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Symbolic reactive high level task

Finding Nemo : Translating Reactive Tasks to Reactive Controllers Hadas Kress-Gazit joint 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”.

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Symbolic reactive high level task

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  1. Finding Nemo: Translating Reactive Tasks to Reactive ControllersHadas Kress-Gazitjoint work with Georgios Fainekos and George Pappas

  2. “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”

  3. “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”

  4. “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” Symbolic reactive high level task Automatic Correct Efficient Low level sensor based robot control

  5. Problem Sensor inputs Actions robot ? Known workspace high level task Correct robot motion and action

  6. Related work Sensor inputs Actions What to do? robot Known workspace high level task How? robot motion and action

  7. Related work Sensor inputs Actions What to do? robot Known workspace high level task 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.

  8. Related work 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.) How? robot motion and action

  9. Sensor inputs Actions What to do? robot Known workspace high level task Automatic Correct Efficient How? robot motion and action

  10. Formal methods: Verification, Model checkingand Synthesis A short detour

  11. Correct ? System/Program/Design Synthesis Requirements Verification

  12. Requirements System/Program/Design Verification Correct ? • Simulation and testing • Deductive verification • Model checking

  13. a,b b,c a a,b a,b a,c Model checking Requirements Usually in Temporal Logic Finite state systems Correct ? • 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

  14. 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 b,c a a,b a,b a,c Crash Course in Temporal Logic

  15. 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), pq (and), pq (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 b,c a a,b a,b a,c Crash Course in Temporal Logic

  16. Crash Course in Temporal Logic • 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…

  17. a,b b,c a a,b a,b a,c Model checking • []a • ◊(a  c) • [](c → Oc) Correct ? • True • False: (a,b)(a,b)(a,b)… • True

  18. 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

  19. System/Program/Design Synthesis Requirements • 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.

  20. Back to Robotics

  21. Sensor inputs Actions What to do? robot Known workspace high level task Automatic Correct Efficient How? robot motion and action

  22. Discrete Abstraction 8 7 1 9 6 10 12 2 Binary Propositions 11 3 4 5 Temporal logic formula φ Find a counter example for ¬φ Path Hybrid Controller Approach using Model Checking Sensor inputs Actions robot Known workspace high level task Non reactive Correct robot motion and action

  23. 8 7 1 9 6 10 12 2 11 10 11 12 4 9 5 6 1 8 3 2 7 3 4 5 Approach using Model Checking • 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

  24. Approach using Model Checking • 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 wecan’t do reactive tasks. G. E. Fainekos, H. Kress-Gazit, and G. J. Pappas. Temporal logic motion planning for mobile robots. ICRA , 2005.

  25. G. E. Fainekos, H. Kress-Gazit, and G. J. Pappas. “Temporal logic motion planning for mobile robots”. ICRA, 2005. G. E. Fainekos, H. Kress-Gazit, and G. J. Pappas. “Hybrid Controllers for Path Planning: A Temporal Logic Approach”. CDC, 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. IEEE Robotics & Automation Magazine, March 2007: 61-70 Workshop on “Symbolic Approaches for Robot Motion Planning and Control”, Robotics: Science and Systems, 2006 M. M. Quottrup, T. Bak and R. Izadi-Zamanabadi. “Multi-robot planning : a timed automata approach”. ICRA, 2004. A. Bicchi, A. Marigo and B. Piccoli. “Feedback encoding for efficient symbolic control of dynamical systems”.IEEE Trans. Autom. Control, Jan 2006. Invited session “Symbolic Methods for Control of Mobile Robots”, ICRA, 2007

  26. Discrete Abstraction 8 7 1 9 6 10 12 2 Binary Propositions 11 3 4 5 Temporal logic formula φ Automaton Hybrid Controller Approach using Synthesis Sensor inputs Actions robot Known workspace high level task Reactive ! H. Kress-Gazit, G. E. Fainekos and G. J. Pappas. Where’s Waldo? Sensor Based Temporal logic motion planning. ICRA , 2007. Correct robot motion and action

  27. 8 7 1 9 6 10 12 2 11 3 4 5 “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”

  28. Sensor inputs Discrete Abstraction 8 7 1 Actions 9 6 10 12 2 Binary Propositions 11 3 4 5 robot Known workspace Temporal logic formula φ high level task Automaton Reactive ! Hybrid Controller Correct robot motion and action Approach using Synthesis

  29. 8 7 1 9 6 10 12 2 11 3 4 5 Constructing φ Sensor inputs Discrete Abstraction Actions robot Known workspace Sensor (Input) propositions: X = {SenseNemo, SenseFire, HearBaby,… } = {sNemo} Robot (Output) propositions: Y = {Room1, Room2,…,Room12, Beep, RecordVideo,… } = {r1, r2,…, r12,Beep }

  30. Structured English 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” ??? (MURI SUBTLE) H. Kress-Gazit, G. E. Fainekos and G. J. Pappas. From Structured English to Robot Motion, IROS, San Diego, CA, Oct 2007. To appear.

  31. 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 …

  32. Constructing φ We consider LTL formulas of the form: Assumptions about the environment Desired robot behavior *Note that only if the assumptions are met ( is true), the desired behavior is guaranteed ( must be true).

  33. Initial Conditions Transitions Goals Example 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

  34. 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

  35. Sensor inputs Discrete Abstraction 8 7 1 Actions 9 6 10 12 2 Binary Propositions 11 3 4 5 robot Known workspace Temporal logic formula φ high level task Automaton Hybrid Controller Correct robot motion and action Approach using Synthesis

  36. 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.

  37. 8 7 1 9 6 10 12 2 11 5 3 4 Example 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” Beep r8 sNemo sNemo Beep r5 sNemo r9 r10 r8 r12 r5 r9 sNemo Beep r1 sNemo r10 r1 sNemo r9 r11 r12 Beep r3 r3 r11 sNemo sNemo

  38. Sensor inputs Discrete Abstraction 8 7 1 Actions 9 6 10 12 2 Binary Propositions 11 3 4 5 robot Known workspace Temporal logic formula φ high level task Automaton Hybrid Controller Correct robot motion and action Approach using Synthesis

  39. Hybrid controller • We employ a set of “simple” controllers that drive the robot from one region to an adjacent one, based on itsdynamics. • 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 basedcomposition of these controllers

  40. 8 7 1 9 6 10 12 2 11 5 3 4 Example 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” Beep r8 sNemo Beep r5 sNemo sNemo r9 r10 r8 r12 r5 r9 sNemo Beep r1 sNemo r10 r1 sNemo r11 r9 r12 r3 r11 Beep r3 sNemo sNemo

  41. 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

  42. Extensions • Complex Dynamics 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. *Images courtesy of David C. Conner

  43. 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) )…

  44. 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” 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.

  45. 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

  46. Demo

  47. 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

  48. Thanks You

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