Symbolic reactive high level task

Finding Nemo: Translating Reactive Tasks to Reactive

Controllers

Hadas Kress-Gazitjoint work with Georgios Fainekos and George

Pappas

“Look for Nemo. If he is in a red zone, sound the alarm and go to the office. If he is in

another zone, take him to one of the parking lots”







Symbolicreactive

high level task

Low levelsensor based robot control

Automatic

Correct Efficient

“Look for Nemo. If he is in a red zone, sound

the alarm and go to the office. If he is in

another zone, take him to one of the parking

lots”

“Look for Nemo. If he is in a red zone, sound

the alarm and go to the office. If he is in

another zone, take him to one of the parking

lots”

Problem

Known workspacerobot

Actions

Sensor inputs

Correct robot motion and action

high leveltask ?

Related work


Actions

Sensor inputs

high leveltask

Whatto do?

robot motion and action

How?

Related work


Actions

Sensor inputs

high leveltask

Whatto do?

Planning and AI• S. Russell and P. Norvig. Artificial Intelligence, A Modern Approach.

Prentice Hall, second edition, 2003.• P. Bertoli, A. Cimatti, M. Pistore, M. Roveri and P. Traverso. MBP : A

model based planner. In In Proc. IJCAI’01 Workshop on Planning under Uncertainty and Incomplete Information, 2001.

• S. M. LaValle. Planning Algorithms. Cambridge University Press, Cambridge, U.K., 2006.

Related work


How?

Motion Planning

• R. R. Burridge, A. A. Rizzi, and D. E. Koditschek, “Sequential composition of dynamically dexterous robot behaviors,” International Journal of Robotics Research, vol. 18, no. 6, pp. 534–555, 1999.

• S. M. LaValle. Planning Algorithms. Cambridge University Press, Cambridge, U.K., 2006. (Sampling based, etc.)


Actions

Sensor inputs

high leveltask

Whatto do?


How?

Automatic

Correct Efficient

Formal methods: Verification, Model

checkingand Synthesis

A short detour

System/Program/DesignSystem/Program/Design

RequirementsRequirements

Synthesis

VerificationCorrect ?Correct ?

System/Program/DesignSystem/Program/Design

RequirementsRequirements

VerificationCorrect ?Correct ?

• Simulation and testing• Deductive verification• Model checking

Finite state systemsFinite state systems

RequirementsUsually in

Temporal Logic

RequirementsUsually in

Temporal Logic

Correct ?Correct ?

Model checking

a,b

a,b

a,c

a,b

ab,c

•Exhaustive search of the state space •Algorithm is guaranteed to terminate with the correct answer.•If there is a bug, (sometimes) a counter-example is given

Crash Course in Temporal Logic

• Propositional logic:– if a = b = c = True in our world, then f = True

if a = b = True but c = False in our world, then f = False

• What if the “world” is not static?– We can discuss the truth of statements of the form:

• a is always True• c is eventually True• b and c are never True together• If c is True, then c stays True forever• It is possible that c will become True• b is True in the next state

a,b

a,b

a,c

a,b

ab,c

cbaf


Linear Temporal Logic (LTL)– Truth is evaluated along infinite computation paths

• (a,b),a,a,a…• (a,b),(a,b),(a,c),(a,c),…• (a,b),a,a,a,(a,b),(a,b),(a,c),(a,c),…

– Formulas: • Atomic propositions (a,b,c…)• Boolean combinations

¬p (not), pq (and), pq (or) • Temporal operators

Op (next), qUp (until), ◊p (eventually), []p (always)

– Examples:• []a = “a is always true”• ◊(a c) = “(a and c) is eventually true”• Ob = “b is true in the next state”

a,b

a,b

a,c

a,b

ab,c


• Robotic Task examples:• “Visit rooms 1,2,3 while avoiding corridor 1”:

[] ¬(corridor1) ◊(room1) ◊(room2) ◊(room3)

• “ If the light is on, visit rooms 1 and 2 infinitely often”:[]( (LightOn) -> ([]◊(room 1) []◊(room 2)) )

• “If you are in room 3 and Mika is there, beep”[]( (room3) (SeeMika) -> (Beep) )

• And much more…

Model checking

•[]a•◊(a c)•[](c → Oc)

•[]a•◊(a c)•[](c → Oc)

Correct ?Correct ?

a,b

a,b

a,c

a,b

ab,c

•True •False: (a,b)(a,b)(a,b)…•True

Model checking

•Great book: Model Checking. Clarke, E.M., Grumberg, O., and Peled, D. MIT Press, 2000.

•Many tools (SPIN, NuSMV, UPPAAL…)

•Extensively used in the hardware design world

System/Program/DesignSystem/Program/DesignRequirementsRequirements

Synthesis

•Given a formula, create the system

•Synthesis of the full LTL is double exponential in the size of the formula

•For a specific fragment, it is polynomial in the state space.

