‫Let's now derive the four control actions with which we can control the use of his position and orientation,
‫the first control action is thrust and its unit, of course, is Newton.
‫And let's call thrust you want.
‫So our first control action will be you one, which is thrust.
‫In other words, thrust is one of our system inputs.
‫And for now, let's assume that there is no gravity.
‫We only have thrust that is generated from the four propellers, from the four motors.
‫And by the way, we abbreviate more with M so M one and two and three and then four are just more.
‫One more, two more, three and more four.
‫If you look at the universe here, then you can see the four propellers rotating at the same rate.
‫Even though M1 and M3 rotate counterclockwise and M2 and M4 rotate clockwise, all of them generate
‫the same thrust force upwards.
‫And so if all of them rotate a sigma age radians per second and you add a small amount of rotation that
‫we call Delta A. which is also in radians per second, and you apply this Delta A equally to all of
‫them, to all of the propellers, then all propellers generate the same amount of more thrust in the
‫body frame the Z direction.
‫If you add them all together, you will have a global thrust, which is you one and that you one generates
‫this acceleration, small z double dot, that is acceleration in the body frame Z direction.
‫Now if the body frame Z is aligned with the inertial frame Z axis, in other words, if the V is not
‫tilted, then the acceleration points upward in the big Z direction as well.
‫And if Delta A is equal in negative for all propellers, then that means that you're you one still points
‫in the body frame Z direction, but it is smaller.
‫And of course, if we assume gravity, then obviously to take off the ground, you're you one must be
‫greater than the force of gravity.
‫Right.
‫So if you have your force of gravity downwards and then you're you one upwards, then you one as a force
‫needs to be bigger than force of gravity.
‫And of course, we are talking about the magnitudes because the direction of the new one is upwards
‫and the direction of the force of gravity is downwards.
‫But the magnitude of you want needs to be bigger than the magnitude of the force of gravity.
‫Then the drone will take off.
‫Otherwise it won't.
‫And so we have our view one, which is our first control action.
‫This is what the controller will find for the drone.
‫And we have acceleration generated from you, one which is small Z, double dot this one and they are
‫related with mass.
‫So you one equals mass times, small Z double dot.
‫Remember, mass is resistance to linear acceleration and this is assuming that there is no force of
‫gravity.
‫You one is the only force that is applied to the drone.