Part Feeding

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Part Feeding

• Frank van der Stappen

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Part Feeding
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Conventional Manipulation

• Anthropomorphic robot arms (accompanied by
  advanced sensory systems) performing
  pick-and-place operations.

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Conventional Manipulation

• Anthropomorphic robot arms/hands advanced
  sensory systems
• expensive
• not always reliable
• complex control

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RISC

• Simplicity in the factory Whitney 86 instead
  of ungodly complex
  robot hands Tanzer Simon 90.
• Reduced Intricacy in Sensing and Control Canny
  Goldberg 94
• simple planable physical actions, by
• simple, reliable hardware components
• simple or even no sensors.

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Part Feeding

• Feeders based on various actions push, squeeze,
  topple, pull, tap, roll, vibrate, wobble, drop,

Parts Feeder
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Feeding by pushing

• Rectangle can be oriented by 2 push actions.
• Result of push computable from geometry.

45?
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Pushing

• Polygonal part with n vertices
• Center of mass
• No friction
• Push continues until part stabilizes

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Pushing

• Part starts to rotate in clockwise direction
  (with respect to the pushing jaw)

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Pushing

• and continues to rotate until

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Pushing

• it stabilizes on a stable edge.

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Pushing

• Distance from center of mass to jaw decreases
  during the rotation.

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Pushing

• Part starts to rotate in counterclockwise
  direction (with respect to the pushing jaw)

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Pushing

• and continues to rotate, even through unstable
  edges, until

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Pushing

• it stabilizes on a stable edge.

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Pushing

• Distance from center of mass to jaw decreases
  during the rotation.

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Pushing

• Unstable equilibrium no rotation but any
  perturbation will lead to rotation.

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Radius Function

• Links every orientation to the distance from the
  center of mass to the tangent line with that
  orientation.

f
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Radius Function

• Part rotates to decrease the distance to the
  (supporting line of) the jaw, which is tangent to
  the part during pushing.

r(f)
f
initial orientation
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Radius Function

• Part rotates to decrease the distance to the
  (supporting line of) the jaw, which is tangent to
  the part during pushing.

r(f)
f
final orientation
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Radius Function

• Part rotates to decrease the distance to the
  (supporting line of) the jaw, which is tangent to
  the part during pushing.

r(f)
f
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Radius Function

• Part rotates to decrease the distance to the
  (supporting line of) the jaw, which is tangent to
  the part during pushing.

r(f)
f
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Push Function
r(f)

• Links every initial orientation of the part to
  its final orientation after pushing.

f
f0
p(f)
f0
f
f0
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Radius and Push Function
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Oblivious Plans
Actual orientation of part is unknown at any
stage. Objective reduce number of possible
orientations of the part with every application
of the jaw.
Reorientation of jaw and push maps two
orientations of the part onto one.
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Push Diagram

• Can we orient a polygonal part with n
  vertices?Can we reduce the number of possible
  orientations to just 1, regardless of the initial
  orientation?

Polygonal partpush function has n steps, and no
ramps.
p(?)
?
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Push Actions

• Distinguish
• Left half-step part rotates clockwise into
  stable orientation.
• Right half-step part rotates counterclockwise
  into stable orientation.

p(?)
?
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Push Plan

• Let a be the length of the longest right
  half-step, and a-µ be larger than the length of
  the second largest right half-step.
• Idea Repeatedly push and reorient by a-µ.

p(?)
a
?
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Plan Execution

• Initially Any orientation is possible.

p(?)
?
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Plan Execution

• PushPart settles in stable orientations.

p(?)
?
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Plan Execution

• After pushDiscrete set of possible orientations.

p(?)
?
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Plan Execution

• Reorient by a-µNew set of possible orientations.

p(?)
?
a-µ
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Plan Execution

• PushPart settles in stable orientations.

p(?)
?
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Plan Execution

• After pushSmaller discrete set of possible
  orientations.

p(?)
?
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Plan Execution

• Reorient by a-µNew set of possible orientations.

p(?)
?
a-µ
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Plan Execution

• PushPart settles again in stable orientations.

p(?)
?
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Plan Execution

• After pushYet smaller discrete set of possible
  orientations.

p(?)
?
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Plan Execution

• Reorient by a-µNew set of possible orientations.

p(?)
?
a-µ
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Plan Execution

• PushPart settles in stable orientation.

p(?)
En un momento dadoJohan Cruyff, FC Barcelona,
73-78 Only one possible orientation!
?
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Parallel-Jaw Grippers

• Every 2D part can be oriented by a sequence of
  push or squeeze actions.
• Shortest sequence is efficiently computable
  Goldberg 93.

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Feeding with Fences

• Every 2D part can be oriented by fences over
  conveyor belt.
• Shortest fence design
  efficiently
  computable
  Berretty, Goldberg,
  Overmars, vdS 98.

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Feeding by Toppling

• Shortest sequence of pins and their heights
  efficiently computable
  Zhang,
  Goldberg, Smith, Berretty, Overmars 01.