‫Welcome back.
‫You see, in engineering, it's very important to know in advance what kind of product you're designing,
‫you need to know very well what you want your product to do.
‫The requirements of your product should be specified as much as possible.
‫Why?
‫Well, first of all, if your clients tell you that they want X and you give them Y, then that would
‫make them pretty unhappy.
‫And we don't want them to be unhappy.
‫Right.
‫But another reason why you want to know exactly what your product will be doing is because then you
‫will be able to know where you can simplify your mathematics.
‫In other words, where you can make certain approximations.
‫If we want our drone to perform some kind of super complicated acrobatic maneuvers, well, then your
‫math will probably get harder.
‫But there are a lot of applications for drones that do not require high speed.
‫Nowadays, wind turbines are becoming pretty popular.
‫And so what you might want to do, you might want to send a drone there to perform an inspection.
‫Maybe this drone has some cameras and then you can inspect for cracks in the structure.
‫I know that they do it with airplanes as well, since airplanes are big structures and they constantly
‫must be inspected for cracks in the structure, then I know that they are using drones for that as well,
‫where a drone would fly close to an aircraft with cameras and then inspect for any possible problems.
‫So if there is some kind of crack here in the material, in the structure, they would know about it.
‫So in both cases, they would fly around this object and then inspect for some kind of problems in the
‫structure.
‫Obviously, in that case, the drone should fly pretty slowly.
‫The drones cannot fly fast because if it starts flying fast, then it won't be able to follow this trajectory.
‫It will just overshoot if it flies very fast.
‫And then there is no point.
‫The goal is to inspect the aircraft and find possible problems in the structure.
‫The drone should take its time and fly around the aircraft or the wind turbine and then inspect all
‫the surface area.
‫That means that we already know that the trajectories that we will give to our drone, they will not
‫require the drone to fly fast.
‫In other words, if we plot our X dimension as a function of time, Y dimension as a function of time,
‫and then a Z dimension as a function of time, we will not have some kind of crazy trajectories there.
‫We will have smooth trajectories like this and these smooth trajectories.
‫They have small slopes, which means that your X dot, y dot and Z, that will be small, so your velocities
‫will be small.
‫Now how does a drone generate velocities?
‫You know that it has four thrust vectors generated by those four propellers.
‫And so if you want to have some kind of velocity, then you have to tilt your drone, either like this
‫or like that.
‫Furthermore, don't forget that we are dealing with a drone.
‫We are not dealing with a car or other objects that experience some kind of significant friction force.
‫Let's imagine that this is our drone and it is hovering right now.
‫So you want this drone to go there and you want your velocity in that direction to be more or less constant.
‫So what you will do, you will slightly tilt your drone so it will have some kind of horizontal component.
‫And because of that, the drone will start moving in this direction.
‫But what will happen if you keep your drone tilted as a function of time?
‫Well, then you will keep having this horizontal component.
‫And you know, that force equals mass times the.
‫Celebration, so for as long as you keep your drone tilted, you will have a component in this direction
‫that will cause acceleration.
‫And so if you just keep this drone tilted like that, then the drone will start moving in this direction
‫faster and faster.
‫But we didn't want that.
‫We wanted stable, smooth, not so fast velocity with small accelerations.
‫So in order to do that, the drone can tilt for a short period of time, get its desired velocity in
‫this direction, and then get back to its hovering position.
‫However, even though there is no tilt anymore, your drone will still go in this direction because
‫what forces with the drone experience at that time, you don't have friction with the ground?
‫Well, there is force of gravity, of course, but that's perpendicular to this motion, so it won't
‫affect it.
‫And yes, you have a very small drag force here.
‫But if our velocities are very small, then our air resistance will be very small.
‫And so you will need some time to slow down.
‫And then let's say that now you want the drone to go in this direction.
‫So you would give it a small tilt.
‫There will be a small horizontal component in this direction and the drone will start flying in this
‫direction.
‫And then very shortly you will go back to the hovering position.
‫Then these two horizontal components will, of course, disappear.
‫But since you're a drag force will be very small in a forward velocity, will not decrease significantly
‫right away.
‫And this kind of behavior allows us to assume, at least in our mathematics, that our fi and theta
‫are zero radians, because when your drone flies close to a hovering position, then these two angles
‫indeed are very close to zero during most of the time.
‫But remember, we are only able to make this assumption because we are not designing a controller for
‫some kind of racing or acrobatics drone.
‫We are designing a controller for a drone that would perform these kind of functions like structure
‫inspection.
‫And so now if we are able to say that, then if you look at this transfer matrix, then tell me what
‫will this transfer matrix become if I substitute PHI and Theta Angles here with zeros?
‫So let it be your exercise and let's look at it in the next video.