Abstract

This paper briefly discuss the robot motion planning problem and some of its solutions. It begins by some terminologies, and then presents an O(n log n) algorithm, which is relatively fast but does not find the optimal (shortest) path. It touches upon Minkowski sums, a crucial mathematical tool in the motion planning problem. Visibility graphs are then introduced, emphasizing its importance in finding the shortest path. An O(n2 log n) algorithm which computes the visibility graph is presented. Lastly, Dijkstra’s algorithm is described to illustrate how visibility graphs are used to find the shortest path.
 

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