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10.2 Configuration Space
Figure 10.1 Reduction of a 6DOF world space to a 2DOF configuration space. 353
10.2 Configuration Space
The physical space robots and obstacles exist in can be thought of as the
CONFIGURATION SPACE world space. The configuration space,or Cspace for short, is a data structure
which allows the robot to specify the position (location and orientation) of
any objects and the robot.
A good Cspace representation reduces the number of dimensions that a
planner has to contend with. Consider that it takes six dimensions (also
DEGREES OF FREEDOM called degrees of freedom or DOF) to represent precisely where an object is. A
;
person may specify the location of the object as a (x;yz ) coordinate in some
frame of reference. But an object is three-dimensional; it has a front and back,
top and bottom. Three more degrees are needed to represent where the front
of the chair is facing, whether it is tilted or not, or even upside down. Those
are the Euler (pronounced “Oiler”) angles, ; ;
, also known as pitch, yaw,
and roll.
Six degrees of freedom is more than is needed for a mobile ground robot in
most cases for planning a path. The z (height) coordinate can be eliminated
if every object the robot sits on the floor. However, the z coordinate will be
of interest if the robot is an aerial or underwater vehicle. Likewise, the Euler
angles may be unnecessary. Who cares which way the robot is facing if all
the robot wants to do is to plan a path around it? But the pitch of a planetary
rover or slope of an upcoming hill may be critical to a mission over rocky
terrain.
Fig. 10.1 shows a transformation of an object into Cspace. In general, met-
ric path planning algorithms for mobile robots have assumed only two DOF,
including for the robot. For path planning purposes, the robot can be mod-
eled as round so that the orientation doesn’t matter. This implicitly assumes
