Problem $3(40$ points$)$

For the above quadrotor configuration, it is hovering in the air with a yaw $=0$ at

$(1)$ Please derive the condition of rotors' angular velocity in order to perform the following tasks:

$($i$)$ lift,

$(5$ points$)$

$($ii$)$ yaw,

$(5$ points$)$

$($iii$)$ roll with an infinite small angle, and,

$(5$ points$)$

$($iv$)$ pitch with an infinitely small angle.

$(5$ points$)$

$(2)$ The drone moves a certain distance from current location to right.

$($i$)$ Please provide the sequence of motions required for this movement.

$(10$ points$)$

$($ii$)$ What changes in motor rotation speeds are necessary during these

motions? $($A detailed description is good enough$)$

$(10$ points$)$