Original subtitles

The quadrotor geometry is quite simple.

It consists of four independently controlled rotors

mounted on a rigid frame.

The mechanical simplicity makes it very attractive.

There are no flapping hinges.

The blades are short and stubby, so even when the robot turns suddenly,

the gyroscopic moments don't cause the blades to flap.

And this makes it easier to control the vehicle.

So in the quadrotor, you'll find that if you look at rotors 1 and 3.

And rotor 2 and 4, they're pitched in opposite directions.

So in fact, if you look at the arrows denoting the directions of rotation.

Omega 1 and omega 3 are positive counterclockwise,

when viewed from the top.

While omega 2 and omega 4 are positive counterclockwise,

when viewed from the bottom.

If you vary the speeds of these independent motors, the rotors,

you'll be able to control the position and orientation of the robot.

Let's see how that works.

Let's see how the roll and pitch work first.

If you take one of the rotors and spin that rotor faster,

you will cause the robot to pitch in one direction.

If you spin the other rotor faster, you're gonna have its pitch or

roll in the other direction.

And this is what's going on in this simple video clip.

Except that this vehicle is really small and the roll and

pitch velocity can reach speeds of up to 2,000 degrees per

second as this vehicle autonomously performs flips.

One question you should ask yourself is how do you get the robot to steer or

to yaw?

So now let's look at translation.

So imagine you want to move the vehicle from one side to another,

just translating it along the horizontal direction.

What you really have to do is to pitch the robot forward so

that the trust factor points in the horizontal direction.

That allows the vehicle to accelerate forward.

But then when you get close to the destination, you want to stop the vehicle.

And for that, you have to pitch it in the opposite direction,

creating a reverse thrust that allows it slow down when it gets to its destination.

And then you have to pitch it back to equilibrium.

So the translation maneuver can be quite complicated,

involving rolling or pitching while translating.

And this is all happening autonomously as the vehicle goes through these obstacles.

In this case they're hoops.

The vehicle know exactly where the hoops are and

all it's doing is planning trajectories as it goes through the known hoop positions.

And it can even do this if the hoop is thrown into the air.

We'll actually take snapshots of the hoop, extrapolates the hoops position, and

then plans trajectories.

Going through the hoop safely without colliding with any surface of

the obstacle.

So here's something else you might think about.

The robot obviously has six degrees of freedom.

It can translate in all three directions, it can also rotate.

So how many different ways can you translate or rotate the robot?

And how many of these are independent given that there are only four propellers?