‫Welcome back.
‫In this lecture, we're going to start looking at a drone from control systems point of view.
‫Let's look at the UAE more closely.
‫This is a typical quadcopter here.
‫It has four propellers or let's call them motors.
‫They are located on the edges of their respective beams.
‫And all of them are at an equal distance from the center.
‫And the distances here, the M and the two beams themselves are perpendicular to each other.
‫The first thing that we're going to do, we're going to attach an X, Y and Z body frame to it.
‫This frame is attached to the drone.
‫Always it moves with it.
‫It's important to note that this is a body frame around with small X, Y and Z axis and not the inertial
‫frame with big X, Y and Z axis.
‫And the inertia frame is fixed to the ground.
‫So we fixed the initial frame to the ground and we fix the body frame to the drone and to determine
‫the position of the body frame within the inertia frame.
‫We can have a position vector here that points to the origin of the body frame from the origin of the
‫inertia frame, and we can call it P vector, the position vector, the body frame can translate and
‫rotate within the inertia frame.
‫In fact, that is how we describe the drones position and orientation in our 3D space.
‫And now we're going to call the propeller that is on the positive small side, more one on the positive
‫small Y side.
‫We have more to negative small Exide model three and negative small Y side motor four.
‫Let's now try to identify the inputs and outputs of the drone using the plant block model.
‫Now, obviously, you need to measure or estimate the UVs position in the initial frame and for that
‫you need the big X dimension, the big Y dimension and the big Z dimension, because you have to know
‫the position of the drone in the inertia frame.
‫So you need to know these axes here, the big X, Y and Z axis.
‫However, there is more to that.
‫You also need to know the orientation of the drone in the inertial frame.
‫You can describe the drones orientation in the inertia frame using three angles roll pitch and your
‫which are Phi Theta and PSI respectively.
‫I will treat that extensively in the next section when we learn about 3D rotation matrices.
‫And so these triangles are to describe the drones body frame orientation in the inertial frame and you
‫can call it body frame orientation in the inertia frame or angular position in the inertial frame or
‫the drones attitude in the inertia frame.
‫So different terminology, but the same meaning.
‫But in addition, we can also measure the drones angular velocity about its own body frame, X, Y and
‫Z axis.
‫We're going to use the variables P, Q and R to describe the rotational velocity of the drone about
‫the body frame X, Y, Z axis.
‫Since they are rotational velocities, their units are radians per second, so peak are radians per
‫second.
‫OK, but how do we now determine if the rotation is positive or negative?
‫I mean, let's say that your drone is rotating about this small x axis.
‫Is it rotating, let's say, at two radians per second or at minus two radians per second?
‫How do you determine that the convention is to use the right hand rule to determine if the direction
‫of rotation is positive or negative if you wrap your right hand around a body X?
‫Y and Z axes in the same way like the rotation happens around those axis and if your thumb points in
‫the positive direction of that axis.
‫So in this case, it's in the positive direction, in the positive y direction and in the positive Z
‫direction.
‫If that's the case, then the rotation is positive.
‫If your thumb, however, points in the opposite direction, then the angles have negative radians and
‫therefore the rotation is negative.
‫So now, for example, if this is your body frame X and now you rotate about the axis like this, then
‫you would grab this axis like this where you can see the knuckles here and now you see that your thumb
‫points in the opposite direction to the positive x axis.
‫Right.
‫So that means that now your rotation would be negative.
‫So you would say that your P is, let's say, minus four radians per second.