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Introduction

Multi-Target Composition

Multiple Composition via LTL Realizability

Conclusions

Realizing Multiple Autonomous Agents through Scheduling of Shared Devices Sebastian Sardina1 1

Giuseppe De Giacomo2

Department of Computer Science and Information Technology RMIT University Melbourne, AUSTRALIA

2

Dipartimento di Informatica e Sistemistica Sapienza Universita’ di Roma Rome, ITALY

September 16, 2008 Sardina & De Giacomo (ICAPS’08)

Realizing Multiple Autonomous Agents

September 16, 2008

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Introduction



Conclusions

The Centralized Behavior Composition [IJCAI’07] Environment (description of actions; prec. & effects)

Available Behaviors (description of the behavior of available agents/devices)

Sardina & De Giacomo (ICAPS’08)


September 16, 2008

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Introduction



Conclusions


Target Behavior (desired behavior)




September 16, 2008

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Introduction



Conclusions


Controller





September 16, 2008

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Introduction



Conclusions


Synthesize a centralized controller that realizes the target behavior in the environment by suitably coordinating the available behaviors.

Controller





September 16, 2008

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Introduction



Conclusions

The Multiple Behavior Composition [ICAPS’08] Environment (description of actions; prec. & effects)

Controller

Target Target Behaviors Behavior (desired (desired behaviors) behavior)




September 16, 2008

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Introduction



Conclusions


Synthesize a scheduler that fairly realizes all target agents in by suitably operating the available devices and preserving the full agents’ autonomy.

Scheduler

Target Target Agents Behaviors Behavior (desired (desired (autonomous) behaviors) behavior)

AvailableBehaviors Devices Available (logic ofofexisting devices;ofpartially-controllable) (description the behavior available agents/devices)



September 16, 2008

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Introduction



Conclusions

Concentrating on TSs: Vending Machine Transition systems (TSs) may be used to describe the logic of some device, module, process, agent, etc.

S0

collect

20c S1 big

10c S2 small

S3


collect

S4


September 16, 2008

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Introduction



Conclusions


S0

collect

20c S1 big

10c 10c

S2 small

S3


collect

S4


September 16, 2008

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Introduction



Conclusions


S0

collect

20c S1

10c 10c

collect

S2

tilt big S3

small 10c

S5

20c

S4

tilt



September 16, 2008

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Introduction



Conclusions


S0

collect

20c S1

10c 10c

collect

S2

tilt big S3

small 10c

S5

20c

S4

tilt I

Different actions in a state express the client’s options or choice points.



September 16, 2008

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Introduction



Conclusions


S0

collect

20c S1

10c 10c

collect

S2

tilt big S3

small 10c

S5

20c

S4

tilt I

Different actions in a state express the client’s options or choice points.

I

Nondeterministic transitions express choice not under the control of users.



September 16, 2008

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Introduction



Conclusions

Multiple Target Composition

I

Task: to realize a community of agents rather than one isolated agent. I

I

I

Agents request the execution of actions; actions are performed by devices.

Possible applications: I

Robot ecologies.

I

Ambient intelligence.

Imagine an “intelligent” house: Devices vacuum cleaner, video cameras, grabbing/moving robot, etc. Agents surveillance agent, cleaning agent, ambient agent, etc.



September 16, 2008

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Introduction



Conclusions


Scheduler

Target Agents Behaviors Behavior ic istTarget determinmou(desired s (desired (autonomous) behaviors) behavior) autono

rministic nondete servable fully ob ontrollable c partially




September 16, 2008

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Introduction



Conclusions

Multiple Target Composition: The Setting I

Each target is an autonomous agent that deliberates within its capabilities. I

The deterministic target behavior stands for the agent’s capabilities.



September 16, 2008

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Introduction



Conclusions



I

At each point, every target agent is requesting (the execution) of an action. I

I


The agent wants the action to be performed in the environment.

Agents are, in principle, independent. I

Agents are not “fussy” on when their actions will be done.



September 16, 2008

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Introduction



Conclusions



I


I



I



After a target has been satisfied (by the execution of its action); it may request its next action.



September 16, 2008

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Introduction



Conclusions



I


I



I



After a target has been satisfied (by the execution of its action); it may request its next action.

