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Sensing Intelligence Motion - How Robots & Humans Move - Vladimir J. Lumelsky Part 4

Tham khảo tài liệu 'sensing intelligence motion - how robots & humans move - vladimir j. lumelsky part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 66 A QUICK SKETCH OF MAJOR ISSUES IN ROBOTICS Theorem 2.9.4. For any finite maze Fraenkel s algorithm generates a path of length P such that P 2D 2 pi 2.24 where D is the length of M-line and pi are perimeters of obstacles in the maze. In other words the worst-case estimates of the length of generated paths for Trumaux s Tarry s and Fraenkel s algorithms are identical. The performance of Fraenkel s algorithm can be better and never worse than that of the two other algorithms. As an example if the graph presents a Euler graph Fraenkel s robot will traverse each edge only once. 2.9.2 Maze-to-Graph Transition It is interesting to note that until the advent of robotics all work on labyrinth search methods was limited to graphs. Each of the strategies above is based solely on graph-theoretical considerations irrespective of the geometry and topology of mazes that produce those connectivity graphs. That is why constructs like the M-line are foreign to those methods. M-line was not of course a part of the works above it was introduced here to make this material consistent with the algorithmic work that will follow. One can only speculate with regard to the reasons Perhaps it might be the power of Euler s ideas and the appeal of models of graph theory. Whatever the reason the universal substitution of mazes by graphs made the researchers overlook some additional information and some rich problems and formulations that are relevant to physical mazes but are easily lost in the transition to general graphs. These are for example a the fact that any physical obstacle boundary must present a closed curve and this fact can be used for motion planning b the fact that the continuous space between obstacles present an infinite number of options for moving in free space between obstacles and c the fact that in space there is a sense of direction one can use for example a compass which disappears in a graph. See more on this later in this and next chapter. Strategies that take into .