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The Challenge of Duration Uncertainty

The Challenge of Duration Uncertainty. David E. Smith John Bresina, Keith Golden, Richard Dearden, Nicolas Meuleau, Sailesh Ramakrishnan, Rich Washington. Outline. The Problem objectives (goals) actions Approaches (neo-) classical MDP heuristic augmentation. Operational Characteristics.

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The Challenge of Duration Uncertainty

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  1. The Challenge of Duration Uncertainty David E. Smith John Bresina, Keith Golden, Richard Dearden, Nicolas Meuleau, Sailesh Ramakrishnan, Rich Washington

  2. Outline • The Problem • objectives (goals) • actions • Approaches • (neo-) classical • MDP • heuristic augmentation

  3. Operational Characteristics • Brain dead • radiation • power • Safety • no risky operations • Communication • twice/day

  4. Operational Characteristics • Brain dead • radiation • power • Safety • no risky operations • Communication • twice/day 3. Uplink 1. Plan on the ground Compress long …………… Visual servo (.2, -.15) Dig(5) Drive(-1) NIR Drive(2) Warmup NIR 2. Extensive checking/simulation

  5. The Planning Problem • Initial conditions • start time • pose • power available • … • Possible science objectives • images • samples Compress Visual servo (.2, -.15) Dig(5) Drive(-1) NIR Drive(2) …………… Warmup NIR Maximize Scientific Return

  6. The Objectives • Initial conditions • start time • pose • power available • … • Possible science objectives • images • samples • Decision Theoretic: • objectives are valued • choose Compress v=100 v=30 Visual servo (.2, -.15) Dig(5) Drive(-1) NIR Drive(2) …………… Warmup NIR Maximize Scientific Return

  7. The Real Problem E > .1 Ah  = .05 Ah  = .02 Ah E > .6 Ah  = .2 Ah  = .2 Ah E > 3 Ah  = 2 Ah  = .5 Ah E > 7 Ah  = 5 Ah  = 2.5 Ah V = 10 Compress t [10:00, 14:00]  = 600s  = 60s  = 1000s  = 500s  = 60s  = 1s  = 40s  = 20s …………… Visual servo (.2, -.15) Dig(60) Drive (-1) NIR Drive (2) …………… V = 100 Warmup NIR  = 400s  = 20s E > 5 Ah  = 3 Ah  = .5 Ah

  8. Uncertain Usage Uncertain resource usage E > .1 Ah  = .05 Ah  = .02 Ah E > .6 Ah  = .2 Ah  = .2 Ah E > 3 Ah  = 2 Ah  = .5 Ah E > 7 Ah  = 5 Ah  = 2.5 Ah V = 10 Compress t [10:00, 14:00]  = 600s  = 60s  = 1000s  = 500s  = 60s  = 1s Uncertain durations  = 40s  = 20s Visual servo (.2, -.15) Dig(60) Drive (-1) NIR Drive (2) …………… V = 100 Warmup NIR  = 400s  = 20s E > 5 Ah  = 3 Ah  = .5 Ah

  9. Time & Resource Constraints Resource constraints E > .1 Ah  = .05 Ah  = .02 Ah E > .6 Ah  = .2 Ah  = .2 Ah E > 3 Ah  = 2 Ah  = .5 Ah E > 7 Ah  = 5 Ah  = 2.5 Ah V = 10 Compress Time constraints t [10:00, 14:00]  = 600s  = 60s  = 1000s  = 500s  = 60s  = 1s  = 40s  = 20s Visual servo (.2, -.15) Dig(60) Drive (-1) NIR Drive (2) …………… V = 100 Warmup NIR  = 400s  = 20s E > 5 Ah  = 3 Ah  = .5 Ah

  10. E > .02 Ah  = .01 Ah  = 0 Ah E > 10 Ah  = 5 Ah  = 2.5 Ah E > .1 Ah  = .05 Ah  = .02 Ah E > .6 Ah  = .2 Ah  = .2 Ah t [9:00, 14:30]  = 5s  = 1s HiRes V = 10 t [10:00, 14:00]  = 600s  = 60s E > 3 Ah  = 2 Ah  = .5 Ah  = 1000s  = 500s  = 60s  = 1s  = 40s  = 20s Visual servo (.2, -.15) Dig(60) Drive (-2) NIR V = 100 t [9:00, 16:00]  = 5s  = 1s t [10:00, 13:50]  = 600s  = 60s  = 120s  = 20s Lo res Rock finder NIR V = 50 V = 5 E > .02 Ah  = .01 Ah  = 0 Ah E > .12 Ah  = .1 Ah  = .01 Ah E > 3 Ah  = 2 Ah  = .5 Ah How hard is it?

