# Keith Kotay and Daniela Rus

AI and Robotics

Dec 1, 2013 (4 years and 7 months ago)

169 views

Generic Distributed Algorithms for
Self
-
Reconfiguring Robots

Keith Kotay and Daniela Rus

MIT Computer Science and Artificial
Intelligence Laboratory

MIT CSAIL

Self
-
Reconfiguring Robot

Multiple functionalities

Form follows function

Versatile

Robust

Extensible

MIT CSAIL

Generic distributed algorithms

Non
-
persistent modules

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

Synchronous update model

Methodology

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

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

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

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

MIT CSAIL

Locomotion Rule Set

(ICRA 2002)

MIT CSAIL

Locomotion Example
(ICRA 2002)

N
S
E
W

MIT CSAIL

Self
-
Assembly Example 1

Rule set

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

Internal state: direction, location

Rows act independently

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

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

MIT CSAIL

Reconfiguration Algorithm

Rule set for non
-
convex shapes

33 rules

-
D start and goal shapes

Layers must be connected components

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

MIT CSAIL

Reconfiguration Algorithm

Ruleset developed
by Kohji Tomita,
AIST

MIT CSAIL

Reconfiguration Algorithm

Old A
-
2 Rule

New A
-
2 Rule

New Stopping Rule

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

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

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

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

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