generic distributed algorithms for self-reconfiguring robots
DESCRIPTION
Generic Distributed Algorithms for Self-Reconfiguring Robots. Keith Kotay and Daniela Rus MIT Computer Science and Artificial Intelligence Laboratory. Self-Reconfiguring Robot. Multiple functionalities Form follows function. Advantages Versatile Robust Extensible. Methodology. - PowerPoint PPT PresentationTRANSCRIPT
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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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