Didier El Baz, Vincent BoyerLAAS-CNRS, Toulouse
Julien Bourgeois, Eugen Dedu, KahinaBoutoustous
LIFC, Montbéliard
Project ANR-06-ROBO-0009 Smart Surface
dMEMS 2010 1
1. Introduction
2. The Smart Surface
3. Distributed discrete state acquisition
4. Concurrent part differentiation
5. Smart surface simulator
6. Tests
7. Conclusions
8. Perspective
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Smart Surface for conveying, positionning and sorting micro parts.
MEMS-based micro robotics distributedsystem.
Array of micro modules.
Fig 1. Communication network
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Rich problematic
Scarcity of resources:
- sensors;
- memory occupancy;
- computing power.
Faults.
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Small parts that cover a small number of cells.
Air nozzles actuators.
Goals:
- MEMS with sensors & « intelligence »,
- fully integrated solution
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ACTUATOR
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Distributed control module
Distributed recognition
module
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P2P Communication
Distributed control module
Distributed control module
Distributed control module
Distributed control module
distributed communication management
Distributed recognition
module
Distributed recognition
module
Distributed recognition
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Distributed recognition
module In
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Fig 2. SS
Each cell has to obtain global knowledge of the state of the smart surface:
it must know precisely if there is a part on the smart surface and obtain its representation.
Initially a cell detects only if there is a part on itor not (0-1 information).
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Fig 3. Distributed state acquisition
Mathematical model
Assumption:
- only one sensor per cell
Notations:
- n denotes the number of cells.
Augmented local state of the i-th cell:
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.,...,1,1,0 nixn
i
Augmented global state:
Fixed point problem:
find smallest which satisfies:
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.1,02n
Ex
.xFx
Ex *
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,,...,1,,, nixxF iiii
,,...,1,,,,, niiNjxxxF jjjiji
iNj
ljlili iNlnlixxxF .,,...,1,,,,,
Fixed point mapping:
,10
, iix
,00
, iix
Distributed synchronous state acquisition:
- successive approximation method
(discrete iteration):
- initial approximation:
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,...1,0,1 kkxFkx
,,,...,1,,00
, ijnjix ji
otherwise.
if there is a part on the i-th cell.
Clearly, is not the only fixed point of .
Importance of choosing a good initial approximation in order to converge to a solution that makes sense.
The approximation is a sub-solution.
The mapping is monotone.
The discrete iteration converges to .
The number of iterations is bounded by the largest Manhattan distance + 1.
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*x F
0x
F
kx *x
Distributed asynchronous algorithms:
we assume that there is a set of times at whichone or more sub-vectors are updated,
The sets are infinite.
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,,,..., ,,1
1
1 iTkxxFxks
n
ks
i
k
iini
.,1 iTkxx k
i
k
i
Tix
.,,...,1,,0 , iTknjikks ij
,lim , ks ijk
iT
The asynchronous iteration converges to from
Robustness, efficiency.
Implementation on Smart Surface Simulator (SSS).
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kx*x
0x
Parts may occupy any position.
Parts may have any orientation.
Cells compute concurrently severaldifferentiation criteria.
- region-based criteria
- contour-based criteria
Few references available in a resource scarcitycontext (Ishida et al., Tabbone et al. 2006, …)
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.,...,1,11
)(1
)(mj
qjg
q
ic
jr
i
i
A first gap-based method
- single reference position;
- subset of criteria
- comparison of criteria values:
part vs reference;
- fault tolerant;
- decision based on the smallest gap.
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.,...,1,11
min)('1
)(mj
qjg
q
ic
jr
Dd
i
di
A second gap-based method
- multiple reference positions.
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Multithreaded Java code designed for multicore machines.
Evaluation and validation of criteria, distributed algorithms, stopping criteria.
Study of communications.
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Build a smart surface and micro parts.
Place, rotate the parts, introduce sensor faults.
Choose computation scheme, criteria and differentiation method.
Display state of cells & activity graph.
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Multithreaded SSS carried out on Intel QuadroXeon 3.0 GHz.
Comparison of gap-based methods and total differentiation methods (Boutoustous et al. 2008).
Results for three parts: square, L and I shapes.
Randomly generated set of tests, 200 draws.
17 criteria considered, selection of criteria.
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Differentiation rates (total differentiation).
Surface (S), product of Angles (A).
Combination of criteria.
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Criteria Sq I L Average
S 37% 52% 57.3% 48.8%
A 33.5% 40.5% 48.5% 40.8%
Criteria Sq I L Average
S & A 59.5% 74% 68% 67.2
Gaps-based methods.
First gap g.
Second gap g’
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Criteria Sq I L Average
S 100% 99% 98% 99%
A 100% 99% 78% 92.3%
S & A 100% 100% 96.5% 98.8%
Criteria Sq I L Average
S 100% 99% 98% 99%
A 100% 99% 78% 92.3%
S & A 100% 99.5% 79% 92.8%
Mathematical foundations of smart surface state acquisition.
Distributed algorithms & stopping criteria.
Convergence results.
Differentiation based on gaps.
Multithreaded Java Smart Surface Simulator.
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Implementation of the gap-baseddifferentiation method on the Smart Surface testbed in Femto.
Combined part differentiation and control.
Differentiation methods not based on criteria
e.g.: Radon transform.
Exploit natural parallelism of the cell array.
Fault tolerance.
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