Algorithm for computing a collision-free path in the free space - M.deBerg et.al., Computational Geometry
- 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
Adding Nodes and Computing Paths
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.
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