Manipulating Parts with an Array of Pins Sebastien Blind - - PDF document

Manipulating Parts with an Array of Pins

Sebastien Blind Christopher McCullough Srinivas Akella Jean Ponce Beckman Institute for Advanced Science and Technology University of Illinois at Urbana-Champaign USA

Parts Feeding

Bringing parts in unknown initial configurations to goal configurations for automated assembly Important for products such as VCRs, cell phones, auto instrument panels “Pachinko Machine”: Simple modular device for flexible parts feeding:

Pachinko Machine

Array of binary actuated pins on a vertical plate

Industrial Need

Flexible systems that:

• automatically plan how to orient

a given part

• enable designers to evaluate part
• rientability

Benefits:

• Reduce time and cost to

manufacture new products

• Enable computer-aided design

and virtual prototyping

Minimalist Design

A parts nest and transfer device Hardware: Modular, reconfigurable design Simple, yet flexible Software: Simplify geometric representations Part comes to rest in potential energy minima

Related Work

Parts feeding: Boothroyd et al.(1982); Hitakawa(1988); Mani and Wilson(1985); Erdmann and Mason(1986); Peshkin and Sanderson(1988); Goldberg(1990); Brost(1991); Caine(1994); Rao and Goldberg(1994); Krishnasamy, Jakiela and Whitney(1996); Wiegley et al.(1996); Akella et al.(1997) Equilibrium configurations and capture regions: Brost(1991); Kriegman(1997); Mason, Rimon, and Burdick(1995) Modular fixturing: Brost and Goldberg(1996); Wallack and Canny(1997); Sudsang, Ponce, and Srinivasa(1997) Manipulation with fingers: Fearing(1986); Rus(1993); Abell and Erdmann(1995); Leveroni and Salisbury(1996); Farahat, Stiller, and Trinkle(1995) Force fields: Bohringer, Bhatt, and Goldberg(1995); Luntz, Messner, and Choset(1997); Reznik and Canny(1998); Bohringer, Donald, Kavraki, and Lamiraux(1999)

Manipulating Parts with an Array of Pins

“Pachinko machine” to catch, transfer, and orient parts Array of binary actuated pins on a vertical plate

Assumptions

• 1. Polygonal part of known shape
• 2. Frictionless pins
• 3. No friction between part and plate
• 4. Dissipative dynamics

Part can bounce, slide, or roll; its exact motion is not predicted Parts not captured by pins are recirculated

Overview

Identify equilibrium configurations Compute capture regions of equilibria Build transition graph and perform search

3.5 4 1 2 3

• 7
• 6.5

3.5 4 1 2 3

A B C D A B C D C B A D

Questions

• How do we identify contact and

equilibrium configurations?

• How do we compute capture

regions?

• How do we generate plans?

Configuration Space

Object configuration: Transform object to a point in its configuration space x y θ , , ( )

Configuration Space

Object configuration: Transform object to a point in its configuration space x y θ , , ( )

Configuration Space Obstacle

Section of configuration space obstacle Contact curves

• 1
• 0.5

0.5 1 1.5

• 1
• 0.5

0.5 1 1.5 2

x y

1 2 3 4 5 6

• 0.5

0.5 1 1.5

y theta

Configuration Space Obstacle

Section of configuration space obstacle Vertex curves

• 4
• 2

2 4 6 8 x

• 5
• 4
• 3
• 2
• 1

1 2 y 1 2 3 4 5 6 q

• 6
• 4
• 2

2 4 y

Critical Configurations

Equilibrium configurations Saddle point configurations

• x

y θ θ Γ Γ T

1 2

Γ

3

• x

y θ θ M Γ

• x

y θ θ T Γ

3

Γ

2

Γ

1

• x

y θ θ M Γ

• x

y θ θ Γ M

• x

y θ θ Γ Γ

1 2

Γ

3

T

Equilibrium Configurations

For each pair and triple of edges, find all two or three pin contacts for part equilibrium

Capture Region

Brost (1991); Kriegman (1997) Set of configurations guaranteed to reach equilibrium configuration Exact object motion does not matter, assuming dissipative dynamics

O equilib

• O max
• O min
• Maximal Height

Capture Region

Brost (1991); Kriegman (1997) Set of configurations guaranteed to reach equilibrium configuration

Max Height is 1.33594 3.5 4 4.5 5 q 1 2 3 4 x

• 1

1 2 3.5 4 4.5

Computing Capture Regions

Potential saddle points, Boundary representation

• x

y θ θ T Γ

3

Γ

2

Γ

1

• x

y θ θ M Γ

• x

y θ θ Γ M

• x

y θ θ Γ Γ

1 2

Γ

3

T

Computing Capture Regions

Compute capture region of given equilibrium using y-slices

A B C D A B C D

Identifying Equilibria in Capture Region

For each equilibrium, identify all equilibria that can be translated to interior of its capture region

• λV +µV

1 2

Ej Ci C-obstacle

Transition Graph

Equilibrium configurations Link each equilibrium to all equilibria whose capture regions include it

1 2 3 4 5 6

• 7.5
• 5
• 2.5

2.5 5 1 2 3 4 5 6

• 7.5
• 5
• 2.5

2.5 5

Example Plan

Summary

• Pachinko machine is a modular

and reconfigurable device for parts feeding

• Use configuration space

representation to identify equilibria and compute capture regions

• Plan generation reduces to graph

search

• Broader applicability as

manipulation device for parts

• rienting, transport, sorting, and

assembly

Future Work

• Use sensor information
• Model friction effects
• Improve graph connectivity
• Parts sorting and recognition