Lecture 9
24-354 General Robotics
Fall-05. Prof. Howie Choset

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• Today's Outline:
  1. Roadmap review:
  2. Cellular decompsition
  
  
• Trapezoid Cellular Decomposition
  
  
  
  
  
• Join the midpoints of all of the cells (nodes)
  
  
• We can remove the world and we are left with an abstraction to a graph.
  
  
  
  
• Boustrophedon Cellular Decomposition
  
  • Trapezoid decomposition is nice, but it only works for polygonal worlds.
  • Boustrophedon decomposition is based on critical points rather than vertice s to decompose the world into cells.
    
    
  • In this example a vertical line was used to sweep out the space. The criti cal points occur when an obstacle changes the connectivity of the line. (The res ulting graph is superimposed on the world.)
  • An obstacle is monotone with respect to a line if the line is broken only o nce by the obstacle.
• Cellular decomposition is important to coverage because within a cell, the world can be traversed in simple back and forth motions. This is because the ce lls are monotone (with respect to a vertical line in both trapezoid and Boustrop hedon decomposition.)
  • A region is monotone with respect to a line if the line is broken only once by the region.