600 km/s and descent at a rate of 5 m/sec. Wind might blow it off course at a rate of 0.5 m/sec. But still this plane goes in one direction only. The same is true for  angular velocity, an object rotates just with one speed, but we express its speed over three separate axes.

Let us take a look at the output of a typical gyro sensor. The graph below shows the output of a digital three axis gyro sensor (ITG-3200) over a period of 17 seconds. The X-axis is the time axis, the Y-axis shows the angular velocity expressed in degrees per second. After five seconds from the start of the measurement I rotated the gyro sensor clockwise for about 180 degrees. This took me about 3 seconds. After about 11.5 seconds I rotated the sensor back (counter clockwise). This graph tells us quite a lot. First, we notice that the sensor is a three axis sensor. It returns three different signals at any given time. Second, we can see that the rotation I made took place of the third axis, this is the Z-axis. It means that I rotated the sensor in the XY-plane. This is true, I had the sensor flat on my desk and I rotated it while keeping it flat. Third, a clockwise rotation is expressed as a negative angular velocity and a counter-clockwise rotation as a positive angular velocity. This is a matter of convention and is called the right-handed orientation system. Fourth, we can see that  when at rest the gyro signal is close to, but not exactly, zero. This is because the sensor is not perfect, it has a bit of an error. We’ll look into this error and ways to compensate for this later. And finaly, we cannot read the change of 180 degrees in orientation from the graph. This is because the sensor does not measure the orientation, instead it measures the angular velocity (speed of rotation). It is however possible to calculate the (change in) orientation from the angular velocity as I’ll explain later.

## Offset and drift correction

Let us concentrate on the error in the sensor signal right now. Below is a graph taken over a period of ten minutes while the sensor was at stand still all the time. A perfect sensor would output a rate of velocity of zero for all three axes all the time. Obviously this sensor does not.  The X-axis signal is around 2 instead of zero. This error is called the offset error. Every axis has its own offset error. For the X-asis this is around 2, for the Y-axis it is about 3.3 and for the Z-axis it is about -1.5. It is easy to correct for the offset error once you know how big it is. You just substract the offset error from the sensor signal to get a corrected value. The offset error itself can be calculated by taking the mean of a number of samples, take 100 for example.

The offset itself may seem constant, but in reality it is not. The offset of a sensor  is influenced by several factors and can change over time as a result. This is called sensor drift. One of the biggest factors contributing to sensor drift is temperature. You can notice this when one starts using a sensor. When being used, the temperature of a sensor rises a bit. It gets hotter then the ambient temperature. As a result the offset of the sensor changes. If you need a very good signal you should take this into account and let the sensor warm up before calculating the offset.
Some gyro sensors, like the Hitechnic gyro for example,  are seriously affected by changes in input voltage. As the NXT is battery powered this is a serious problem. Starting the motors of the NXT will result in a power drop and thus in a change in offset. There is a trick to avoid this if you have a sensor mux with an external power supply. Like this one from Mindsensors. In general I advise you to choose another gyro.
Even when temperature and power are constant the offset of a gyro will still vary a bit over time. This variation is called random walk.

There is a very elegant technique to deal with sensor drift. This is to constantly but slowly update the offset error of the sensor. Instead of treating the offset as a constant you  treat it as a value that can change over time. To calculate the offset you now use the moving average of the most recent samples as the offset. Then you always have an up-to-date offset. Calculating the moving average however is CPU intensive and you also need a lot of memory to store the samples. Therefore it is better to use a low-pass filter instead of a moving average. This does not use extra memory and little computing power but the effect is the same.
This technique will work very well when the sensor is at stand still. But will it work well when it is rotating? Any rotation will  influence the calculated offset. So of possible one should pause updating the offset while the sensor rotates? Sometimes another sensor can help to detect a rotation. A compass, an accelerometer or  motor encounters can all be off help.
However, there is also another solution. This one is based on the notion that a rotation in one direction is very often compensated with a rotation in another direction. A balancing robot for example stays upright, so in the long term it does not rotate. It might lean forward and backward for short moments of time. But this forward and backward rotations cancel each other out on the long run. So in the long run the average signal of the sensor equals the offset of the sensor, even when there are rotations from time to time. This means that even under dynamic circumstances one can constantly update the sensor offset. One only has to make sure to use enough samples so that there is enough time for rotations to cancel each other out. This technique is useful for balancing robots where rotations are short. It is less useful for slow turning robots where rotations have a long duration.

## Converting angular velocity to direction

There are situations where one needs to know the direction of the sensor. In navigation for example one needs to know in what direction a robot is heading. A gyro can provide this kind of information. There are some limitations though. So how do you transform angular velocity into direction? This is done by integration. This might seem difficult. But it really is not. If a robot rotates for 2 seconds at a speed of 90 degrees per second, it has rotated for 180 degrees. So integration is nothing more than time multiplied with speed. The graph below shows both the (offset corrected) angular velocity and the direction. During the test I rotated the sensor four times with 90 degrees clockwise, 360 degrees counter clockwise, 90 degrees counter clockwise and 90 degrees clockwise. After this the sensor was back at its start direction. The  line representing the direction, labeled Rotation 2, clearly shows the steps of 90 degrees that I made. Careful examination of the data shows that according to the sensor the robot rotated with -358.8 degrees at max, where as I tried to rotate it with -360 degrees. This makes the sensor, and the integration, pretty accurate. However, after turning the sensor back to its start direction the calculated direction is not zero as is to be expected. Instead, it is about 5.7 degrees. This is not so good. What makes it even worse, there is no way to correct this. At least, not without the aid of another sensor of user intervantion. This is the main drawback of integration. Over time small errors (in the offset corrected) signal build up to become a large error in the integrated data.

But integration can be very useful nevertheless. Suppose a robot that needs to make exact turns. Using integration you can do so. But you need to reset the initial direction to zero just before making the term. This way the error in each turn will only be equal to the integration error that built up during this turn. This is small as making a turn does not last that long. In other words, you can make your individual turns accurate but not the overall direction of the robot.

But wait, there is one more thing. Integration only gives a change in direction. To know the real direction one should also know the direction before the changes took place. Quite often this initial direction can be assumed to be zero. But this is arbitrary and does not relate to the world. Although it might be all you need. If you need to relate the orientation of your sensor to the real world you need to align the sensor with the real world (make it point north) or you need another sensor that can do this for you. This could be a compass sensor.