AssemblyDisassembly Planning and Sequencing

1
Assembly/Disassembly Planning and Sequencing
Based on
Disassembly Sequencing Using a Motion Planning
Approach Sundaram, Remmler, Amato (2001)
Geometric Reasoning about Mechanical
Assembly Wilson, Latombe (1994)
2
Assembly/Disassembly Problem
-Sandia National Labs
3
Ground Rules

• Assemblies are composed of component parts that
  can be divided into subassemblies
• Assembly and disassembly are related
• Assembled products have more constraints
• Assembly can be derived from disassembly
• Disregard tools and robotic manipulators
• Implementation of algorithm is separate problem
• Treat each part of assembly as free-moving robot
• All contact between components is Edge-Edge

4
Assembly Planning Basics

• Problem is of two interrelated parts
• Motion planning for subassemblies
• Sequencing of motions
• Early Attempt
• computer performs generate-and-test assembly
  sequencing
• Brute force subassembly decomposition
• Exponential time in the number of parts

5
Motion Planning Approach

• Treat each component of assembly as a robot
• Use PRM to plan path and sequence (AssemblyPRM)
• Handles high-dimensional C-space well
• Suffers from extremely narrow passages

Zero clearance
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Directional Sampling

• Determine best direction for sampling
• Use geometry of components

Sampling Cones
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Determine Direction

• Simple approach
• Use normal to adjacent faces
• Doesnt always work
• Only normals are considered in AssemblyPRM
• Requires face normal to narrow passage

Blocked Motion
Valid Motion
8
Directional Blocking Graph -Wilson, Latombe

• Properties of DBG
• Based on internal structure of assembly
• Shows how components block each other
• One graph for each direction
• Translations only

9
Non-Directional Blocking Graph

• Describe translations in directions
• Translations represented within unit circle
• Circle is divided into regions
• Regions correspond to translations of parts
• DBG is constant within each region

10
Using Translation Cone

• NDBG translations are represented by unit circle
• Diameters of circle are drawn parallel to contact
  edges
• Regions represent a range of translations with
  common DBG

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Using Translation Cone

• Heres another example

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Find Blocking Relations

• Sample random vectors
• One vector v per region
• Dot Product of v and edge normal
• Blocking condition if strictly positive

R1
R2
R4
R3
13
Find Blocking Relations

• Sample random vectors
• One vector v per region
• Dot Product of v and edge normal
• Blocking condition if strictly positive

R1
R2
R4
R3
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Find Blocking Relations

• Sample random vectors
• One vector v per region
• Dot Product of v and edge normal
• Blocking condition if strictly positive

v1
v1
R1 v1 N1 lt 0 v1 N2 lt 0
R1
N1
N2
R2
R4
R3
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Find Blocking Relations

• Sample random vectors
• One vector v per region
• Dot Product of v and edge normal
• Blocking condition if strictly positive

v1
v1
R1 v1 N1 lt 0 v1 N2 lt 0
R1
N1
N2
R2
R4
R2 v2 N1 lt 0 v2 N2 gt 0
N1
N2
R3
v2
v2
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Using NDBG

• Given NDBG G
• Region R
• Direction d
• Part P
• Pi is free to translate in direction d if node Pi
  in G(R,d) contains no arcs

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3D NDBG

• Translation directions are represented in unit
  sphere
• Plane-plane contacts are represented as arcs of
  circles
• Resultant regions are of dimensions 2, 1, and 0
  (corresponding to faces, edges, and vertices)

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NDBG with Rotations

• Attach Cartesian frame to each part
• 3D vector describes motion
• Motion is from one frame to another
• D (dx, dy, ? )
• Jacobian matrix gives blocking relations

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Back to AssemblyPRM

• Model assembly as stack S of configurations
• Loop until disassembled
• Pop configurations from S
• Sample new configurations - Expand()
• Push configurations on S
• Add configurations to roadmap
• Component parts are at pre-determined distance
  from each other

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Expand Function

• Determine direction for sampling
• Amatos group used face normals
• Might be able to use NDBG
• Sample nodes
• How many? More than one but the paper doesnt
  specify
• Check for collision
• Return set of sampled configurations

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Additions to AssemblyPRM

• Subassemblies
• Treat groups of component parts as one unit
• Simultaneous Disassembly
• Multiple parts must be moved in a coordinated
  fashion
• Rotations

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Simultaneous Disassembly

• More than one part must be moved at a time
• In algorithm
• First try to find a serial disassembly sequence
• If step 1 fails, try two parts simultaneously
• Continue to increase until a sequence is found

-Latombe
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Subassemblies

• Treat group of parts as single unit
• Plan disassembly
• Identify promising subassemblies
• Generate translation directions

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Implementation/Assumptions

• Direction function uses contact edge normals to
  identify removal directions
• Algorithm will fail on assemblies that do not
  contain edges normal to the direction required
  for disassembly
• Paper does not discuss this limitation, or how it
  would fare with a more robust direction function

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Experimental Results

• AssemblyPRM
• Face normals for direction
• Translations only
• Subassemblies not seen in results
• Paper doesnt specify if the algorithm uses
  subassemblies
• 3D models
• Some constrained to motions in 2D

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Experimental Results Swap
Pure PRM (2 robots, 337 s)
AssemblyPRM (2 robots, 10 s)
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Experimental Results Puzzle
AssemblyPRM (6 parts, 37 s)
28
Experimental Results Puzzle_Blocked
AssemblyPRM(6 parts, 91 s)
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Experimental Results Puzzl3d
AssemblyPRM(10 parts, 211 s)
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Experimental Results Pentomino
AssemblyPRM(12 parts, 1723 s)
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Conclusions

• PRM techniques allow for disassembly planning
• AssemblyPRM works well on most experimental cases
• Experiment was limited
• No rotations
• No subassemblies
• Part selection not optimized, as seen in
  Pentomino puzzle
• Direction algorithm may be limited

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Conclusions

• NDBG Provides method of describing translations
  in all directions
• Disassembly Planning is for small motions
• Implementation is not considered

33
Impact of Tools on Assembly
With Tools
Without Tools
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Future work

• Integrate NDBG and AssemblyPRM
• Add rotation and subassembly planning to
  AssemblyPRM

35
References

• Sujay Sundaram, Ian Remmler, Nancy M. Amato,
  "Disassembly Sequencing Using a Motion Planning
  Approach", In Proc. IEEE Int. Conf. Robot. Autom.
  (ICRA), pp. 1475-1480, May 2001
• R.H. Wilson and J.C. Latombe. Geometric Reasoning
  About Assembly. Artificial Intelligence, 71(2),
  1994.