Computing rectilinear shortest paths in two dimensions has been solved optimally using a number of different techniques. A variety of related problems have been solved, including minimizing the number of bends in the path, the total rectilinear distance, or some combination of both. However, solutions to the 3D versions of these problems are less common. We propose a solution to the 3D minimum-bend path problem, which has theoretical as well as practical interest. Applications include motion planning problems where straight line motion is preferred over taking arbitrary turns. We employ our results in motion planning for self-repair in self-reconfigurable robots.
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