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Coping with Time & Continuous Quantities

Coping with Time & Continuous Quantities. David E. Smith desmith@arc.nasa.gov. Collaborators: Jeremy Frank, Ari Jónsson. The Ambitious Spacecraft. Observation-1 priority time window target instruments duration Observation-2 Observation-3 Observation-4 …. Objective:

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Coping with Time & Continuous Quantities

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  1. Coping with Time & Continuous Quantities David E. Smith desmith@arc.nasa.gov • Collaborators: • Jeremy Frank, Ari Jónsson

  2. The Ambitious Spacecraft Observation-1 priority time window target instruments duration Observation-2 Observation-3 Observation-4 … Objective: maximize science return

  3. Complications Observation-1 priority time window target instruments duration Observation-2 Observation-3 Observation-4 … angle between targets  turn duration linked calibration target1 target2 … consumables: fuel power data storage cryogen Objective: maximize science return

  4. The Spacecraft’s Choices Observations Instrument Calibration target Ordering Communication Instrument Status

  5. The Spacecraft’s Choices Observations Instrument Calibration target Ordering Communication Instrument status continuous time time constraints concurrent actions metric resources optimization

  6. The Choice Spectrum planning job-shop scheduling

  7. The Choice Spectrum planning job-shop scheduling R3 R7 R1 • Job1 • task1 < task2 < task3 < … • Job2 • Job3 • … Ordering choices only

  8. planning job-shop scheduling The Choice Spectrum cascading levels of choice … … … … … … …

  9. The Choice Spectrum resource choices (RCSP) planning job-shop scheduling 5 11 umfagoggin clavitracle fernambulator [8,17] Task4 Task7 Task2 Task5 Task1 Task8 Ordering choices Resource choices Task3 Task6

  10. resource choices (RCSP) alternative processes planning job-shop scheduling process3 process7 Task4 Task7 Task2 Task5 Task1 Task8 Task3 Task6 The Choice Spectrum process8 Ordering choices Resource choices Process choices

  11. The Choice Spectrum ambitious spacecraft alternative processes planning job-shop scheduling resource choices (RCSP) Observation choices Instrument choices Calibration target choices Ordering choices Communication choices Instrument status choices

  12. The Choice Spectrum alternative processes planning job-shop scheduling resource choices (RCSP) • Subset Selection • ambitious spacecraft • observation scheduling • process planning

  13. Strips Assumptions Instantaneous actions No time constraints No concurrent actions No continuous quantities Bleak?

  14. Some STRIPS Operators • TakeImage (?target, ?instr): • Pre: Status(?instr, Calibrated), Pointing(?target) • Eff: Image(?target) • Calibrate (?instrument): • Pre: Status(?instr, On), Calibration-Target(?target), Pointing(?target) • Eff: ¬Status(?inst, On), Status(?instr, Calibrated) • Turn (?target): • Pre: Pointing(?direction), ?direction ≠ ?target • Eff: ¬Pointing(?direction), Pointing(?target) no time, no resources

  15. Outline Resources Reusable Consumable Time Uncertainty?

  16. Resources Discrete Continuous single/multiple(metric) Reusable instruments bandwidth Consumable solid rockets fuel

  17. Reusable Resources(single-capacity) TakeImage (?target, ?instr): Res: ?instr Pre: Status(?instr, Calibrated), Pointing(?target) Eff: Image(?target) Prevent concurrent actions • Mutual exclusion between actions: • Graphplan trivial • Satplan ¬A1 ¬A2 • POCL A1<A2 A2<A1

  18. Reusable Resources(multiple-capacity) • Suppose: 2 cameras • Simple approach: name the cameras TakeImage (?target, ?instr): Res: ?instr Pre: Status(?instr, Calibrated), Pointing(?target) Eff: Image(?target) • Mutual exclusion between actions: • Graphplan trivial • Satplan ¬A1 ¬A2 • POCL ?instr1≠?instr2 A1<A2 A2<A1

  19. Reusable Resources(multiple-capacity) • 2 Cameras: • Not named TakeImage (?target): Res: Camera(1) Pre: Pointing(?target) Eff: Image(?target) Capacity(Camera)=2 Explicit checking of concurrent actions to ensure:  usage ≤ capacity

  20. Reusable Resources(multiple-capacity)  usage > capacity • Mutual exclusion between sets of actions: • Graphplan n-ary mutex • Satplan ¬(A1 A2 A3 …) • POCL A1<A2 A2<A1 A1<A3 A3<A1 … • Profiling heuristics • Sadeh, Fox, Beck • O-Plan • Graph Techniques • IxTeT

  21. Summary Resources Reusable Single-capacity  binary mutex easy Multiple-capacity  n-ary mutex tricky specialized algorithms search heuristics Consumable Time Uncertainty?

