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The Minkowski sum is used to generate the configuration space in many applications. On Slide 45 of this presentation you can find an example for using the Minkowski sum to generate the configuration space for the piano mover problem.


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It is a bit of both. The repulsive potentials help create a way to represent an environment that is conducive to planning. In the area of repulsive potentials, a simple gradient descent from a point will take you to the minimum, i.e., some collision free point. At the same time, the attractive potential increases as you move away from the goal, so ...


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