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I'm just starting up with IMU's and I really want to work on my own flight controller, but a question always hits my mind and I am not able to find answer anywhere, so I'm here.

Will multiple IMUs will help improving stability of a quadcopter? averaging out the values of all the multiple IMUs should reduce the drift, which is a function of time, but I have no experience with IMUs and just cant figure out about the amount of error correction by adding one extra IMU, will it be just additive? or Exponential?

This question was also posted on the Electrical Engineering Stack Exchange site.

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    $\begingroup$ Please don't cross post the same question to multiple Stack exchange sites. Pick the one which seems most appropriate and then it can be migrated to the other if necessary. This question now has answers on both the Robotics and Electrical Engineering stack exchange sites. $\endgroup$ – Mark Booth May 9 '17 at 9:49
  • $\begingroup$ Apologies from me as I'm new to stack exchange and didn't knew that questions can be migrated. $\endgroup$ – Tanishq Jaiswal May 9 '17 at 13:05
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    $\begingroup$ No problem, using Stack exchange effectively is definitely a skill that you have to learn, so we try to help where we can. In any case, welcome and thanks for your question. $\endgroup$ – Mark Booth May 10 '17 at 9:48
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Multiple IMU systems are used to make more accurate measurements. However, the main purpose of these systems is to take multiple measurements and make use of the differences between these measurements to obtain the most accurate result. The use of multiple sensors in the robotics is used for measurement of different body parts. In order to increase the accuracy of measurement with the use of more than one IMU, the position and fusion method of the sensors are important. You probably will not see much change if you place each sensor at the same place or very close. However, if you are installing sensors for the center and arms separately for a multicopter, you can provide insulation by removing the arm vibrations (propeller or motor vibration). So you have made a more accurate measurement.

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  • $\begingroup$ positioning and fusion of IMUs will be too difficult to do at home, without sophisticated instruments. Am I right? $\endgroup$ – Tanishq Jaiswal May 8 '17 at 15:30
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    $\begingroup$ no, it is not too complicated. You should observe outputs of the IMU and decide how to substract/remove vibrations ( fusion ) $\endgroup$ – acs May 8 '17 at 15:56
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Already from a probability point of view one can argue that the standard deviation of the mean drift goes down when stacking multiple IMU's together. However, things might also turn out nastier when the odds are not in your favour (e.g. in the unlucky event that both IMU's have exactly the same drift).

There are ways in which you can benefit much more from having multiple IMU's though, rather than just stacking them together. If placing them on different locations of the body, then you end up with more measurements than system states (i.e. an overdefined observation space). These different measurements can be combined using observers (e.g. by using a Kalman filter) to get much more accurate results.

Example: Consider a 2D pendulum in a gravityless environment of length $r$ with two IMU's, located at $r/2$ and at $r$ from the joint to which the pendulum is connected. The centripetal acceleration measured at $r$ should be double that of the one measured at $r/2$ (i.e. $r\omega^2$ instead of $r\omega^2/2$, where $\omega$ is the rotational velocity of the pendulum). If it's not, then you know something is wrong. A bit of smart observing will (in most cases) help you track down the error.

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  • $\begingroup$ will the positioning of IMUs at different places require sophisticated instruments? $\endgroup$ – Tanishq Jaiswal May 8 '17 at 15:38
  • $\begingroup$ As for hardware, the difficulty is only in knowing where exactly you place your IMU's, because this will be important for your model. In general, the further apart the better. Not knowing where your second IMU is located will lead to more uncertainties. The main challenge however is likely more that from a software point of view: observation. $\endgroup$ – JJM Driessen May 8 '17 at 15:43
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For a quadcopter, I would argue that the benefit of multiple imu's does not justify the effort. The bias issue you mentioned might be reduced but unless you can guarantee zero bias you still have to run the exact same bias compensation algorithms (which are pretty mature anyhow).

You could try gain benefit by somehow averaging the redundant readings but even that's non-trivial because you have to account for how much of the differences in readings is due to difference sensor locations. While straight-forward theoretically, it still requires significant effort to implement correctly plus eats up cpu cycles.

For robotics in general, multiple imu's are most useful in situations where parts move relative to each other (e.g., a robot arm with a sensor on different links). Quadcopter's are generally treated as rigid bodies; and if it's not rigid you need to put your effort into making it rigid.

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