- 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

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