Randomized Planning for Short Inspection Paths

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Randomized Planning for Short Inspection Paths

• Tim Danner Lydia E. Kavraki
• Presentation by Ted Hwang

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The Problem

• watchman route problem
• given a workspace, plan a route so every point on
  the boundary of the workspace is visible from
  some point on the route

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Constraints on the Problem

• Angle of incidence
• Range

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The Approach

• Use discrete sensing events rather than
  continuous sensing over the entire path.
• Next best view algorithm
• Optimize for path length and extend the method to
  3D.

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2D Inspection

• 2D is sufficient for some applications.
• Divide path computation into two parts
• solving an art gallery guard problem to choose a
  set of sensing locations
• connecting these locations with a short path

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Solving the Art Gallery Guard Problem

• Use a randomized, incremental algorithm.
• Randomly select a point on the boundary which is
  not yet guarded

• Construct the points visible region and clip
  using visibility constraints.
• Sample k times in the region and pick the best
  sample.

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Connecting the Guards

• Use graph algorithms -- the problem can be recast
  as a Traveling Salesman Problem.
• Shortest paths graph
• straight line between two points, or more complex
  to avoid obsticles
• Graphs arising from R2 and R3 obey the triangle
  inequality and are suitable for the minimum
  spanning tree-based approximation to the
  traveling salesman problem.

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2D Experimental Results
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3D Inspection

• The general algorithm for 2D will work largely
  unchanged in 3D.
• It is relatively easy to compute a visibility
  polygon in 2D, but it is the difficult to compute
  a visibility polyhedron in 3D.

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Visibility Volume Problem

• The visibility volume is needed to
• determine the portion of the environment a given
  point can see
• determine the region to sample for potential
  guards for a given point on the boundary
• These two purposes can be treated separately in
  3D and allow us to avoid explicitly computing
  visibility volumes.

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Guard Selection

• Need to determine what boundaries are visible
  from a guard and subtract it from boundaries
  already visible.
• Use the binary space partitioning tree to resolve
  circular conflicts by splitting polygons as
  necessary.

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Guard Selection Cont.

• Select random points and test if they lie in the
  visibility polyhedron by checking their
  intersection with the visibility range sphere and
  incidence angle cone.
• Since the two functions of the visibility
  polyhedron can be fulfilled without an explicit
  representation, we can avoid the problem of
  computing the polyhedron.

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Connecting the Guards

• In 2D, obstacle vertices can be used to compute
  optimal shortest paths, but there is no simple
  analog in 3D.
• Choose random points in free space similar to the
  probabilistic roadmaps approach.

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3D Experimental Results
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Future Work

• Incorporate dynamics.
• Optimize the path for different variables, such
  as energy consumption.
• Selectable inspection regions.
• Directional sensors.

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