  22. Consumable Resources • Turn (?target): • Pre: Pointing(?direction), ?direction ≠ ?target • Fuel ≥ Angle(?direction,?target) *ConsumptionRate • Eff: ¬Pointing(?direction), Pointing(?target) • Fuel –= Angle(?direction,?target) *ConsumptionRate • Simple approach: • wait until all variables are instantiated

  23. LP Approaches • Zeno: • open conditions: P1, P2, P3, P4, P5, E1, E2, E3 • constraints: Fuel ≤ 10 Simplex

  24. LP Approaches: LPSAT • Turn (?target): • Pre: Pointing(?direction), ?direction ≠ ?target • Fuel ≥ Angle(?direction,?target) *ConsumptionRate • Eff: ¬Pointing(?direction), Pointing(?target) • Fuel –= Angle(?direction,?target) *ConsumptionRate • ¬Turn-T3-T71 v • {Pointing-T31C11 •  ¬Pointing-T32 Pointing-T72C22} • C11Fuel1 ≥ Angle(T3,T7) *ConsumptionRate • C22Fuel2 = Fuel1 – Angle(T3,T7) *ConsumptionRate SAT engine Simplex

  25. ILP planning • ¬Turn-T3-T71 v • {Pointing-T31C11 •  ¬Pointing-T32 Pointing-T72C22} • C11Fuel1 ≥ Angle(T3,T7) *ConsumptionRate • C22Fuel2 = Fuel1 – Angle(T3,T7) *ConsumptionRate Kautz & Walser Vossen et al. • ¬Turn-T3-T71 v Pointing-T31 • ¬Turn-T3-T71 v C11 • ¬Turn-T3-T71 v ¬ Pointing-T32 • ¬Turn-T3-T71 v Pointing-T72 • ¬Turn-T3-T71 v C22 • C11Fuel1 ≥ Angle(T3,T7) *ConsumptionRate • C22Fuel2 = Fuel1 – Angle(T3,T7) *ConsumptionRate

  26. ILP planning ¬Turn-T3-T71 v Pointing-T31 ¬Turn-T3-T71 v C11 ¬Turn-T3-T71 v ¬ Pointing-T32 ¬Turn-T3-T71 v Pointing-T72 ¬Turn-T3-T71 v C22 C11Fuel1 ≥ Angle(T3,T7) *ConsumptionRate C22Fuel2 = Fuel1 – Angle(T3,T7) *ConsumptionRate (1 - Turn-T3-T71) + Pointing-T31 ≥ 1 M(1 - Turn-T3-T71) + (1 + D11 ) ≥ 1 (1 - Turn-T3-T71) + (1 - Pointing-T32 ) ≥ 1 (1 - Turn-T3-T71) + Pointing-T72 ≥ 1 M(1 - Turn-T3-T71) + (1 ± D21 ) ≥ 1 D11=Fuel1 – Angle(T3,T7) *ConsumptionRate D22=Fuel2 – (Fuel1 – Angle(T3,T7) *ConsumptionRate)

  27. Summary Resources Reusable Consumable Equality and Inequality conditions POCL + LP slow SAT + LP fast ILP medium Graphplan ? Concurrent continuous change ugly! Time Uncertainty?

  28. Concurrent Continuous Change • Turn (?target): • Pre: Pointing(?direction), ?direction ≠ ?target • Fuel ≥ Angle(?direction,?target) *ConsumptionRate • Eff: ¬Pointing(?direction), Pointing(?target) • Fuel –= Angle(?direction,?target) *ConsumptionRate Fuel Fuel = F(t) Time Fuel Fuel Time Time

  29. Outline Resources Time Uncertainty?

  30. Pointing(Earth) Status(Cam2, Calibrated) ¬ Image(A7) Pointing(A7) Status(Cam2, Calibrated) ¬ Image(A7) Turn(A7) World Description • State-centric: • for each time describe propositions that are true • Proposition-centric: • for each proposion describe times it is true Turn(A7) Pointing(Earth) Pointing(A7) Status(Cam2, Calibrated)

  31. B A A before B B A A meets B A A overlaps B B A contains B A A = B B A starts B A B A A A ends B B B Allen’s Ordering Relationships

  32. TakeImage Schema • TakeImage (?target, ?instr): • Pre: Status(?instr, Calibrated), Pointing(?target) • Eff: Image(?target) TakeImage(?target, ?instr)A $P {Status(?instr, Calibrated)P Contains(P, A)} $Q {Pointing(?target)Q Contains(Q, A)} $R {Image(?target)R  Meets(A, R)}

