## Algorithm for computing a collision-free path in the free space - M.deBerg et.al., Computational Geometry

BACKGROUND
• The 2D environment in which the robot walks around is known as the work space.
• A robot is represented with a reference point (x, y), usually within the robot or somewhere in its exterior. Hence, we can say a robot R translates and is located at R(x, y). The origin R(0, 0) is the starting position of the robot.
• If the robot is rotational, then we can add a third parameter to the representation. For example, R(3, 8, pi/3), where pi/3 is the angle of rotation from the robots original state, ie., 0 or 2pi.
• The robot R(x, y, angle) is mapped to a configuration space in 3 dimensions. When a robot translates in a 2D environment, its work space is identical to its configuration space.
• The obstacles in the work space, where the robot cannot move to, are grouped together and called the forbidden configuration space, or forbidden space for short.
• The rest of the space, where the robot does not intersect with any obstacles, is known as the free space.
• A path for the robot maps to a curve in the configuration space.

CINDERELLA GRAPHS DEPICTING ALGORITHM FOR COMPUTING A COLLISION FREE PATH
Trapezoidal Map Composition
Determining Forbidden and Free Space
Home

The trapezoidal map T(E) obtained by drawing two vertical extensions from every segment endpoint, and going upward until a segment (or bounding box) is hit, and one going downward until a segment (or bounding box) is hit.
Please enable Java for an interactive construction (with Cinderella).