RealTime Robot Motion Planning Using Rasterizing Computer Graphics Hardware

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Real-Time Robot Motion Planning Using Rasterizing
Computer Graphics Hardware
Lengyel, Reichert, Donald, and Greenberg
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Piano Movers Problem

• Given a rigid polyhedral object P, and polyhedral
  obstacles, find a continuous collision-free path
  moving P from a start to a goal configuration.
• This paper develops an algorithm which uses
  graphics hardware and other techniques to solve
  this problem quickly.

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Minkowski Sum

• Convolve robot with obstacle to grow the
  obstacle at a particular robot orientation.
• Can be computed in O(n) time.

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C-space rasterization

• Choose a pixel resolution
• For a given robot orientation, fill each enlarged
  obstacle with an obstacle color
• This generates a c-space bitmap

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C-space voxelization

• Create N c-space bitmaps evenly spaced over
  0,2?
• Each ?-slice must actually represent a sector
  ? - d ?, ? d ?
• Together they form a voxel
  array (rectangular torus)

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Navigation Function

• Start from goal with distance 0
• Move to every free and unassigned direct
  neighbor, and assign distance incremented by 1
• Repeat until all free cells connected to goal are
  assigned a distance
• Paradox

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Path Generation

• From any numbered location, simply follow the
  arrows to the goal. This is a shortest path.
• Pre-processing?

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Example 1
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Example 2

• 3.5D representation

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Conclusion

• Complete planner at a given resolution
• Fast (due to graphics hardware)
• Can handle any polyhedral geometry?