1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control...
-
Upload
marina-poore -
Category
Documents
-
view
215 -
download
1
Transcript of 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control...
![Page 1: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/1.jpg)
1October 16th, 2009
Meaning to motion:Transforming specifications to
provably-correct control
Hadas Kress-GazitCornell University
George PappasUniversity of Pennsylvania
![Page 2: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/2.jpg)
2October 16th, 2009
SUBTLE MURI
![Page 3: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/3.jpg)
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.”
![Page 4: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/4.jpg)
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.”
![Page 5: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/5.jpg)
5October 16th, 2009
Known workspaceDynamic environment
Actions
Sensor
inputs
Correct robot
motion and action
high leveltask
Automatic
Correct by construction
robot
![Page 6: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/6.jpg)
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
![Page 7: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/7.jpg)
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”
![Page 8: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/8.jpg)
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…
![Page 9: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/9.jpg)
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.
![Page 10: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/10.jpg)
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
![Page 11: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/11.jpg)
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
![Page 12: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/12.jpg)
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
![Page 13: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/13.jpg)
13October 16th, 200913
• Map, Regions of interest
Discrete Abstractions
![Page 14: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/14.jpg)
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()
![Page 15: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/15.jpg)
15October 16th, 200915
• Locative prepositions
Discrete Abstractions
“If you hear the alarm, stay between A and D”
“Always stay within 5 of B”
![Page 16: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/16.jpg)
16October 16th, 200916
• Locative prepositions
Discrete Abstractions
“Never go through within 2 of between A and D”
![Page 17: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/17.jpg)
17October 16th, 2009
Hybrid ControllerRoom 1
Room 5
Bisimilar low-level controllers: PAR or Feedback Control
Room 1
Room 1, searched
![Page 18: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/18.jpg)
18October 16th, 2009
Guarantee• If the task is feasible, a controller will
be created and the robot’s behavior will be correct, if the environment behaves well.
![Page 19: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/19.jpg)
19October 16th, 2009
Simulation
![Page 20: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/20.jpg)
20October 16th, 2009
Challenge
“If you see a bomb, pick it up and take it to room 13 and then resume the search”
![Page 21: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/21.jpg)
21October 16th, 200921
• Projective locative prepositions – ‘to the right of’, ‘in front’…
• MetaPARs• Integration with UMass Lowell
Year 3…
![Page 22: 1 October 16 th, 2009 Meaning to motion: Transforming specifications to provably-correct control Hadas Kress-Gazit Cornell University George Pappas University.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551c54cc550346b1458b4f02/html5/thumbnails/22.jpg)
22October 16th, 200922
Thank you