  11. Utility 20 13:20 15 13:40 10 14:00 Power 5 Start time 14:20 14:40 How hard is it?

  12. E > .02 Ah  = .01 Ah  = 0 Ah E > 10 Ah  = 5 Ah  = 2.5 Ah E > .1 Ah  = .05 Ah  = .02 Ah E > .6 Ah  = .2 Ah  = .2 Ah t [9:00, 14:30]  = 5s  = 1s HiRes V = 10 Utility t [10:00, 14:00]  = 600s  = 60s E > 3 Ah  = 2 Ah  = .5 Ah  = 1000s  = 500s  = 60s  = 1s  = 40s  = 20s Visual servo (.2, -.15) Dig(60) Drive (-2) NIR V = 100 20 t [9:00, 16:00]  = 5s  = 1s t [10:00, 13:50]  = 600s  = 60s 13:20 15  = 120s  = 20s 13:40 10 Lo res Rock finder NIR V = 50 V = 5 14:00 E > .02 Ah  = .01 Ah  = 0 Ah E > .12 Ah  = .1 Ah  = .01 Ah E > 3 Ah  = 2 Ah  = .5 Ah 5 Power 14:20 Start time 14:40 Whazzzzup?

  13. Visual servo (.2, -.15) Lo res Rock finder NIR Warmup NIR ∆t = ∆p = The Culprits Continuous time (& resources) Continuous outcomes Time (& resource) constraints Concurrency Power Storage Time t [10:00, 14:00] E > 2 Ah NIR

  14. Visual servo (.2, -.15) Lo res Rock finder NIR Warmup NIR ∆t = ∆p = The Culprits Continuous time (& resources) Continuous outcomes Time (& resource) constraints Concurrency Power Storage Time t [10:00, 14:00] E > 2 Ah NIR Goal choices Optimization Simplicity constraints

  15. Outline • The Problem • objectives (goals) • actions • Approaches • (neo-) classical • MDP • Heuristic augmentation

  16. Disjunction Probability CGP CMBP C-PLAN Fragplan Non Observable Buridan UDTPOP p SENSp Cassandra PUCCINI SGP QBF-Plan GPT MBP C-Buridan DTPOP C-MAXPLAN ZANDER Mahinur ¬p Partially Observable Goal selection & optimization STRIPS model of action no concurrency no time no resources Discrete action outcomes JIC Plinth Weaver PGP Fully Observable WARPLAN-C CNLP Classical Planning under Uncertainty Problems

  17. p ¬p STRIPS model of action no concurrency no time no resources Discrete action outcomes MDP’s & POMDPS Advantages Disjunction Probability Goal selection &optimization CGP CMBP C-PLAN Fragplan Non Observable Buridan UDTPOP SENSp Cassandra PUCCINI SGP QBF-Plan GPT MBP C-Buridan DTPOP C-MAXPLAN ZANDER Mahinur POMDPs Partially Observable Problems JIC Plinth Weaver PGP MDPs Fully Observable WARPLAN-C CNLP

  18. Outline • The Problem • objectives (goals) • actions • Approaches • (neo-) classical • MDP • Heuristic • Conservative planning • Augmentation

  19. Utility 20 13:20 15 13:40 10 14:00 5 Power 14:20 Start time 14:40 Conservative Planning Assume Dt=  +  t [9:00, 14:30]  = 5s  = 1s t=13:40 t=14:05 t=14:06 t=14:07 1500s HiRes V = 10 t [10:00, 14:00]  = 600s  = 60s  = 1000s  = 500s  = 60s  = 1s  = 40s  = 20s Visual servo (.2, -.15) Dig(60) Drive (-2) NIR V = 100 t [9:00, 16:00]  = 5s  = 1s t [10:00, 13:50]  = 600s  = 60s  = 120s  = 20s Lo res Rock finder NIR V = 50 V = 5

