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
1 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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)
Realizing Multiple Autonomous Agents
September 16, 2008
2 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
The Centralized Behavior Composition [IJCAI’07] Environment (description of actions; prec. & effects)
Target Behavior (desired behavior)
Available Behaviors (description of the behavior of available agents/devices)
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
2 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
The Centralized Behavior Composition [IJCAI’07] Environment (description of actions; prec. & effects)
Controller
Target Behavior (desired behavior)
Available Behaviors (description of the behavior of available agents/devices)
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
2 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
The Centralized Behavior Composition [IJCAI’07] Environment (description of actions; prec. & effects)
Synthesize a centralized controller that realizes the target behavior in the environment by suitably coordinating the available behaviors.
Controller
Target Behavior (desired behavior)
Available Behaviors (description of the behavior of available agents/devices)
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
2 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
The Multiple Behavior Composition [ICAPS’08] Environment (description of actions; prec. & effects)
Controller
Target Target Behaviors Behavior (desired (desired behaviors) behavior)
Available Behaviors (description of the behavior of available agents/devices)
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
2 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
The Multiple Behavior Composition [ICAPS’08] Environment (description of actions; prec. & effects)
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)
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
2 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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
Sardina & De Giacomo (ICAPS’08)
collect
S4
Realizing Multiple Autonomous Agents
September 16, 2008
3 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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 10c
S2 small
S3
Sardina & De Giacomo (ICAPS’08)
collect
S4
Realizing Multiple Autonomous Agents
September 16, 2008
3 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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
10c 10c
collect
S2
tilt big S3
small 10c
S5
20c
S4
tilt
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
3 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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
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.
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
3 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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
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.
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
3 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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.
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
4 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
The Multiple Behavior Composition [ICAPS’08] Environment (description of actions; prec. & effects)
Scheduler
Target Agents Behaviors Behavior ic istTarget determinmou(desired s (desired (autonomous) behaviors) behavior) autono
rministic nondete servable fully ob ontrollable c partially
Available Behaviors (description of the behavior of available agents/devices)
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
5 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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.
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
6 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
Multiple Target Composition: The Setting I
Each target is an autonomous agent that deliberates within its capabilities. I
I
At each point, every target agent is requesting (the execution) of an action. I
I
The deterministic target behavior stands for the agent’s capabilities.
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.
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
6 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
Multiple Target Composition: The Setting I
Each target is an autonomous agent that deliberates within its capabilities. I
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
I
The deterministic target behavior stands for the agent’s capabilities.
Agents are not “fussy” on when their actions will be done.
After a target has been satisfied (by the execution of its action); it may request its next action.
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
6 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
Multiple Target Composition: The Setting I
Each target is an autonomous agent that deliberates within its capabilities. I
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
I
The deterministic target behavior stands for the agent’s capabilities.
Agents are not “fussy” on when their actions will be done.
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)
Realizing Multiple Autonomous Agents
September 16, 2008
6 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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.
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
7 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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)
Realizing Multiple Autonomous Agents
September 16, 2008
7 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
An Example: The Working Scheduler t1A
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
An Example: The Working Scheduler t1A
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
An Example: The Working Scheduler t1A
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
An Example: The Working Scheduler t1A
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
An Example: The Working Scheduler t1A
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
An Example: The Working Scheduler t1A
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
An Example: The Working Scheduler t1A
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
An Example: The Working Scheduler t1A
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
An Example: The Working Scheduler t1A
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
An Example: The Working Scheduler t1A
