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I am a newbie in this drone field. I am curious to know what type of rotation and translation a dualcopter can achieve ? By rotation and translation i mean can it be able to roll, pitch and yaw like quadcopters? If not, in any copter what makes them to roll pitch and yaw? Furthermore are there any dualcopter design that have movable wings that will rotate the rotors itself or do up and down motion while flying?

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A dualcopter, of the form you are talking about, can control all roll, pitch, yaw and it's altitude.

To do so, it employs two rotors running in opposite directions to cancel any torque. This would give the copter the ability to control its altitude and yaw (by changing the relative speeds of both the rotors).

For the rest, such a copter usually employs rotors which can tilt forward and backward, therefore, when you want to move forward, both the rotors tilt forward, and both tilt backwards if you want to move backwards. They usually tilt in opposite directions rather than changing their relative speeds for yaw control which gives it a better yaw authority.

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A quick google search yields this video of an RC dual copter that looks like it is able to control its pitch, roll and yaw: https://www.youtube.com/watch?v=_cwCHgmDbz0

Skip to 5:50 for the part where he actually flies it.

As for quadcopters, there is a well known video circulating on the internet of a presentation given at a TED conference by Raffaello d'Andrea of ETH Zurich about quadcopters in which he clips opposing rotors of a quadcopter and demonstrates that he is still able to control the height of the quadcopter using a specialized control algorithm. The video can be found here. https://www.youtube.com/watch?v=w2itwFJCgFQ

In it, he mentions that "we relinquish control of yaw (z axis rotation), but roll, pitch and acceleration can still be controlled with algorithms that exploit this new configuration." I'm not sure if you're looking into a control algorithm like this because the craft continuously rotates during flight.

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Check out this video: https://www.youtube.com/watch?v=csfAOCdkCdU and this relevant one: https://www.youtube.com/watch?v=t369aSInq-E

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