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A three-dimensional object representation technique for generating spherical geometries and a fast procedure for computing distances using this geometry are presented. An object is approximated by an infinite number of spheres. The shortest distance between two objects is obtained by finding the two spheres, one from each object, that are closest. Exceptional numerical results have been obtained, for example, the maximum time for computing self-collision for a standard PUMA robot arm is equal to 2.3 ms with an error in distance of less than 1 cm. It is noted that this makes the new technique an invaluable tool for computing distances and therefore permits collision detection in real-time. This technique has been applied to a complex robotic system consisting of two PUMA robots, each mounted on a three-degree-of-freedom platform used to study robotic assembly of structures in space.>
Tornero et al. (2002) studied this question.
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