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       (a) Robot in quadrant 1.                                 (b) Robot in quadrant 2.

       (c) Robot in quadrant 3.                                 (d) Robot in quadrant 4.

       Fig. 5. Path-planning with GA-PRM algorithm.

performance metrics for each algorithm with three distinct                         VII. DISCUSSION
lines. Each line corresponds to one of the performance mea-
sures, and the x-axis displays the names of the algorithms. On  The comparison experiment between our new path-planning
the y-axis, we can see the average value for each metric. To    method and existing ones, presented in Table I, reveals impor-
make it clearer, circular markers are used to denote the data   tant insights. These results provide valuable information about
points for each algorithm. This visual representation enables   how our approach could be applied in practical, real-world
an easy understanding of how each algorithm performs in         situations and how it might advance the field.
terms of these metrics.
                                                                   1. Path length: The GA-PRM algorithm showed an aver-
                                                                       age path length of 25.62 units. This indicates that the
                                                                       robot’s paths planned by the GA-PRM algorithm were
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