The Geometrical Representation of Path
نویسندگان
چکیده
The path planning problem for arbitrary devices is rst and foremost a geometrical problem. For the eld of control theory, advanced mathematical techniques have been developed to describe and use geometry. In this paper, we use the notions of the ow of vector elds and geodesics in metric spaces to formalize and unify path planning problems. A path planning algorithm based on ow propagation is brieey discussed. Applications of the theory to motion planning for a robot arm, a maneuvering car, and Rubik's Cube are given. These very diierent problems (holonomic, non-holonomic and discrete, respectively) are all solved by the same uniied procedure.
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