Conclusion

            We first solved the problem of robot motion planning with an algorithm involving trapezoidalizing the free space and breadth-first searching the road map. This algorithm takes only O(n log n) but does not find the optimal path. We also described how to reduced the problem of polygonal robot to point robot by Minkowski sums. We then turned to visibility graphs, which are guaranteed to give us the shortest path. We described in detail an O(n2 log n) algorithm to compute the visibility graph of a set of obstacles. We also stated that there are other more efficient algorithms, including one which uses arrangements and takes O(n2). Finally, we described how to compute the shortest path by Dijkstra’s algorithm, which takes O(n2) run time.

References

J. O’Rourke, Computation Geometry in C, Cambridge University Press, 1994.

M. deBerg et al, Computational Geometry: algorithms and applications, Springer Verlag, 1997.
 

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