FranckPetit EnablingCommunicationinSwarmofDeterministicDeafandDumbRobots

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Introduction Model Roadmap Protocols Conclusion

Enabling Communication in Swarm of Deterministic Deaf and Dumb Robots

Franck Petit

LiP6, UPMC Paris 6

Franck Petit Enabling Communication in Swarms of Deterministic Robots 1/39

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Stigmergy

Figure:Pierre-Paul Grass ´e

Stigmergy

Mechanism of spontaneous, in- direct coordination between so- cial insects using no direct means of communication to per- form some basic cooperative tasks.

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Stigmergy

Mechanism of spontaneous, in- direct coordination between so- cial insects using no direct means of communication to per- form some basic cooperative tasks.

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Stigmergy

Any communication only occurs in an implicit way, in general by modifying the environment

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Stigmergy

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Stigmergy

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Stigmergy

Figure:The food is located at less than 100m.

Figure:The food is located very near the hive.

Figure:The food is in the direction to the sun.

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Related Works

1 [Beckers et al., Artificial Life, 1994]

From local actions to global taks: Stigmergy and collective Robotics.

2 [Matari´c, Robotics and Autonomous Systems, 1995]

Stigmergy does not addressed explicit communication as tasks by themselves.

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Related Works

From local actions to global taks: Stigmergy and collective Robotics.

Issues and approaches in the design of collective autonomous agents.

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Related Works

Emergent behavior and specific tasks only.

Issues and approaches in the design of collective autonomous agents.

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Related Works

Explicitvs.Implicit Communication.

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Related Works

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Related Works

=⇒Deaf and dumb robots are not allowed to chat together.

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Implicit −→ Explicit Communication

We introduce the use of movements as a mean tochat among a cohort ofdeaf and dumb robots.

No need to have additional devices to communicate Communication backup (fault-tolerance)

Enable the use of distributed algorithms

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Implicit −→ Explicit Communication

No need to have additional devices to communicate

Communication backup (fault-tolerance) Enable the use of distributed algorithms

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Implicit −→ Explicit Communication

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Implicit −→ Explicit Communication

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Basic Settings

Asynchronous

No (explicite) means of communication

Non Oblivious

Autonomous

Moving onto the plan Unlimited Vision

Unit begin

begin

end

−−−−−

y

x

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Other Capabilities

Chirality(Handedness agreement)

(the orientation of they-axis is inferredw.r.t.thex-axis)

Eithersense of direction(North agreement) or not Either (observable)IDsor not (anonymous)

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Other Capabilities

Eithersense of direction(North agreement) or not

Either (observable)IDsor not (anonymous)

With Sense of Direction→

y x

Without Sense of Direction→

y

x y

x

x y

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Other Capabilities

Eithersense of direction(North agreement) or not Either (observable)IDsor not (anonymous)

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Computation

SYm[Suzuki Yamashita 96]

An inifinite sequence of time instants{t₀,t₁, . . . ,t_i, . . .}

At each time instantt_i, each robot is eitheractiveoridle Int_i, everyactiverobot executes the following phases:

1 Observeall the positions

2 Computea destinationd

3 Movetowardd

Note: The distance traveled in 1 step by any robotris bounded byσr.

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Roadmap

One-to-one deterministic communication protocols as a mean to transfer messages between deaf and dumb robots.

1 Movements can provide implicitacknowledgments

2 One-to-one communicationamong a pair of robots

3 One-to-one communication amongnrobots equipped with observableIDsandsense of direction

4 One-to-one communication amongndisorientedand anonymousrobots

5 Motion Containment and Visibility Limitation

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Roadmap

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Roadmap

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Roadmap

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Roadmap

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Roadmap

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Implicit Acknowledgement

Lemma

Let r and r⁰ be two robots. Assume that r always moves in the same direction each time it becomes active. If r observes that the position of r⁰ has changed twice, then r⁰must have observed that the position of r has changed at least once.

Corollary

Let r and r⁰ be two robots. Assume that r always moves in the same direction on Line l as soon as it becomes active. If r observes that the position of r⁰ has changed twice, then r⁰ knows the Line l and the direction towards which r moved.

