Original subtitles

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.