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

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Generic distributed algorithms Cellular automata paradigm

•Non-persistent modules Proposed for self-reconfiguring robots by

Hosokawa et al. (ICRA 1998)•Synchronous update model

Methodology

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Methodology

Approach1. Use abstract module with simple motions2. Create rule sets using only local information3. Prove rule sets produce correct

reconfigurations4. Instantiate rule sets onto real systems

RSS 2005 MIT CSAIL

Methodology

Approach1. Use abstract module with simple motions2. Create rule sets using only local information3. Prove rule sets produce correct

reconfigurations4. Instantiate rule sets onto real systems

= cell = no cell or obstacle= current cell

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RSS 2005 MIT CSAIL

Methodology

Approach1. Use abstract module with simple motions2. Create rule sets using only local information3. Prove rule sets produce correct

reconfigurations4. Instantiate rule sets onto real systemsProof methods1. Logical argument2. Graph properties3. Statistical argument

• Bounds size of error region with some confidence

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Metamorphic Module – Chirikjian et al.

Fracta Module – Murata et al. Crystal Module – Rus et al.

Methodology

Approach1. Use abstract module with simple motions2. Create rule sets using only local information3. Prove rule sets produce correct

reconfigurations4. Instantiate rule sets onto real systems

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Locomotion Rule Set (ICRA 2002)

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Locomotion Example (ICRA 2002)

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Self-Assembly Example 1

Rule set 19 rules: 9 x 2 (east, west), 1 other Internal state: direction, location Rows act independently

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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

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Reconfiguration Algorithm

Two-phase algorithm1. Non-local phase

• Reconfigure so that each row has the correct number of modules

• Align rows with the goal shape2. Local phase

• Locomotion to the goal shape location• Self-assembly into the goal shape

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Reconfiguration Algorithm

Rule set for non-convex shapes 33 rules 2½-D start and goal shapes

• Layers must be connected components

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Algorithm Correctness

Non-convex shape rule setStart 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

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Reconfiguration Algorithm

Ruleset developed by Kohji Tomita,

AIST

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Reconfiguration Algorithm

Old A-2 Rule

New A-2 Rule

New Stopping Rule

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Reconfiguration Algorithm

New non-convex shape rule set 66 rules 2½-D start and goal shapes

• Layers must be connected components Reduction in structure voids

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Reconfiguration Algorithm

New non-convex shape rule set 66 rules 2½-D start and limited 3-D goal shapes

• Layers must be connected components Reduction in structure voids

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Algorithm Correctness

New non-convex shape rule setStart 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

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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

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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