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Algorithm For Convex Obstacle

Observation:

As edges of A circumnavigates B in CCW
egdes of A appear in CW direction
B: CCW -A is reflection of A about origin A_and_B Polar_Plot

figure The resultant polar plot.





























Resultant CSp

figure The resultant configuration Space.
 


































Minkowski Sum =

Set Addition. Minkoski Sum

Algorithm: If A and B are convex then

  1. Draw the polar plot of all edges of B (each edge plotted as if beginning at origin.
  2. Draw the polar plot of (-A) or edges of A in CW.
  3. Starting at any edge trace the contour CCW along the edges of the combination.

 



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