All language subtitles for 02_2-2-rr-arm.en

Configuration space is a general concept
that can be applied to a lot of robots.

This slide shows a simple planar arm
with two revolute joints, one and two.

Here again, we can think of all
the possible configurations of this robot.

And associate them with a tuple of
joint angles theta 1 and theta 2.

In this case, the two angles can
freely range from 0 to 360 degrees.

The following movie shows our planar
two link robot moving around.

Along with a corresponding
trajectory in configuration space.

Note, that as a robot moves continuously,

the red dot corresponding to the robot's
configuration space coordinates.

Appears to disappear from one side of
the graph and appear on the other.

This is really just a consequence
of the way that rotations work.

Namely, configurations corresponding to
theta 1 equals 0, and theta 1 equals 360,

are the same.

Similarly, configurations
corresponding to theta 2 equals 0, and

theta 2 equals 360, are also the same.

This means that for this example,
the configuration space can actually be

associated with a 2D surface
of a taurus or doughnut.

Once again, we can introduce
obstacles into the environment.

And consider which configurations become
infeasible, because of collision.

This figure shows
the robot the obstacles and

the corresponding situation and
configuration space.

Notice, that because of the way
we have chosen coordinates for

configuration space.

The simple polygonal
obstacles actually turn into

interesting shape in configuration space.

Once again, the path planning problem
corresponds to guiding the robot

from one configuration to another.

Here's an example of a trajectory.

Through configuration space, it guides
a robot from one position to another.

Note that in this case, the topology of
the configuration space comes into play.

In order to avoid the suave of
configuration space obstacle,

in the center of the figure.

The position of the robot
appears to disappear

from the bottom of the figure and
reappear at the top.

In order to get to
the final configuration.