Useful Definitions

Configuration space
        This concept is used in robot motion planning among stationary, known objects (case I).  The configuration space is a transformation from the physical space in which the robot is of finite-size into another space in which the robot is treated as a point.  In other words, the configuration space is obtained by shrinking the robot to a point, while growing the obstacles by the size of the robot.  The figures below illustrates the conecpt of configuration space.  In figure a, P and Q are fixed obstacles in physical space, and R is the robot, whose orientation is fixed.  Figure b shows the corresponding configuration space.

Free Space
        The free space of a configuration space simply consists of the areas not occupied by obstacles.  Any configuration within this space is called a free configuration.

Free Path
        The free path between an initial configuration and a goal configuration is the path which lies completely in free space and does not come into contact with any obstacles.