Back to Robotics


Actions

Sensor inputs

high leveltask

Whatto do?


How?

Automatic

Correct Efficient

PathPath

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5

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11


Actions

Sensor inputs

Hybrid ControllerHybrid Controller


high leveltask

Binary Propositions

Binary Propositions

DiscreteAbstraction

Temporal logic formula φ Temporal logic formula φ

Approach using Model Checking

Non reactive

Find a counter

example for ¬φ

• Example

“Go to room 4” φ = ◊(room4)

Model check the formula ¬◊(room4)

The formula is False and the counter example is:room1, room9, room12, room11, room4


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3 4

8 7

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5

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11

1

2

3

87

6

5

910

4

1112


• Advantages– Fast – example with 9250 regions took

55 seconds– Many tools

• NuSMV• SPIN

• Disadvantages– Paths are not optimal– Result is a path – not a plan, so we can’t

do reactive tasks. G. E. Fainekos, H. Kress-Gazit, and G. J. Pappas. Temporal logic

motion planning for mobile robots. ICRA , 2005.

IEEE Robotics & Automation Magazine, March 2007: 61-70

Workshop on “Symbolic Approaches for Robot Motion Planning and Control”, Robotics: Science and Systems, 2006

Workshop on “Symbolic Approaches for Robot Motion Planning and Control”, Robotics: Science and Systems, 2006

Invited session “Symbolic Methods for Control of Mobile Robots ”, ICRA, 2007

Invited session “Symbolic Methods for Control of Mobile Robots ”, ICRA, 2007

G. E. Fainekos, H. Kress-Gazit, and G. J. Pappas. “Temporal logic motion planning for mobile robots”. ICRA, 2005.

M. Kloetzer and C. Belta. “A fully automated framework for control of linear systems from ltl specifications”. HSCC, 2006.

J. McNew and E. Klavins. “Locally interacting hybrid systems with embedded graph grammars”. CDC, 2006.

A. Bicchi, A. Marigo and B. Piccoli. “Feedback encoding for efficient symbolic control of dynamical systems ”.IEEE Trans. Autom. Control, Jan 2006.

M. M. Quottrup, T. Bak and R. Izadi-Zamanabadi. “Multi-robot planning : a timed automata approach”. ICRA, 2004.

G. E. Fainekos, H. Kress-Gazit, and G. J. Pappas. “Hybrid Controllers for Path Planning: A Temporal Logic Approach”. CDC, 2005.

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Actions

Sensor inputs

Automaton Automaton



high leveltask

Binary Propositions

Binary Propositions

DiscreteAbstraction


Approach using Synthesis

Reactive !

H. Kress-Gazit, G. E. Fainekos and G. J. Pappas. Where’s Waldo? Sensor Based Temporal logic motion planning. ICRA , 2007.

“Nemo may be sitting in one of rooms 1, 3, 5 and 8. Starting in corridor 12, look for him in

these rooms. If at some point you see him, stop and beep”

“Nemo may be sitting in one of rooms 1, 3, 5 and 8. Starting in corridor 12, look for him in

these rooms. If at some point you see him, stop and beep”

1

2

3 4

8 7

6

5

12 10

9

11

Binary Propositions

Binary Propositions

DiscreteAbstraction


1

2

3 4

8 7

6

5

12 109

11


Actions

Sensor inputs

Automaton Automaton



high leveltask

Reactive !


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5

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Constructing φ

robot

Actions

Sensor inputs Discrete

Abstraction

Sensor (Input) propositions: X = {SenseNemo, SenseFire, HearBaby,… } = {sNemo}

Robot (Output) propositions:Y = {Room1, Room2,…,Room12, Beep, RecordVideo,… } = {r1, r2,…, r12,Beep }

Known workspace

Constructing φ

“Nemo may be in one of rooms 1, 3, 5 and 8. Starting in corridor 12, look for him in these rooms.

If at some point you see him, stop and beep”



Structured English

(MURISUBTLE

)

???

H. Kress-Gazit, G. E. Fainekos and G. J. Pappas. From Structured English to Robot Motion, IROS, San Diego, CA, Oct 2007. To appear.

Structured English Interface“Nemo may be in one of rooms 1, 3, 5 and 8.

