1October 16th, 2009

Meaning to motion:Transforming specifications to

provably-correct control

Hadas Kress-GazitCornell University

George PappasUniversity of Pennsylvania

2October 16th, 2009

SUBTLE MURI

3October 16th, 2009

Example Mission• Murray starts in room 11.• “Search rooms 1,2,3 and 4. If you see a

dead body, abandon the search and go to room 11. If you see a bomb, pick it up and take it to room 13 and then resume the search.”

4October 16th, 2009

“Search rooms 1,2,3 and 4. If you see a dead body, abandon the search and go to room 11. If you see a bomb, pick it up and take it to room 13 and then resume the search.”

5October 16th, 2009

Known workspaceDynamic environment

Actions

Sensor

inputs

Correct robot

motion and action

high leveltask

Automatic

Correct by construction

robot

6October 16th, 2009

Known workspaceDynamic environment

Actions

Sensor

inputs

Correct robot motion and action

high leveltask

robot

Automaton Automaton

Hybrid ControllerHybrid Controller

Binary Propositions

Binary Propositions

DiscreteAbstraction

LTL formula φ LTL formula φ

7October 16th, 2009

Linear Temporal Logic (LTL)Syntax:

Semantics: Truth is evaluated along infinite computation paths σ ((a,b),a,a,a… (a,b),(a,b),(a,c),(a,c),…)

a,b

a,b

a,c

a,b

ab,c

“next”

“always”

“until”

“eventually”

8October 16th, 20098

Linear Temporal Logic (LTL)• 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…

9October 16th, 20099

Why LTL ?• Formal description of tasks• Many algorithms and tools • Compositional • Suitable for specifications that can be

encoded as finite state machines

• Not context free – Can’t encode “for every person you saw

before, beep exactly once” if there is no upper bound on the number of people.

10October 16th, 2009

“Search rooms 1,2,3 and 4. If you see a dead body, abandon the search and go to room 11. If you see a bomb, pick it up and take it to room 13 and then resume the search.”

...V¤(r1 ! (° r1 _ ° r5))V¤(r2 ! (° r2 _ ° r6))

...V¤§ (sawDead ! r11)V¤§ ((haveBomb^: sawDead) ! r13)

MetaPAR

11October 16th, 2009

Automaton synthesis

• LTL formula converted to an automaton such that every execution is guaranteed to satisfy the formula (achieve the task) – if feasible

12October 16th, 2009

Known workspaceDynamic environment

Actions

Sensor

inputs

Correct robot motion and action

high leveltask

robot

Automaton Automaton

Hybrid ControllerHybrid Controller

Binary Propositions

Binary Propositions

DiscreteAbstraction

LTL formula φ LTL formula φ

13October 16th, 200913

• Map, Regions of interest

Discrete Abstractions

14October 16th, 200914

• Robot abilities, simulated and real

Discrete Abstractions

Search(), Approach(), Track(),Follow()

(Ongoing work with Umass Lowell) (Ongoing work with George Mason, UPenn)

pickUp(), Drop()

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• Locative prepositions

Discrete Abstractions

“If you hear the alarm, stay between A and D”

“Always stay within 5 of B”

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• Locative prepositions

Discrete Abstractions

“Never go through within 2 of between A and D”

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Hybrid ControllerRoom 1

Room 5

Bisimilar low-level controllers: PAR or Feedback Control

Room 1

Room 1, searched

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Guarantee• If the task is feasible, a controller will

be created and the robot’s behavior will be correct, if the environment behaves well.

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Simulation

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Challenge

“If you see a bomb, pick it up and take it to room 13 and then resume the search”

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• Projective locative prepositions – ‘to the right of’, ‘in front’…

• MetaPARs• Integration with UMass Lowell

Year 3…

22October 16th, 200922

Thank you