The Toppling Graph: Designing Pin Sequence for Part Feeding

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The Toppling GraphDesigning Pin Sequence for
Part Feeding
Tao Zhang Gordon Smith Ken Goldberg ALPHA Lab,
UC Berkeley
Robert-Paul Berretty Mark Overmars CS Dept.,
Utrecht Univ.
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The Problem
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Pin Sequence Design An Example
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The SolutionDesigning Pin Sequence

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Related Work

• Lozano-Perez 86 part feeding as a dual of
  motion planning
• Erdmann and Mason 88 sensorless manipulation
• Trinkle 92 orienting parts in the vertical
  plane using gripper
• Goldberg 93 orienting parts in the horizontal
  plane using gripper

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• Fences over conveyor belts
• Peshkin and Sanderson 88 a numerical search
  algorithm
• Akella et al. 97 1-JOC analysis
• Berretty et al. 97 a polynomial-time algorithm
• Wiegley et al. 98 a complete algorithm
• Toppling manipulation
• Lynch 99 toppling analysis
• Zhang et al. 00 compensatory grasping

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Approach

• Compute critical pin heights

• Plan pin sequence

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Critical Pin Heights

• Toppling Graph

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Functions

• Radius function R(?) height of the COM as the
  part rotates
• Vertex height functions Vi(?) height of vertex i
  as the part rotates

q
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Rolling Height Function
Z
X
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Rolling Height Function Computation
1wil(?) (2?t zi cos ?il ? cos(?il-?) ?
cos?il - 2?txisin?il ?t? sin(?il-?) ?t?
sin?il) / (2?t sin(?il -?i)), Hil(?) xi
sin? zi cos? wil sin(?i ?).
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Rolling Height Function Graph
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Jamming Height Functions
Z
X
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Toppling Graph
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Physical Experiment

• using an Adept Flex Feeder conveyor belt
• ?t 53? ? 2? and ?p 5? ? 2?.
• Comparison of prediction with experiment.

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Pin Planning
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Pin Planning (Cont.)

• Total running time O(n3n) in the worst case

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Conclusion

• Toppling Graph
• Vertex height functions
• Rolling height functions
• Jamming height functions
• Pin sequence planning

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Future Work

• Optimal gripper jaw design
• -- topple parts by a set of pins

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Future Work(Cont.)