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Most small quadcopters use rigid rotors with some fixed pitch. In principle, I can imagine it might be possible for such a rigid-prop quadcopter to hover upside-down, but that apparently requires reversing the direction of rotation of all 4 motors.

(This is very different from the way some "standard" single-rotor model helicopters can hover upside-down by continuing to spin that rotor in "the same direction", but moving the swash plate to give negative blade pitch).

Is it possible for a rigid-prop quadcopter to hover upside-down?

When I build a quadcopter so it can switch from flying upright to flying upside-down and back again in mid-flight, what do I do differently than a normal quadcopter designed to always fly right-side-up?

(Related: "Can you run a BLDC motor backwards without damage?" )

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You can run a brushless DC motors backwards using a H-bridge. Basically you'll need to program your microcontroller/microprocessor onboard to flip the polarity of 2 of the wires of the bldc (a bldc has 3 wires, switching any 2 wires will reverse the spin)

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