the corresponding total shadow areas were calculated at each point. The shadow areas

were saved to a data file and later analyzed using MATLAB. Three- dimensional plots

were created (see figure 2.8) that contain the x and y locations of the robot and the

corresponding total shadow area. These plots are used to visualize where the maximum

and minimum shadow areas occur. Points occupied by an obstacle have a maximum

shadow area, which assumes the entire map is a shadow region.


 minimum
 shadow area obstacle






 3000,







 20 10
 10 robot x position
 robot y position 0 0

Figure 2.8: A plot of the shadow areas for a single robot placed at every point on the map
 (except obstacle locations)

 Although this method provides a reasonable estimate of the shadow areas, it takes

approximately seven minutes to determine a solution for a single robot. Optimization of

this method is imperative once multiple robots are introduced.

 Line-of-Sight and Shadow Area Method Revisited

 After experimenting with the line-of-sight method mentioned earlier, it was decided

that this method proved to be entirely too slow for this application. Due to the nature in

which the line-of-sight function is used, the speed to determine a solution is of utmost