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I would like to know why axis can be controlled independently in a quadcopter. I mean, I was told that you can control $x$ and $y$ independently but I couldn't find a demonstration

Edit: the testbench that is used when you want to see how the response of a quadcopter would be is a one arm quadcopter (i.e, just 2 propellers like this: enter image description here

That testbench can be used because you can control how the response of the $x$ axis is and then use the $y$ axis. And, when you put both axis together, each axis response would be as they were in the testbench

How can we demonstrate that?

Or, the question would be: why you can use a one-arm testbench for a quadcopter?

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  • $\begingroup$ Do you mean translation of the entire quadcopter along the $x$ and $y$ axes? $\endgroup$ Dec 4, 2019 at 10:17
  • $\begingroup$ Ah, you meant rotation around $x$ and $y$, that makes more sense. $\endgroup$ Dec 5, 2019 at 11:56

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With that testbench you are only testing the tracking performance of the rotation around a given axis. The dynamics of each of those rotations is dominated by the inertia around that axis, also known as moment of inertia. The moment of inertia contribution of point masses around a given axis can defined as $I=\sum_i m_i\,r_i^2$, with $m_i$ and $r_i$ the mass and (shortest) distance to the rotation axis of each point mass respectively. The removed arms of the quadcopter would contribute to this inertia. However, its contribution will be very small, since the mass of those arms would be very close the axis of rotation and thus $r_i$ would be very small.

It can also be noted that in-flight the propellers, on the arms that are removed on your testbench, would be spinning. This spinning would add angular momentum which would also cause precession. The propellers used on a quadcopter often are relatively small and light weight. Therefore, their moment of inertia and also their angular momentum is small. This causes the effect of precession to be small as well.

To summarize, removing an arm does change the dynamics of the rotation around a given axis. However, these changes are small compared to the remaining dynamics.

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  • $\begingroup$ OK, but in a quadcopter you can first control the step response in one axis and then in the other. You don't have to do both simultaneously. Why that happens? $\endgroup$
    – Unnamed
    Dec 7, 2019 at 12:50

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