Starting in corridor 12, look for him in these rooms. If at some point you see him, stop and beep”



Environment starts with not Nemo…

You start in r12

If you are sensing Nemo then stay there

Beep if and only if you are sensing Nemo

If you are not sensing Nemo then go to r1…

Constructing φ

We consider LTL formulas of the form:

Assumptions aboutthe

environment

Desired robot

behavior

se

*Note that only if the assumptions are met ( is

true), the desired behavior is guaranteed ( must

be true).

es

Nemo

Nemo

Nemo

911

12

NemoNemo

NemoNemo

Nemo

[]

[]

)[](

)[](

)([]

[]

)[](

}8,5,3,1{

}8,5,3,1{

12

}8,5,3,1{

sr

rsr

Beeps

rrr

Beeprr

True

ssr

ss

s

ii

iii

ii

ii

Initial Conditions

Transitions

Goals

ExampleTask: “Nemo may be sitting in one of rooms 1, 3, 5 and 8. Starting in corridor 12, look for him in these rooms. If at some point you see him, stop and beep”

Sensor (Input) propositions: X = {sNemo}Robot (Output) propositions: Y = {r1, r2,…, r12,Beep}

Task: “Nemo may be sitting in one of rooms 1, 3, 5 and 8. Starting in corridor 12, look for him in these rooms. If at some point you see him, stop and beep”

Sensor (Input) propositions: X = {sNemo}Robot (Output) propositions: Y = {r1, r2,…, r12,Beep}

Environment Assumptions Desired behavior

Why this structure?

• Can be efficiently synthesized into an automaton

• No significant loss of expressivity with respect to the full LTL

• Clear distinction between assumptions and desired behavior

Automaton Automaton

robot

high leveltask

1

2

3 4

8 7

6

5

12 109

11Actions

Sensor inputs



Binary Propositions

Binary Propositions

DiscreteAbstraction


Known workspace


Automaton synthesis• Synthesis algorithm due to Piterman,

Pnueli and Sa’ar (VMCAI 2006)

• Polynomial (n3) in the number of states (as opposed to double exponential in the length of the formula)

• Basically, solves a game between the environment and the robot. If the robot wins, an automaton is extracted.



r12r9

r8r9r10

r5

r10

r11

r3 r11r12

r9

Beep

r1r1sNemo

sNemo

sNemosNemo

sNemo

sNemo

s Nemo

sNemo

3 4

8 7

6

5

12 109

11

1

2

Beep

r8

Beep

r3

Beep

r5


Automaton Automaton


robot

high leveltask

1

2

3 4

8 7

6

5

12 109

11Actions

Sensor inputs

Binary Propositions

Binary Propositions

DiscreteAbstraction


Known workspace


Hybrid controller• We employ a set of “simple” controllers that

drive the robot from one region to an adjacent one, based on its dynamics.– Belta et. al. (CDC 2004) – Conner et. al. (IROS 2003, RSS 2006,IROS

2007)

– Lindemann et. al. (RSS 2006, ICRA 2007)

• The automaton governs the sensor based composition of these controllers



3 4

8 7

6

5

12 10

9

11

1

2

r12r9

r8

Beep r5

Beepr8

r9r10r5

r10

r11

Beep r3

r3 r11r12

r9

Beepr1 r1

sNemo

sNemo

sNemosNemo

sNemo

sNemo

sNemo sNemo

When will this break?• Logical inconsistency – “go to room 1 and always

stay in room 4”• Topologically impossible – “go to room 5 and always

avoid room 10”

→ No automaton is synthesized

• Environment behaves badly – – Sensors inputs contradict assumptions ( is

false)– “Violent” environment

→ Execution may be incorrect or terminated prematurely

e

D. C. Conner, H. Kress-Gazit, H. Choset, A. Rizzi and G. J. Pappas. Valet parking without a valet, IROS, San Diego, CA, Oct 2007. To appear.

Extensions• Complex Dynamics

*Images courtesy of David C. Conner

Extensions• Multi Robot

– Naturally captured in a decentralized way– The environment of each robot contains

all other robots

– “ If robot 2 is in the kitchen, do not go there” X = {Robot2Kitchen,… }, Y = {Kitchen, Hall, Bedroom,… }

… []( Robot2Kitchen → ¬O(Kitchen) ) …

H. Kress-Gazit, D. C. Conner, H. Choset, A. Rizzi and G. J. Pappas. Courteous cars: Decentralized multi-agent traffic coordination, Special Issue of the IEEE Robotics and Automation Magazine on Multi-Agent Robotics. To appear.

Extensions• Multi Robot

“Drive around the environment, while obeying traffic rules, until you find a free parking space, and then park”

“Leave the block, while obeying traffic rules, through Exiti”

Summery

Method for transforming high level reactive tasks into low level robot control

• Advantages– Sensor based– Automatic– Efficient– Correct by construction– Interface between discrete planning and

continuous control

Demo

What’s next?

• Natural language interface• Feedback\Dialog with the user • Unknown workspace (SLAM ?)• Verify sensor models obey

assumptions• Incorporate cost• On the fly extraction of automata• Experiments

Thanks You

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Symbolic reactive high level task

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