The task: always satisfy every agent forever... Sardina & De Giacomo (ICAPS’08)


September 16, 2008

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Introduction



Conclusions

Formal Setting: Scheduler Programs I

Whole framework defined by: I I

I

Available system: Sa = (D1 , . . . , Dn ). Target system: St = (T1 , . . . , Tm ).

Scheduler program P = hPa , Pt i for an available system Sa and a target system St is a pair of functions: 1

Pa : H × Am 7→ A × {1, . . . , n} action to execute + one available device

2

Pt : H 7→ 2{1,...,m} target agents that may advance one step

I

Other notions: agent trace, target trace, runs, realize a trace, etc.



September 16, 2008

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Introduction



Conclusions

Formal Setting: Scheduler Programs I

Whole framework defined by: I I

I

Available system: Sa = (D1 , . . . , Dn ). Target system: St = (T1 , . . . , Tm ).

Scheduler program P = hPa , Pt i for an available system Sa and a target system St is a pair of functions: 1

Pa : H × Am 7→ A × {1, . . . , n} action to execute + one available device

2

Pt : H 7→ 2{1,...,m} target agents that may advance one step

I

Other notions: agent trace, target trace, runs, realize a trace, etc.

Concurrent Composition A scheduler P = (Pa , Pt ) is a concurrent composition of the target system St in the available system Sa iff P fairly realizes every possible target system trace Λt . Sardina & De Giacomo (ICAPS’08)


September 16, 2008

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Introduction



Conclusions

An Example t1A

a b

t2A

t1B

d

e

t2B

c

s11

t3B

TB

o2

D1 a

t4B

r

TA

o1

o1 o2

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction



Conclusions

An Example t1A

a b

t2A

t1B

d

e

t2B

c

s11

t3B

TB

o2

D1 a

t4B

r

TA

o1

o1 o2

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction



Conclusions

An Example t1A

a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

a o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction



Conclusions

An Example t1A

a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

a o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction



Conclusions

An Example t1A

a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

a o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction



Conclusions

An Example t1A

a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

a·d o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

8 / 14

Introduction



Conclusions

An Example t1A

a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

a·d o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction



Conclusions

An Example t1A

a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

a·d o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction



Conclusions

An Example t1A

a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

a·d ·e o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction



Conclusions

An Example t1A

a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

a·d ·e o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction



Conclusions

An Example t1A

a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

a·d ·e o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction



Conclusions

An Example: The Working Scheduler t1A

a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

d o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction



Conclusions


a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

d o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction



Conclusions


a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

d ·e o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

8 / 14

Introduction



Conclusions


a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

d ·e o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction



Conclusions


a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

d · e · o1 o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction



Conclusions


a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

d · e · o1 o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction



Conclusions


a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

d · e · o1 · a o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

8 / 14

Introduction



Conclusions


a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

d · e · o1 · a o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction



Conclusions


a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

d · e · o1 · a · r o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction



Conclusions


a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

d · e · o1 · a · r o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

8 / 14

Introduction



Conclusions


a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

d · e · o1 · a · r · c o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

8 / 14

Introduction



Conclusions


a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

d · e · o1 · a · r · c o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction



Conclusions


a b

t2A

t1B

d

e

t2B

c

o1 o2

t3B

t4B

r

TA

TB

d · e · o1 · a · r · c o1 s11

o2

D1 a

s21

r s13

s12

r

D3 d

s23

D2 b

c2 s22

r

e

s33 c



September 16, 2008

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Introduction


Realizability


Conclusions

[Pnueli+Rosner, 1989]

I : input variables O: output variables Game: I

System: chooses from 2I

I

Controller: chooses from 2O

Infinite Play:



September 16, 2008

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Introduction


Realizability


Conclusions




I


Infinite Play: i0



September 16, 2008

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Introduction


Realizability


Conclusions




I


Infinite Play: i0 O0



September 16, 2008

9 / 14

Introduction


Realizability


Conclusions




I


Infinite Play: i0 , i1 O0



September 16, 2008

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Introduction


Realizability


Conclusions




I


Infinite Play: i0 , i1 O0 , O1



September 16, 2008

9 / 14

Introduction


Realizability


Conclusions




I


Infinite Play: i0 , i1 , i2 , . . . O0 , O1



September 16, 2008

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Introduction


Realizability


Conclusions




I


Infinite Play: i0 , i1 , i2 , . . . O0 , O1 , O2 , . . .



