(from Google maps)

Motion of rotating polygon (car)

Now consider a polygonal robot moving around in 2D. For example, a car or truck might be moving around the roads near the Siebel Center shown in the areal view above. In the simplified map below , we have two crossing roads defined by four obstacles (red). The car (blue) can move forwards and rotate.

To specify the robot's position, we need to give its (x,y) position and also its orientation. So the robot's configuration space is three dimensional.

See the following slides for two worked examples from Howie Choset:

• Configuration space obstacle for a rectangular object with a moving rectangular robot
• Moving an L-shaped object through some tight doorways

Issues

So this 2D problem with simple polygonal obstacles has a 3D configuration space with quite complex obstacles.

The dimensionality of the configuration space gets even larger in many real-world situations. For example, if we

• move objects in 3D (e.g. drones, assembly of 3D parts)
• robots with more degrees of freedom, e.g. arm with more than one joint, arm mounted on mobile base