All language subtitles for 02_quadrotors.en

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?