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

dMEMS 2010 2

Smart Surface for conveying, positionning and sorting micro parts.

MEMS-based micro robotics distributedsystem.

Array of micro modules.

Fig 1. Communication network

dMEMS 2010 3

Rich problematic

Scarcity of resources:

- sensors;

- memory occupancy;

- computing power.

Faults.

dMEMS 2010 4

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

SE

NS

OR

ACTUATOR

SE

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OR

ACTUATOR

SE

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OR

ACTUATOR

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ACTUATOR

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Distributed control module

Distributed recognition

module

PART

Po

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nd

rew

ard

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

module

Distributed recognition

module In

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P2P Communication

distributed communication management

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P2P Communication

distributed communication management

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P2P Communication

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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:

dMEMS 2010 8

.1,02n

Ex

.xFx

Ex *

dMEMS 2010 9

,,...,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:

dMEMS 2010 10

,...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).

dMEMS 2010 13

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, …)

dMEMS 2010 14

.,...,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.

dMEMS 2010 15

.,...,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’

dMEMS 2010 21

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.

dMEMS 2010 22

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.

dMEMS 2010 23

dMEMS 2010 24