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
An Example: The Working Scheduler t1A
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
8 / 14
Introduction
Multi-Target Composition
Realizability
Multiple Composition via LTL Realizability
Conclusions
[Pnueli+Rosner, 1989]
I : input variables O: output variables Game: I
System: chooses from 2I
I
Controller: chooses from 2O
Infinite Play:
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
9 / 14
Introduction
Multi-Target Composition
Realizability
Multiple Composition via LTL Realizability
Conclusions
[Pnueli+Rosner, 1989]
I : input variables O: output variables Game: I
System: chooses from 2I
I
Controller: chooses from 2O
Infinite Play: i0
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
9 / 14
Introduction
Multi-Target Composition
Realizability
Multiple Composition via LTL Realizability
Conclusions
[Pnueli+Rosner, 1989]
I : input variables O: output variables Game: I
System: chooses from 2I
I
Controller: chooses from 2O
Infinite Play: i0 O0
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
9 / 14
Introduction
Multi-Target Composition
Realizability
Multiple Composition via LTL Realizability
Conclusions
[Pnueli+Rosner, 1989]
I : input variables O: output variables Game: I
System: chooses from 2I
I
Controller: chooses from 2O
Infinite Play: i0 , i1 O0
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
9 / 14
Introduction
Multi-Target Composition
Realizability
Multiple Composition via LTL Realizability
Conclusions
[Pnueli+Rosner, 1989]
I : input variables O: output variables Game: I
System: chooses from 2I
I
Controller: chooses from 2O
Infinite Play: i0 , i1 O0 , O1
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
9 / 14
Introduction
Multi-Target Composition
Realizability
Multiple Composition via LTL Realizability
Conclusions
[Pnueli+Rosner, 1989]
I : input variables O: output variables Game: I
System: chooses from 2I
I
Controller: chooses from 2O
Infinite Play: i0 , i1 , i2 , . . . O0 , O1
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
9 / 14
Introduction
Multi-Target Composition
Realizability
Multiple Composition via LTL Realizability
Conclusions
[Pnueli+Rosner, 1989]
I : input variables O: output variables Game: I
System: chooses from 2I
I
Controller: chooses from 2O
Infinite Play: i0 , i1 , i2 , . . . O0 , O1 , O2 , . . .
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
9 / 14
Introduction
Multi-Target Composition
Realizability
Multiple Composition via LTL Realizability
Conclusions
[Pnueli+Rosner, 1989]
I : input variables O: output variables Game: I
System: chooses from 2I
I
Controller: chooses from 2O
Infinite Play: i0 , i1 , i2 , . . . O0 , O1 , O2 , . . . Infinite play: i0 · O0 · i1 · O1 · i2 · O2 . . .
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
9 / 14
Introduction
Multi-Target Composition
Realizability
Multiple Composition via LTL Realizability
Conclusions
[Pnueli+Rosner, 1989]
I : input variables O: output variables Game: I
System: chooses from 2I
I
Controller: chooses from 2O
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
9 / 14
Introduction
Multi-Target Composition
Realizability
Multiple Composition via LTL Realizability
Conclusions
[Pnueli+Rosner, 1989]
I : input variables O: output variables Game: I
System: chooses from 2I
I
Controller: chooses from 2O
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)
Realizing Multiple Autonomous Agents
September 16, 2008
9 / 14
Introduction
Multi-Target Composition
GR(1) Formulas I
Multiple Composition via LTL Realizability
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).
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
10 / 14
Introduction
Multi-Target Composition
GR(1) Formulas I
Multiple Composition via LTL Realizability
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).
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
10 / 14
Introduction
Multi-Target Composition
GR(1) Formulas I
Multiple Composition via LTL Realizability
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).
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 .
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
10 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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.”
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
11 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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 )
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
11 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
11 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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)
Realizing Multiple Autonomous Agents
September 16, 2008
12 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
Discussion 1
Extends basic behavior composition problem [IJCAI’07; AAAI’07; KR’08].
2
Agent coordination can be achieved by having synchronization devices.
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
13 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
Discussion 1
Extends basic behavior composition problem [IJCAI’07; AAAI’07; KR’08].
2
Agent coordination can be achieved by having synchronization devices.
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
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
13 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
Discussion 1
Extends basic behavior composition problem [IJCAI’07; AAAI’07; KR’08].
2
Agent coordination can be achieved by having synchronization devices.
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).
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
13 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
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.
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
14 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
Conclusions 1
Defined the concurrent composition problem. I I I I
2
Synthesis technique: reduction to realizability of GR(1) LTL formulas. I I
3
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.
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/
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
14 / 14
Introduction
Multi-Target Composition
Multiple Composition via LTL Realizability
Conclusions
Conclusions 1
Defined the concurrent composition problem. I I I I
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
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.
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]
Sardina & De Giacomo (ICAPS’08)
Realizing Multiple Autonomous Agents
September 16, 2008
14 / 14
