CS 326 A: Other Roadmaps and Cell Decomposition Techniques

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CS 326 A Other Roadmaps and Cell Decomposition
Techniques

• Families of path planning techniques
• RoadmapRepresent the connectivity of the free
  space by a network of 1-D curves
• Cell ecompositionDecompose the free space into
  simple cells and represent the connectivity of
  the free space by the adjacency graph of these
  cells
• Potential fieldDefine a function over the free
  space that has a global minimum at the goal
  configuration and follow its steepest descent

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Roadmap Techniques

• Visibility graphStarted with the Shakey project
  at SRI in the late 60s. Can produce shortest
  paths in 2-D configuration spaces.
• Voronoi diagram (and other median axes)Developed
  by Computational Geometry people. Generate paths
  that maximizes clearance. Applicable mostly to
  2-D configuration spaces
• SilhouetteSophisticated complete general method
  that applies to spaces of any dimension.

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Visibility Graph
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Voronoi Diagram
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Cell Decomposition

• Two main families of techniques
• Exact cell decompositionThe free space F is
  represented by a collection of non-overlapping
  cells whose union is exactly FExamples
  trapezoidal, cylindrical decompositions
• Approximate cell decompositionThe free space F
  is represented by a collection of non-overlapping
  cells whose union is included in FExamples
  quadtrees, octrees

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Trapezoidal Decomposition (Exact)
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Octree Decomposition (Approximate)