Adaptation and Awareness in Robot Ensembles

Matthias HölzlLudwig-Maximilians-Universität München

AWARENESS Summer SchoolDecember 5, 2011

www.ascens-ist.eu

Ensembles

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Ensembles

Massive numbers of nodesExtremely heterogeneousComplex interactions between nodesComplex interactions with humans or other systemsOperating in open and non-deterministic environmentsDynamic adaptation to new

requirementstechnologies andenvironmental conditions

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Swarm Robotics

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Swarm Robotics

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Swarm Robotics

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Ensembles

What is a good model for ensembles?What is adaptivity?What is awareness?What is self-awareness?

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A System Model for Ensembles

Based on Mesarović’s model of general systemsV = (Vi)i∈I : family of setsEnsemble = System = Component = Relation: S ∈ R

((Vi)i∈I

)Modal ensemble:

Set T , binary relation R on TEach Vi is a function space: Vi = F[T → Ai ]

Time ensemble:Modal ensemble where R is a preorder

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Input/Output Configurations

The Vi are divided into input/output configurationsInputs XOutputs YInternal state / awareness sections Z

X = (X1, …, Xk)

Z = (Z1, …, Zm)

Y = (Y1, …, Yl)

(V1, …, Vn) ≅ (X, Y, Z)

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Input/Output Configurations

The Vi are divided into input/output configurationsInputs XOutputs YInternal state / awareness sections Z

X Y

Z

X Y

Z

X Y

Z

X Y

Z

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Combination Operators

A combination operatorcombines components/systems into a new systemmay introduce new inputs/outputs/statesmay introduce complex behavior

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Example: Partial Cascade

S1

S2

X1nc

X2nc

Y1nc

Y2nc

Y1out = X2

in

S1 ∈ R(Xnc1 , (Y nc

1 × Y out1 ))

S2 ∈ R((Xnc2 × X in

2 ),Y nc2 )

Y out1 = X in

2

((x1, x2), (y1, y2)) ∈ S1 . S2 ⇐⇒∃z ∈ Y out

1 : (x1, (y1, z)) ∈ S1 ∧ ((x2, z), y2) ∈ S2

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Goal Satisfaction (Overview)

Model M (Logic)

System Model S(Relational)

Logic

S ⊨ 𝜸

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Goal Satisfaction

Logic LFormulae FM, α |= γ

FS ⊆ F characterizes the relevant properties of S in L

T :M→ FS × Aux → BoolTM : FS × Aux → BoolM characterizes S (using TM):

charTM(M,S) : ⇐⇒ ∀P ∈ FS : ∀α ∈ Aux : M,α |= P ⇐⇒ TM(P,α)

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Goal Satisfaction

S satisfies goal γ, written S |=T γ:

∀M ∈M : charTM(M,S) =⇒ M |= γ

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Heterostatic Ensembles

Maximizing performance instead of simple goal satisfactionA Heterostatic Ensemble consists of

a system S in input/output configuration (X ,Y ,Z)a partially ordered set Ga fitness function φ : X × Y × Z → G

Various notions of ordering possibleweak heterostatic order (relational ordering of domain theory)Egli-Milner ordering. . .

Problem: Can only take “worst case” or “best case” behavior into accountProbabilistic extension (e.g., by stochastic relations)

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Adaptation

Environment η, network or sensors/actuators ν and System SCombination operator ⊗; we write η,ν,S instead of ⊗(η,ν,S)Goal satisfaction in an environment:

η,ν,S 6|= ⊥ Consistencyη,ν,S |= γ Goal Satisfaction

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Adaptation

We usually speak of adaptation when a system works in multiple situationsAdaptation can be

to a new environment: η ′, ν, S |= γto a new network: η,ν ′,S |= γto a new goal: η,ν,S |= γ ′

to a change in the System(?): η,ν,S ′ |= γor any combination thereof

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Adaptation: Example

Two workstations Two workstations, low bandwidth

Mobile phone and workstation Workstation and cluster

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Adaptation: Example

Two mobile phones Two mobile phones and workstation

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Adaptation Domains

Adaptation domain A ⊆ E ×N × G:S can adapt to A, written S A:

S A ⇐⇒ ∀(η,ν,γ) ∈ A : η,ν,S |= γ

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Adaptation Spaces

Adaptation space A: a set of adaptation domains, A ⊆P(E × N × G)Partially ordered by inclusionFor any adaptation space we define a preorder of adaptivity for systems:

S v S ′ ⇐⇒ ∀A ∈ A : S A =⇒ S ′ A

(S ′ is at least as adaptive as S with respect to A)Extension to probabilistic case needed

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Awareness

Awareness is the state or ability to perceive, to feel, or to be conscious of events,objects or sensory patterns. (Wikipedia)Aware: 1. Having knowledge or cognizance (Free Online Dictionary)

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Awareness

Necessary conditions for awareness seem to be:An internal model of the object/state/processChanges in the real world are reflected in the internal model

Awareness is “knowledge in time”Awareness is dual to causal connection

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Awareness

Photo by kimberlykv, used under CC BY 2.0 license, http://www.flickr.com/photos/kimberlykv/6336662270/

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Awareness

Photos by kimberlykv and djburkey, used under CC BY 2.0 (NC) licensehttp://www.flickr.com/photos/kimberlykv/6336662270/ and .../djburkey/193590859/

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Awareness

Photos by kimberlykv and brostad, used under CC BY 2.0 licensehttp://www.flickr.com/photos/kimberlykv/6336662270/ and .../brostad/4662951088/

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Self-Awareness

Let S ' (X ,Y ,Z)Z can contain various awareness sections

awareness of environmentawareness of networkawareness of goals

If Z contains a section ZS that is aware of S we say S has a degree of self awareness

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Literature

Matthias Hölzl and Martin Wirsing.Towards a system model for ensembles.In Gul Agha, Olivier Danvy, and José Meseguer, editors, Festschrift in Honor of CarolynTalcott, LNCS. Springer, 2011.

M. D. Mesarović and Y. Takahara.General Systems Theory: Mathematical Foundations, volume 113 of Mathematics inScience and Engineering.Academic Press, New York, San Francisco, London, 1975.

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Conclusions and Future Work

Denotational system model for ensemblesNotions of adaptation and (self-)awareness

Operational modelsModel of emergenceRelationship to knowledgeAdaptation patterns and white-box adaptation

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Thank you. . .

for your attention

matthias.hoelzl@ifi.lmu.de

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