Figure 4.4 Controlling Quad copter
When a rotors turn, it has to overcome air resistance. The reactive force of the air against the rotor causes a reactive moment called the “Induced moment”. The induced moment acts on the rotor in the direction opposite to the rotation of the rotor.
As everyone knows, conventional helicopter require the tail-rotor to counteract the induced moment, in the hover both sets of diagonal rotors turn in opposite directions (as indicated by the opposite direction of the arrows in Fig.)
As long as all rotors experience the same induced moment which is mostly a function of speed of rotation and rotor blade pitch the sum of all induced moments is zero and there is no horizontal rotation. If one set of rotors, for example the one that turns counter-clockwise in fig., increase their rotational speed or their pitch, the resultant net induced moment will cause the quad copter to rotate clockwise.
It is important to note that because of the diagonal arrangement, this operation has no effect on translation in x or y direction. The effect on up/down motion can be compensated by reducing the pitch speed of the other diagonal pair, although in practice this is not quite so easy without some sort of feedback control.
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