  20. Heuristic Augmentation Plan based on expectations Analyze utility of result Augment add a branch

  21. Just in Case (JIC) Scheduling 1. Seed schedule 2. Identify most likely failure 3. Generate a contingency branch 4. Integrate the branch .1 .4 .2 • Advantages: • Tractable • Simple plans • Anytime

  22. Utility 20 13:20 15 13:40 10 14:00 5 Power 14:20 Start time 14:40 The Seed Assume Dt=  t=13:35 t=13:52 t=13:53 t=13:54 t [10:00, 14:00]  = 600s  = 60s  = 1000s  = 500s  = 60s  = 1s  = 40s  = 20s Visual servo (.2, -.15) Dig(60) Drive (-2) NIR V = 100 V = 50

  23. Utility 20 13:20 15 13:40 10 14:00 5 Power 14:20 Start time 14:40 Failure Point t=13:35 t=13:52 t=13:53 t=13:54 t [10:00, 14:00]  = 600s  = 60s  = 1000s  = 500s  = 60s  = 1s  = 40s  = 20s Visual servo (.2, -.15) Dig(60) Drive (-2) NIR V = 100

  24. Utility 20 13:20 15 13:40 10 14:00 5 Power 14:20 Start time 14:40 Failure Point Assume Dt=  t [9:00, 14:30]  = 5s  = 1s HiRes V = 10 t=13:35 t=13:52 t=13:53 t=13:54 t [10:00, 14:00]  = 600s  = 60s  = 1000s  = 500s  = 60s  = 1s  = 40s  = 20s Visual servo (.2, -.15) Dig(60) Drive (-2) NIR V = 100

  25. Where the Branch *Should* Go t [9:00, 14:30]  = 5s  = 1s HiRes V = 10 1500s t=13:40 t=14:05 t=14:10 t=14:12 t [10:00, 14:00]  = 600s  = 60s  = 1000s  = 500s  = 300s  = 5s  = 120s  = 60s Visual servo (.2, -.15) Dig(60) Drive (-2) NIR V = 100 t [9:00, 16:00]  = 5s  = 1s t [10:00, 14:30]  = 600s  = 60s  = 120s  = 20s Lo res Rock finder LIB V = 50 V = 5 Warmup LIB  = 1200s  = 20s

  26. Why? t [9:00, 14:30]  = 5s  = 1s HiRes V = 10 1500s t=13:40 t=14:05 t=14:10 t=14:12 t [10:00, 14:00]  = 600s  = 60s  = 1000s  = 500s  = 300s  = 5s  = 120s  = 60s Intermediate steps No inherent value Low impact on P Value of alternatives higher Visual servo (.2, -.15) Dig(60) Drive (-2) NIR V = 100 t [9:00, 16:00]  = 5s  = 1s t [10:00, 14:30]  = 600s  = 60s  = 120s  = 20s Lo res Rock finder LIB V = 50 V = 5 Warmup LIB  = 1200s  = 20s

  27. Just in Case (JIC) Planning 1. Seed plan 2. Identify best branch point 3. Generate a contingency branch 4. Integrate the branch ? ? ?

  28. Evaluating Branch Points Probability distributions for time & resources Utility of current plan as a function of time & resources Expected utility of a branch as a function of time & resources Branch condition Utility gain t=13:35 t [10:00, 14:00]  = 600s  = 60s  = 1000s  = 500s  = 60s  = 1s  = 40s  = 20s Visual servo (.2, -.15) Dig(60) Drive (-2) NIR V = 100

  29. Estimating Branch Utility Probability distributions for time & resources Utility of current plan as a function of time & resources Expected utility of a branch as a function of time & resources Build PlanGraph Back-propagate utility distributions t=13:35 t [10:00, 14:00]  = 600s  = 60s  = 1000s  = 500s  = 60s  = 1s  = 40s  = 20s Visual servo (.2, -.15) Dig(60) Drive (-2) NIR V = 100

  30. Visual servo (.2, -.15) Lo res Rock finder NIR Warmup NIR ∆t = ∆p = Final Points Continuous time (& resources) Continuous outcomes Time (& resource) constraints Concurrency Nasty combination! Power Storage Time • Existing approaches • painfully inadequate • Pervasive to • observation planning t [10:00, 14:00] E > 2 Ah World has round dice NIR

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