Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi...

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Synthesis via Sampling-Based Abstractions Some Problems and Initial Ideas Matthias Rungger 2 Morteza Lahijanian 1 Lydia E. Kavraki 1 Paulo Tabuada 2 Moshe Y. Vardi 1 1 Department of Computer Science, Rice University 2 Cyber-Physical Systems Laboratory, UCLA

Transcript of Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi...

Page 1: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Synthesis via Sampling-Based AbstractionsSome Problems and Initial Ideas

Matthias Rungger2 Morteza Lahijanian1

Lydia E. Kavraki1 Paulo Tabuada2 Moshe Y. Vardi1

1Department of Computer Science, Rice University

2Cyber-Physical Systems Laboratory, UCLA

Page 2: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Problem statementGiven a LTL specification ϕ and a control system S , find acontroller C that enforces ϕ on S

Well-known abstraction/refinement approach

1. Compute a finite abstraction S of S

2. Synthesize controller C based on S

3. Refine solution C to C

S

finite

C

S

infinite

C

1.

2.

3.abstract

concrete

=⇒ All done X

So... what is the problem?

2/6

Page 3: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Problem statementGiven a LTL specification ϕ and a control system S , find acontroller C that enforces ϕ on S

Well-known abstraction/refinement approach

1. Compute a finite abstraction S of S

2. Synthesize controller C based on S

3. Refine solution C to C

S

finite

C

S

infinite

C

1.

2.

3.abstract

concrete

=⇒ All done X

So... what is the problem?

2/6

Page 4: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Problem statementGiven a LTL specification ϕ and a control system S , find acontroller C that enforces ϕ on S

Well-known abstraction/refinement approach

1. Compute a finite abstraction S of S

2. Synthesize controller C based on S

3. Refine solution C to C

S

finite

C

S

infinite

C

1.

2.

3.abstract

concrete

=⇒ All done X

So... what is the problem?

2/6

Page 5: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Problem statementGiven a LTL specification ϕ and a control system S , find acontroller C that enforces ϕ on S

Well-known abstraction/refinement approach

1. Compute a finite abstraction S of S

2. Synthesize controller C based on S

3. Refine solution C to C

S

finite

C

S

infinite

C

1.

2.

3.abstract

concrete

=⇒ All done X

So... what is the problem?

2/6

Page 6: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Computing Abstractions

1D: Temperature

T = c(Tenv − T )

2D: Pendulum

.

.

3D: UnicycleRobot

ϕ

x

y

4D: Pendulumon a cart

X

|X | = 100 X |X | = 1002 X |X | = 1003 ?? |X | = 1004

3/6

Page 7: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Computing Abstractions

1D: Temperature

T = c(Tenv − T )

2D: Pendulum

.

.

3D: UnicycleRobot

ϕ

x

y

4D: Pendulumon a cart

X

|X | = 100 X |X | = 1002 X |X | = 1003 ?? |X | = 1004

3/6

Page 8: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Computing Abstractions

1D: Temperature

T = c(Tenv − T )

2D: Pendulum

.

.

3D: UnicycleRobot

ϕ

x

y

4D: Pendulumon a cart

X

|X | = 100 X

|X | = 1002 X |X | = 1003 ?? |X | = 1004

3/6

Page 9: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Computing Abstractions

1D: Temperature

T = c(Tenv − T )

2D: Pendulum

.

.

3D: UnicycleRobot

ϕ

x

y

4D: Pendulumon a cart

X

|X | = 100 X

|X | = 1002 X |X | = 1003 ?? |X | = 1004

3/6

Page 10: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Computing Abstractions

1D: Temperature

T = c(Tenv − T )

2D: Pendulum

.

.

3D: UnicycleRobot

ϕ

x

y

4D: Pendulumon a cart

X

|X | = 100 X

|X | = 1002 X |X | = 1003 ?? |X | = 1004

3/6

Page 11: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Computing Abstractions

1D: Temperature

T = c(Tenv − T )

2D: Pendulum

.

.

3D: UnicycleRobot

ϕ

x

y

4D: Pendulumon a cart

X

|X | = 100 X |X | = 1002 X

|X | = 1003 ?? |X | = 1004

3/6

Page 12: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Computing Abstractions

1D: Temperature

T = c(Tenv − T )

2D: Pendulum

.

.

3D: UnicycleRobot

ϕ

x

y

4D: Pendulumon a cart

X

|X | = 100 X |X | = 1002 X

|X | = 1003 ?? |X | = 1004

3/6

Page 13: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Computing Abstractions

1D: Temperature

T = c(Tenv − T )

2D: Pendulum

.

.

3D: UnicycleRobot

ϕ

x

y

4D: Pendulumon a cart

X

|X | = 100 X |X | = 1002 X

|X | = 1003 ?? |X | = 1004

3/6

Page 14: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Computing Abstractions

1D: Temperature

T = c(Tenv − T )

2D: Pendulum

.

.

3D: UnicycleRobot

ϕ

x

y

4D: Pendulumon a cart

X

|X | = 100 X |X | = 1002 X |X | = 1003 ??

|X | = 1004

3/6

Page 15: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Computing Abstractions

1D: Temperature

T = c(Tenv − T )

2D: Pendulum

.

.

3D: UnicycleRobot

ϕ

x

y

4D: Pendulumon a cart

X

|X | = 100 X |X | = 1002 X |X | = 1003 ??

|X | = 1004

3/6

Page 16: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Computing Abstractions

1D: Temperature

T = c(Tenv − T )

2D: Pendulum

.

.