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Implicit Acknowledgement

Lemma

r r’

Corollary

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Implicit Acknowledgement

Lemma

P0

r r’

Corollary

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Implicit Acknowledgement

Lemma

r’

r P0 P0

Corollary

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Implicit Acknowledgement

Lemma

r’

P0 P0

r

1 P1

Corollary

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Implicit Acknowledgement

Lemma

1 ^P0 ^P0

r

1 P1

r’

P1

Corollary

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Implicit Acknowledgement

Lemma

P0 2

P0 P1

r’

P1 1 r

1 P2

Corollary

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Implicit Acknowledgement

Lemma

Corollary

Let r and r⁰ be two robots. Assume that r always moves in the same direction on Line l as soon as it becomes active. If r observes that the position of r⁰ has changed twice, then r⁰ knows

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One-to-one Communication Among 2 robots

SynchronousSettings

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One-to-one Communication Among 2 robots

SynchronousSettings

0 0 1

1

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One-to-one Communication Among 2 robots

SynchronousSettings

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One-to-one Communication Among 2 robots

SynchronousSettings

0 0 1

1

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One-to-one Communication Among 2 robots

AsynchronousSettings

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One-to-one Communication Among 2 robots

AsynchronousSettings

r’

r

r r’

h H

0 0

1 0

h

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n > 2

Forn≥3 robots, it is necessary to include:

Mechanism avoiding collisions

Deterministic movements addressing information to a specific robot

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n > 2

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n > 2

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Robots with IDs and Sense of Direction

9 11

10 5

4

8 6

1

3

7

12

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Robots with IDs and Sense of Direction

9 11

10 5

4

8 6

1

3

2

7

12

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Robots with IDs and Sense of Direction

9 11

10 5

4

8 6

1

3

7

12

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Robots with IDs and Sense of Direction

9 0 3

6

9

North

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Robots with IDs and Sense of Direction

9 0 3

6

9

North

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Robots with IDs and Sense of Direction

9 0 3

6

9

North

In asynchronousenvironment:r Sent “0” to 3.Asynchronousenvironment?

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Robots with IDs and Sense of Direction

0

1

2

3 0

1 2

3

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Robots with IDs and Sense of Direction

0

1

2

3 0

1 2

3

Asynchronousenvironment

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Robots with IDs and Sense of Direction

0

1

2

3 0

1 2

3

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Robots with IDs and Sense of Direction

0

1

2

3 0

1 2

3

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Robots with IDs and Sense of Direction

0

1

2

3 0

1 2

3

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Robots with IDs and Sense of Direction

0

1

2

3 0

1 2

3

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Robots with IDs and Sense of Direction

0

1

2

3 0

1 2

3

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Robots with IDs and Sense of Direction

0

1

2

3 0

1 2

3

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Disoriented and Anonymous Robots

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Disoriented and Anonymous Robots

Y

X

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Disoriented and Anonymous Robots

O ^Y

X

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Disoriented and Anonymous Robots

O

SEC Y

X

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Disoriented and Anonymous Robots

O

2 4

5

6

7 8

9

10

11

1

12 Y

X

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Disoriented and Anonymous Robots

O

SEC 2

3 4 5

6

7 8

9

10

11

1

12 Y

X

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Disoriented and Anonymous Robots

0 3

9

6

9

North

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Note that the labeling is specific to each robot. However:

Remark 1

Every robot is able to compute the local labeling of all the other robots.

Remark 2

Each robot is able to know to whom a bit is addressed and in particular to itself.

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Remark 1

Remark 2

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Remark 1

Remark 2

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Motion Containment and Visibility Limitation

Definition (Interleaving Degree)

Letk >0 be the interleaving degree such that, for every pair of distinct robotsr andr⁰, for every suffix of computation in whichr is activatedk times,r⁰ is activated at least once.

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Motion Containment and Visibility Limitation

Definition (Interleaving Degree)

Letk >0 be the interleaving degree such that, for every pair of distinct robotsr andr⁰, for every suffix of computation in whichr is activatedk times,r⁰ is activated at least once.

Lemma

Let r and r⁰ be two robots. Assuming an interleaving degree of k ≥ 1, every k moves of r , then r⁰ have observed that the position of r has changed at least once.

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Motion Containment and Visibility Limitation

1 h_r

H r

0

Figure:k =3

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Motion Containment and Visibility Limitation

1 h_r

H r

0

Figure:k =3

Remark (Movement Containment)

For each robot r , the movement is contained within kσr.

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Motion Containment and Visibility Limitation

Remark (Visibility Limitation)

If robot r knows k andσ_r⁰, then thevisibilityof r can bebounded by k(σ_r +σ_r⁰) +δ,δ is equal to the distance between the initial positions of both r and r⁰.

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Motion Containment and Visibility Limitation

Remark (Visibility Limitation)

If robot r knows k andσ_r⁰, then thevisibilityof r can bebounded by k(σ_r +σ_r⁰) +δ,δ is equal to the distance between the initial positions of both r and r⁰.

Remark

AssumingIDs, combined with a “classical”routingprotocol, the protocol for n works provided that each robot knwows n and no movement breaks the graph of observability.

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Perspectives

1 Silent Protocol 2 Absence of chirality

3 Movement Limitation (number and distance) in asynchronous environment

4 Fully asynchronous model (CORDA) 5 Stabilization

6 Crashes