Original subtitles

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.