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In this thesis, a global optimal collision-free path planning
method is proposed by using the propagating interface technique
which is a numerical technique for analyzing and computing
interface motion. To implement the method, a measure, called the
collision probability, is defined. The probability, which is
analog to that of in the potential modeling method, is obtained
by mapping the geometrical relationship between a robot and the
obstacles into a Gaussian distribution domain. The collection of
the associated probability of each grid in the working space
form a potential field. Similar to searching the minimum energy
problem, the propagating interface method can search a
collision-free path by regarding the probability as the
propagating speed. In addition, the interface propagating
technique also can be applied to image segmentation problems in
machine vision. Similar to the ones dealing with collision-free
path planning, the method uses the differential intensity of
each pixel's neighborhood as its propagating velocity.
Therefore, the front of propagating interface should get stuck
around the edge of a detected object.
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