Keith Kotay and Daniela Rus

rucksackbulgeΤεχνίτη Νοημοσύνη και Ρομποτική

1 Δεκ 2013 (πριν από 3 χρόνια και 6 μήνες)

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Generic Distributed Algorithms for
Self
-
Reconfiguring Robots

Keith Kotay and Daniela Rus


MIT Computer Science and Artificial
Intelligence Laboratory

RSS 2005

MIT CSAIL

Self
-
Reconfiguring Robot

Multiple functionalities


Form follows function

Advantages


Versatile


Robust


Extensible

RSS 2005

MIT CSAIL

Generic distributed algorithms


Cellular automata paradigm


Non
-
persistent modules


Proposed for self
-
reconfiguring robots by
Hosokawa et al.
(ICRA 1998)


Synchronous update model


Methodology

RSS 2005

MIT CSAIL

Methodology

Approach

1.
Use abstract module with simple motions

2.
Create rule sets using only local information

3.
Prove rule sets produce correct reconfigurations

4.
Instantiate rule sets onto real systems

RSS 2005

MIT CSAIL

Methodology

Approach

1.
Use abstract module with simple motions

2.
Create rule sets using only local information

3.
Prove rule sets produce correct reconfigurations

4.
Instantiate rule sets onto real systems

=
cell
=
no cell or obstacle
=
current cell
N
S
E
W
RSS 2005

MIT CSAIL

Methodology

Approach

1.
Use abstract module with simple motions

2.
Create rule sets using only local information

3.
Prove rule sets produce correct reconfigurations

4.
Instantiate rule sets onto real systems

Proof methods

1.
Logical argument

2.
Graph properties

3.
Statistical argument


Bounds size of error region with some confidence

RSS 2005

MIT CSAIL

Metamorphic Module


Chirikjian et al.

Fracta Module


Murata et al.

Crystal Module


Rus et al.

Methodology

Approach

1.
Use abstract module with simple motions

2.
Create rule sets using only local information

3.
Prove rule sets produce correct reconfigurations

4.
Instantiate rule sets onto real systems

RSS 2005

MIT CSAIL

Locomotion Rule Set

(ICRA 2002)

RSS 2005

MIT CSAIL

Locomotion Example
(ICRA 2002)

N
S
E
W
RSS 2005

MIT CSAIL

Self
-
Assembly Example 1

Rule set


19 rules: 9 x 2 (east, west), 1 other


Internal state: direction, location


Rows act independently

RSS 2005

MIT CSAIL

Self
-
Assembly Example 2

Rule set


19 rules: 9 x 2 (east, west), 1 other


Internal state: direction, location
, goal shape


Rows act independently


Works for convex 2½
-
D shapes

RSS 2005

MIT CSAIL

Reconfiguration Algorithm

Two
-
phase algorithm

1.
Non
-
local phase


Reconfigure so that each row has the correct number
of modules


Align rows with the goal shape

2.
Local phase


Locomotion to the goal shape location


Self
-
assembly into the goal shape

RSS 2005

MIT CSAIL

Reconfiguration Algorithm

Rule set for non
-
convex shapes


33 rules



-
D start and goal shapes


Layers must be connected components

RSS 2005

MIT CSAIL

Algorithm Correctness

Non
-
convex shape rule set

Start

Goal

Modules

Iterations

PAC Bounds

Square

Pyramid

25

5,000,000

99.9997%
--

0.0003%

Square

Pyramid

81

100,000

99.99%
--

0.01%

Random

Random

9

2,000,000

Not significant

Random

Random

16

1,000,000

Not significant

Random

Random

25

5,000,000

Not significant

Random

Random

49

300,000

Not significant

RSS 2005

MIT CSAIL

Reconfiguration Algorithm

Ruleset developed
by Kohji Tomita,
AIST

RSS 2005

MIT CSAIL

Reconfiguration Algorithm

Old A
-
2 Rule

New A
-
2 Rule

New Stopping Rule

RSS 2005

MIT CSAIL

Reconfiguration Algorithm

New non
-
convex shape rule set


66 rules



-
D start and goal shapes


Layers must be connected components


Reduction in structure voids

RSS 2005

MIT CSAIL

Reconfiguration Algorithm

New non
-
convex shape rule set


66 rules



-
D start and
limited 3
-
D

goal shapes


Layers must be connected components


Reduction in structure voids

RSS 2005

MIT CSAIL

Algorithm Correctness

New non
-
convex shape rule set

Start

Goal

Modules

Iterations

PAC Bounds

Square

Pyramid

25

1,000,000

99.999%
--

0.001%

Square

Pyramid

49

200,000

99.995%
--

0.005%

Square

Pyramid

81

100,000

99.99%
--

0.01%

Square

Hollow Pyramid

25

100,000

99.99%
--

0.01%

Random

Random

25

1,000,000

Not significant

Random

Random

49

200,000

Not significant

Random

Random

81

20,000

Not significant

RSS 2005

MIT CSAIL

Conclusion

Generic, distributed approach


Abstract module


Local rules


Algorithm correctness


Instantiation to real hardware

Algorithms


Self
-
assembly of convex 2½
-
D shapes


Self
-
assembly of non
-
convex 2½
-
D shapes


Extension to limited 3
-
D goal shapes

RSS 2005

MIT CSAIL

Acknowledgements

Boeing

National Science Foundation


Awards IRI
-
9714332, EIA
-
9901589, IIS
-
9818299, IIS
-
9912193, and EIA
-
0202789

Project Oxygen at MIT

Intel

Office of Naval Research


Award N00014
-
01
-
1
-
0675

Zack Butler and Kohji Tomita