3D: UnicycleRobot

ϕ

x

y

4D: Pendulumon a cart

X

|X | = 100 X |X | = 1002 X |X | = 1003 ?? |X | = 1004

3/6

Page 17: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Sampling-based Ideas to Compute Abstractions

Synergistic approach for syntacticallyco-safe LTL

Lower layer:use sampling-based methods to growthe abstraction

Higher layer:use Buchi automaton (from ϕ) andenvironment geometry to guide theexpansion

Use “synergistic” layer to alternatebetween layers

http://msl.cs.uiuc.edu/~lavalle/

A. Bhatia, L. E. Kavraki, and M. Y. Vardi. “Sampling-based motion planning withtemporal goals”. In: ICRA. IEEE, 2010

M. R. Maly, M. Lahijanian, L. E. Kavraki, H. Kress-Gazit, and M. Y. Vardi.

“Iterative Temporal Motion Planning for Hybrid Systems in Partially Unknown

Environments”. In: HSCC. ACM, 2013

Solution (point-to-point)

xinit xend

curse of dimensionality is no problem

4/6

Page 18: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Sampling-based Ideas to Compute Abstractions

Synergistic approach for syntacticallyco-safe LTL

Lower layer:use sampling-based methods to growthe abstraction

Higher layer:use Buchi automaton (from ϕ) andenvironment geometry to guide theexpansion

Use “synergistic” layer to alternatebetween layers

http://msl.cs.uiuc.edu/~lavalle/

Solution (point-to-point)

xinit xend

curse of dimensionality is no problem 4/6

Page 19: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

Sampling-based Ideas to Compute Abstractions

Synergistic approach for syntacticallyco-safe LTL

Lower layer:use sampling-based methods to growthe abstraction

Higher layer:use Buchi automaton (from ϕ) andenvironment geometry to guide theexpansion

Use “synergistic” layer to alternatebetween layers

http://msl.cs.uiuc.edu/~lavalle/

Solution (point-to-point)

xinit xend

curse of dimensionality is no problem

Problem solved?

4/6

Page 20: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

What if we have...

a set of initial states?

Xinit

Solve problem for somesamples of Xinit

Can we use local controllersto enlarge/robustifysolutions?

safety specifications? (infinite behavior)

Xsafe

Xinit

What are good heuristics togrow the abstraction?

How to find loops?

Can we merge close-bysamples?

5/6

Page 21: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

What if we have...

a set of initial states?

Xinit

Solve problem for somesamples of Xinit

Can we use local controllersto enlarge/robustifysolutions?

safety specifications? (infinite behavior)

Xsafe

Xinit

What are good heuristics togrow the abstraction?

How to find loops?

Can we merge close-bysamples?

5/6

Page 22: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

What if we have...

a set of initial states?

Xinit

Solve problem for somesamples of Xinit

Can we use local controllersto enlarge/robustifysolutions?

safety specifications? (infinite behavior)

Xsafe

Xinit

What are good heuristics togrow the abstraction?

How to find loops?

Can we merge close-bysamples?

5/6

Page 23: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

What if we have...

a set of initial states?

Xinit

Solve problem for somesamples of Xinit

Can we use local controllersto enlarge/robustifysolutions?

safety specifications? (infinite behavior)

Xsafe

Xinit

What are good heuristics togrow the abstraction?

How to find loops?

Can we merge close-bysamples?

5/6

Page 24: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

What if we have...

a set of initial states?

Xinit

Solve problem for somesamples of Xinit

Can we use local controllersto enlarge/robustifysolutions?

safety specifications? (infinite behavior)

Xsafe

Xinit

What are good heuristics togrow the abstraction?

How to find loops?

Can we merge close-bysamples?

5/6

Page 25: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

What if we have...

a set of initial states?

Xinit

Solve problem for somesamples of Xinit

Can we use local controllersto enlarge/robustifysolutions?

safety specifications? (infinite behavior)

Xsafe

Xinit

What are good heuristics togrow the abstraction?

How to find loops?

Can we merge close-bysamples?

5/6

Page 26: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

What if we have...

a set of initial states?

Xinit

Solve problem for somesamples of Xinit

Can we use local controllersto enlarge/robustifysolutions?

safety specifications? (infinite behavior)

Xsafe

Xinit

What are good heuristics togrow the abstraction?

How to find loops?

Can we merge close-bysamples?

5/6

Page 27: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

To answer those questions we combine

Sampling-based planning (Rice)

MortezaLahijanian

LydiaKavraki

Control theory (UCLA)

MatthiasRungger

PauloTabuada

Reactive synthesis (Rice)

MosheVardi

6/6

Page 28: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

To answer those questions we combine

Sampling-based planning (Rice)

MortezaLahijanian

LydiaKavraki

Control theory (UCLA)

MatthiasRungger

PauloTabuada

Reactive synthesis (Rice)

MosheVardi

6/6

Page 29: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

To answer those questions we combine

Sampling-based planning (Rice)

MortezaLahijanian

LydiaKavraki

Control theory (UCLA)

MatthiasRungger

PauloTabuada

Are we satisfied?

Reactive synthesis (Rice)

MosheVardi

6/6

Page 30: Synthesis via Sampling-Based Abstractions€¦ · Tabuada Reactive synthesis (Rice) Moshe Vardi 6/6. Title: Synthesis via Sampling-Based Abstractions - Some Problems and Initial Ideas

To answer those questions we combine

Sampling-based planning (Rice)

MortezaLahijanian

LydiaKavraki

Control theory (UCLA)

MatthiasRungger

PauloTabuada

Reactive synthesis (Rice)

MosheVardi

6/6