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Path planning using intervals and graphs. (English) Zbl 1021.65029
Summary: The problem of interest is to find a path with given endpoints such that the path lies inside a compact set 𝕊 given by nonlinear inequalities. The proposed approach uses interval analysis for characterizing 𝕊 by subpavings (union of boxes) and graph algorithms for finding short feasible paths. As an illustration, the problem of finding collision-free paths for a polygonal rigid object through a space that is cluttered with segment obstacles is considered.
MSC:
65K05Mathematical programming (numerical methods)
90C30Nonlinear programming
65G40General methods in interval analysis