All language subtitles for 03_2-3-piano-movers-problem.en

Here's a more complicated example,
once again,

we are considering a robot that
can translate in the plane.

But now,

it can also rotate, this means our
robot now has three degrees of freedom.

Since a rotational degree
of freedom has been added

to its initial two translational degrees.

We can denote the configuration of our
robot with a tuple, tx, ty, and theta,

where tx and ty still denote the position
of a reference point in the plane, and

theta denotes the applied
rotational angle in degrees.

Once again, when we introduce
obstacles into the workspace,

we can think about the set of
configurations that are limited.

In this case, the configuration space has
three dimensions, and the configuration

space obstacles can be thought of as
three dimensional regions in this space.

This movie shows a depiction of
the surface of the configuration space

obstacle corresponding to the obstacles
shown in the previous figure.

The vertical access corresponds to
the rotation theta, while the other

two horizontal axes correspond to
the translational parameters tx and

ty Note again that in this figure,
the surface that we

are visualizing corresponds to the surface
of the configuration space obstacle.

As before, the basic problem in motion
planning is to come up with a trajectory

between a start point and

an end point that avoids all
the configuration space obstacles.

This movie shows a robot moving through
the space, avoiding all of the obstacles.

In this second movie,
we are visualizing the trajectory of

the robot through configuration
space as a red line.

Notice how this red line snakes in and

around the configuration space obstacle
avoiding penetration as it moves

from the start configuration
to the end of configuration.

It is important to understand that this
idea of a configuration space where we

associate coordinates with
the configuration of the robot and

then reason about configurations
that are allowed and disallowed, and

think about the motion of the robot in
terms of trajectories of a point through

configuration space is
actually very general.

Here, for example,
is a plane a robot with six revolute links

In principle, we can think of its motion
in terms of its trajectory of a point,

moving through a six dimensional
configuration space.

If we wanted to, we could introduce
obstacles in the space and

reason about the corresponding
configuration obstacles.

I invite you to ponder what
this configuration space would

actually look like.