September 16, 2008

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Introduction


Realizability


Conclusions




I


Infinite Play: i0 , i1 , i2 , . . . O0 , O1 , O2 , . . . Infinite play: i0 · O0 · i1 · O1 · i2 · O2 . . .



September 16, 2008

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Introduction


Realizability


Conclusions




I


Infinite Play: i0 , i1 , i2 , . . . O0 , O1 , O2 , . . . Infinite play: i0 · O0 · i1 · O1 · i2 · O2 . . . Specification: LTL formula on I ∪ O (typically of the form φass → ψreq ) Strategy: Function f : (2I )∗ → 2O Wining strategy: strategy f s.t. every play π in which Ok = f (i0 · · · ik ) is such that π |= spec



September 16, 2008

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Introduction


Realizability


Conclusions




I


Infinite Play: i0 , i1 , i2 , . . . O0 , O1 , O2 , . . . Infinite play: i0 · O0 · i1 · O1 · i2 · O2 . . . Specification: LTL formula on I ∪ O (typically of the form φass → ψreq ) Strategy: Function f : (2I )∗ → 2O Wining strategy: strategy f s.t. every play π in which Ok = f (i0 · · · ik ) is such that π |= spec Realizability: Existence of winning strategy f for specification. Synthesis: Actually computing a winning strategy. Sardina & De Giacomo (ICAPS’08)


September 16, 2008

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Introduction


GR(1) Formulas I


Conclusions

[Piterman, Pnueli, Sa’ar 2006]

LTL realizability is 2EXPTIME-complete for general LTL formulas. Notice that satisfiablity or validity for LTL is PSPACE-complete

I

Several interesting LTL patterns have been studied (discrete-even control).



September 16, 2008

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Introduction


GR(1) Formulas I


Conclusions



I


I

“General Reactivity (1)” formulas: ϕass → ψreq of a special syntactic shape. I

I

Assumption formula ϕass : the assumptions on the system. agents request actions from their capabilities; requests cannot be withdrawn Requirement formula ψreq : specification to capture. actions are executed if pending; all pending actions are eventually executed



September 16, 2008

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Introduction


GR(1) Formulas I


Conclusions



I


I

“General Reactivity (1)” formulas: ϕass → ψreq of a special syntactic shape. I

I

Assumption formula ϕass : the assumptions on the system. agents request actions from their capabilities; requests cannot be withdrawn Requirement formula ψreq : specification to capture. actions are executed if pending; all pending actions are eventually executed

Theorem (Pitterman, Pnueli, Sa’ar VMCAI’06) Realizability on GR(1) formulas is polynomial in the size of the formula and the possible valuations that satisfy ϕass .



September 16, 2008

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Introduction



Conclusions

Composition via Reduction to LTL GR(1) Formulas I I

Input variables: states of devices/agents, requested actions, etc. Output variables: action executed next & agent “served.”



September 16, 2008

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Introduction



Conclusions

Composition via Reduction to LTL GR(1) Formulas I I I

Input variables: states of devices/agents, requested actions, etc. Output variables: action executed next & agent “served.” We build a GR(1) formula Φ(Sa ,St ) = ϕass → ψreq : V φass = φ[I , O] ∧ j φj [I , O, φ[I ]] 1

2

Initial legal system configuration. V devices/agents start in their initial state: ni=1 s0i Legal transitions of the overall system (as dictated by all TSs). k agents request actions within their capabilities: (t12 ⊃ a3k ∨ a8k )



September 16, 2008

11 / 14

Introduction



Conclusions

Composition via Reduction to LTL GR(1) Formulas I I I

Input variables: states of devices/agents, requested actions, etc. Output variables: action executed next & agent “served.” We build a GR(1) formula Φ(Sa ,St ) = ϕass → ψreq : V φass = φ[I , O] ∧ j φj [I , O, φ[I ]] 1

2

Initial legal system configuration. V devices/agents start in their initial state: ni=1 s0i Legal transitions of the overall system (as dictated by all TSs). k agents request actions within their capabilities: (t12 ⊃ a3k ∨ a8k )

