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Quotient Space Based Problem Solving by Bo Zhang, Ling Zhang

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5.2. The Geometrical Methods of Motion Planning

The problem addressed here is a specific motion planning problem, known as the findpath problem in robotics. The problem is stated as follows: Given the descriptions of an object and a collection of obstacles in a 2- or 3-dimensional space, given also the initial and desired final configurations for the object, to find a collision-free path that moves the object to its goal, or determine that no possible path exists.
The common theme in motion planning work is the idea of representing the problem in such a way that the object to be moved is a point, and the point is moved through a configuration space that may not necessarily be equal to the 2-or 3-dimensional space of the physical problem. It is ...

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