  33. Pointing(?target) contains meets Image(?target) TakeImage(?target, ?instr) contains Status(?instr, Calibrated) Shorthand TakeImage (?target, ?instr) contained-by Status(?instr, Calibrated) contained-by Pointing(?target) meets Image(?target)

  34. meets meets Pointing(?target) Turn(?target) Pointing(?direction) Turn Turn (?target) met-by Pointing(?direction) meets Pointing(?target)

  35. Pointing(?target) contains meets meets Status(?instr, Calibrated) Calibrate(?instr) Status(?instr, On) contains CalibrationTarget(?target) Calibrate Calibrate (?instr) met-by Status(?instr, On) contained-by CalibrationTarget(?target) contained-by Pointing(?target) meets Status(?instr, Calibrated)

  36. Algorithm • Choose: • introduce an action & instantiate constraints • coalesce propositions • Propagate constraints

  37. Pointing(Earth) Status(Cam1, Off) Status(Cam2, On) CalibrationTarget(T17) Initial Plan meets Past Image(?target) Future meets -∞ ∞

  38. Pointing(Earth) Status(Cam1, Off) Past meets Status(Cam2, On) -∞ CalibrationTarget(T17) Expansion 1 before Pointing(A7) contains meets meets Image(A7) Future TakeImage(A7, ?instr) ∞ contains Status(?instr, Calibrated)

  39. Pointing(Earth) Status(Cam1, Off) Status(Cam2, On) CalibrationTarget(T17) Expansion 2 meets meets Pointing(A7) Turn(A7) Pointing(?direction) contains before meets Image(A7) TakeImage(A7, ?instr) Pointing(?caltarget) contains contains meets meets Status(?instr, Calibrated) Calibrate(?instr) Status(?instr, On) contains CalibrationTarget(?caltarget)

  40. meets meets Pointing(A7) Turn(A7) Pointing(?direction) contains Pointing(Earth) before before meets Image(A7) TakeImage(A7, Cam2) Pointing(T17) Status(Cam1, Off) contains contains meets meets Status(Cam2, Calibrated) Calibrate(Cam2) Status(Cam2, On) contains CalibrationTarget(T17) Coalescing

  41. Coalescing meets Pointing(A7) Turn(A7) contains Pointing(Earth) meets before meets Image(A7) TakeImage(A7, Cam2) Pointing(T17) Status(Cam1, Off) contains contains meets meets Status(Cam2, Calibrated) Calibrate(Cam2) Status(Cam2, On) contains CalibrationTarget(T17)

  42. Expansion 3 meets Pointing(?direction) Pointing(A7) Turn(A7) Pointing(Earth) meets contains meets meets meets Image(A7) Turn(T17) TakeImage(A7, Cam2) Pointing(T17) Status(Cam1, Off) contains contains meets meets Status(Cam2, Calibrated) Calibrate(Cam2) Status(Cam2, On) contains CalibrationTarget(T17)

  43. Coalescing meets Pointing(A7) Turn(A7) Pointing(Earth) contains meets meets meets meets Image(A7) Turn(T17) TakeImage(A7, Cam2) Pointing(T17) Status(Cam1, Off) contains contains meets meets Status(Cam2, Calibrated) Calibrate(Cam2) Status(Cam2, On) contains CalibrationTarget(T17)

  44. POCL vs CBI POCL CBI search goal-directed goal-directed strategy temporal before/after complex reasoning protection causal links meets conflicts threats mutex conflict proactive lazy resolution

  45. proposition action action proposition action action threatens action meets meets action proposition action action proposition mutex action proposition Causal Links & Threats POCL CBI Causal links: Threats:

  46. CBI Planners Zeno (Penberthy) intervals, no CSP Trains (Allen) Descartes (Joslin) extreme least commitment IxTeT (Ghallab) functional rep. HSTS (Muscettola) functional rep., activities

  47. Timelines Turn (?target) met-by Pointing(?direction) meets Pointing(?target) Pointing=Turn (?target) met-by Pointing=?direction meets Pointing=?target Pointing: Earth ?direction Turn(A7) A7 ? T17

  48. meets meets Pointing(?target) Turn(?target) Pointing(?direction) Explanatory Frame Axioms Turn (?target) met-by Pointing(?direction) meets Pointing(?target) Pointing(?target) met-by Past or met-by Turn (?target)

  49. A Stupid Question Why should CBI perform any better than POCL? • less commitment • better propagation • timelines

  50. A Stupid Question Why should CBI perform any better than POCL? • less commitment • better propagation • timelines • reachability analysis • heuristic estimators

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