Scale-Free, Approximate Motion Planning For Modular Robots

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Scale-Free, Approximate Motion Planning For
Modular Robots

• Michael De Rosa
• CMU

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Algorithm Overview

• Hole Motion
• Hole Growth/Deletion
• Smoothing (Self-Organizing Criticality)
• Region-based Planning

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Hole Motion

• Uniform hexagonal holes
• Holes collide and reflect off of object boundary,
  other holes
• Holes can move 1 row at a time (not shown)

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Hole Creation/Deletion

• Creation/deletion regions are designated on the
  perimeter
• Creation raises the contour of the object
• Deletion lowers the contour

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Smoothing-Overview

• Smoothing algorithm based on Oslo model of
  sand-pile collapse
• As grains of sand are added, local slope
  increases
• If slope exceeds a threshold, collapses occur

gt1
gt1
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Smoothing, continued

• Smoothing is constantly active in all
  creation/deletion regions
• gravity is determined on a per-region basis
  (either as one of the 6 hex directions, or w.r.t.
  an origin point)
• This smoothing approach provides bounds on
  maximum surface roughness as a function of time

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Regions

• Triangular regions are created either manually,
  or by keyframing between two images
• Ex simple example with one growth region
  smoothing

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Challenges (1)

• Holes bind to closer regions, pinching off areas
  farther away from center of mass
• Pinched off region becomes detached from central
  mass

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Attempted Solutions

• Force regions to wait for further regions to
  complete before activating
• Created deadlock
• Holes bind to deletion regions based on distance
  from desired contour
• Some improvement, but much slower
• Still an open problem, several techniques under
  study

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Challenges (2)

• Creation of holes very sensitive to small
  perturbations in surface roughness
• Solution
• Allow creation of holes that are not fully
  enclosed initially
• Resulted in a 3x speed-up in hole creation

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Morphing Objects
Bending Bar
Circle Into Rectangle
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Global vs Distributed

• Current algorithm assumes only local
  communication between neighbors
• but requires synchronized clocks, and implicit
  locks/transactions between catoms
• We are developing a distributed version that
  operates asynchronously, and tolerates moderate
  clock skew