ψreq = φ0 [I , O] ∧ 1 2 3

V

j

φ0j [I , O, φ[I , O]] ∧

V

k

♦φ0k [I , O]

Initialization of the scheduler. Legal ways of executing actions and assigning them to agents. k an agent is “advanced” if its action was done: (t12 ∧ Fullk ⊃ t3k ) Eventuality to be satisfied by the controller. it is always true that eventually all target agents are satisfied



September 16, 2008

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Introduction



Conclusions

Technical Results Theorem (Soundness & Completeness) There exists a scheduler that is a concurrent composition of the target system St in the system Sa iff the LTL formula Φ, constructed as above, is realizable.

Theorem (Complexity upperbound) Checking the existence of a scheduler that is a concurrent composition of the target system St = (T1 , . . . , Tm ) in the available system Sa = (D1 , . . . , Dn ) can be done in O(m ∗ |A| ∗ u m+n ), where u = max{|T1 |, . . . , |Tm |, |S1 |, . . . , |Sn |}.

Theorem (Complexity characterization) Checking the existence of a scheduler that is a concurrent composition of a target system St in a system Sa is EXPTIME-complete. EXPTIME-hardness from the case of 1 single agent Sardina & De Giacomo (ICAPS’08)


September 16, 2008

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Introduction



Conclusions

Discussion 1

Extends basic behavior composition problem [IJCAI’07; AAAI’07; KR’08].

2

Agent coordination can be achieved by having synchronization devices.



September 16, 2008

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Introduction



Conclusions

Discussion 1


2


3

Analogies with classical planning:

I

don’t plan for actions; but for who perform the actions;

I

planning is a finite game: “get to the goal”;

I

composition is an infinite game: “continuing the play.” 4

Analogies with classical scheduling [Lawler et al. 1993]: I I

agents’ requests = activities; available devices = resources. E.g., Job-Shop-Scheduling (JSS).

Classical scheduling problems are NP-complete



September 16, 2008

13 / 14

Introduction



Conclusions

Discussion 1


2


3

Analogies with classical planning:

I

don’t plan for actions; but for who perform the actions;

I

planning is a finite game: “get to the goal”;

I

composition is an infinite game: “continuing the play.” 4

Analogies with classical scheduling [Lawler et al. 1993]: I I

agents’ requests = activities; available devices = resources. E.g., Job-Shop-Scheduling (JSS).

Classical scheduling problems are NP-complete 5

Realizability is the logical task at the base of the logics ATL and ATL* [Alura, Henzinger, & Kupferman 2002]: I I I

Semantics based on an alternating multi-agent game. General algorithms for ATL* are indeed 2EXPTIME-hard. Practical tools, based on model checking, for the simpler ATL (MOCHA).



September 16, 2008

13 / 14

Introduction



Conclusions

Conclusions 1

Defined the concurrent composition problem. I I I I

Synthesize a scheduler program that implements agents’ action requests... ... by delegating them to the concrete existing devices... ... possibly accommodating the interleaving among the agents... .... in a way that agent autonomy is fully preserved.



September 16, 2008

14 / 14

Introduction



Conclusions

Conclusions 1


2

Synthesis technique: reduction to realizability of GR(1) LTL formulas. I I

3


Leverage on recent results from Verification [Pitterman, Pnueli & Sa’ar’06] Same complexity as the basic composition framework!

There are practical algorithms for realizability in LTL: I I

TLV: www.cs.nyu.edu/acsys/tlv/ Anzu: www.ist.tugraz.at/staff/jobstmann/anzu/



September 16, 2008

14 / 14

Introduction



Conclusions

Conclusions 1


2

Synthesis technique: reduction to realizability of GR(1) LTL formulas. I I

3

Leverage on recent results from Verification [Pitterman, Pnueli & Sa’ar’06] Same complexity as the basic composition framework!

There are practical algorithms for realizability in LTL: I I

4


TLV: www.cs.nyu.edu/acsys/tlv/ Anzu: www.ist.tugraz.at/staff/jobstmann/anzu/

Practical aspects of concern when it comes to implementing the solution: I I

Robot ecologies [Bordignon et al. ’07] [Lundh et al. ’07] Ambient intelligence [Saffiotti & Broxvall ’05]



September 16, 2008

14 / 14

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