Planning, Execution & Learning 1. Conditional Planning

Transcription

1 Planning, Execution & Learning 1. Conditional Planning Reid Simmons Planning, Execution & Learning: Conditional 1

2 Conditional Planning Create Branching Plans Take observations into account when selecting actions Observations Used to Handle Uncertainty Uncertainty arises from non-deterministic actions Uncertainty arises from lack of knowledge Planners Differ With Respect To: Representation of uncertainty (logic, probabilities) Representation of plans (trees, graphs) Representation of observations Search control Planning, Execution & Learning: Conditional 2

3 CNLP (Peot & Smith, 1992) Extensions to SNLP to Create Conditional Plans with Observations Extensions to SNLP Representation Three-valued logic (True, False, Unknown) Observations actions Observe_Road (?loc1?loc2) Pre: Unknown (Clear(?loc1,?loc2)) +α 1 : Clear(?loc1,?loc2) +α 2 : ~Clear(?loc1,?loc2) Contexts Compatible observation labels Planning, Execution & Learning: Conditional 3

4 Conditioning CNLP Extensions to SNLP Can remove threat by separating contexts (i.e., making them incompatible) Propagation of context labels and reasons Contexts: What actions are incompatible Reasons: what goals an action supports Tree-structured plan Goal replication Planning, Execution & Learning: Conditional 4

5 Adding Conditional Operators Q, Unknown(P) Q & Unknown(P) G G P A1 Finish Start Obs1 P ~P a 1 a 2 r: Finish c: {a 1 } r: Finish, Finish 2 c: {} r: Finish, Finish 2 c: {} G G ~P A2 Finish 2 r: Finish 2 c: {a 2 } c: {a 1 } c: {a 2 } Planning, Execution & Learning: Conditional 5

6 Conditionally Planning a Ski Trip Start (at skis home), (at home), Unknown(Clear(b, s)), Unknown(Clear(c, p)), Clear(home, b), Clear(b, c) Get(skis) Go(home, b) Clear(b, s) Go(b, s) (have skis) & (at?r) Finish c: {a 1 } At(b) Observe_road(b, s) Clear(b, s) ~Clear(b, s) a 1 a 2 Go(c, p) (have skis) & (at?r) c: {a 1 } Finish 2 Observe_road(c, p) Clear(c, p) b 1 b 2 ~Clear(c, p) Clear(c, p) Go(c, p) c: {a 2, } b 1 } c: {a 2, } b 1 } Fail Planning, Execution & Learning: Conditional 6

7 CNLP Summary Can Create Conditional Plans with Observation Actions However, no explicit distinction between observations and causal effects Can Handle Disjunctive Uncertainty No notion of which conditions more likely Increases search space tremendously Can Plan with Failure as an Option Planning, Execution & Learning: Conditional 7

8 Buridan (Kushmerick, 1995) Plan to Achieve Goals with Probability Greater Than a Given Threshold Extensions to SNLP Representation Probabilistic (not-deterministic) outcomes of actions Conditioned on current state Mutually exclusive and exhaustive triggers No preconditions (!) Action can occur anywhere Holding Dry Pickup ~Dry Holding Planning, Execution & Learning: Conditional 8

9 Buridan Extensions to SNLP Multiple Causal Links Each link increases probability of achievement Confrontation Reduce likelihood of threat by action A 1 by adding another action A 2 that makes it less likely for A 1 to have the undesired effect Plan Assessment Estimate probability of plan success NP-hard, in general Planning, Execution & Learning: Conditional 9

10 p=0.7 ~Holding, Dry, Clean, ~ Buridan (Partial) Plan Start p=0.3 ~Holding, ~Dry, Clean, ~ Dry Pickup ~Dry Holding Holding Paint Holding ~Holding ~Clean ~Clean Holding & Clean & Finish p > 0.85 Planning, Execution & Learning: Conditional 10

11 Increasing Probability of Success p=0.7 Start p=0.3 ~Holding, Dry, Clean, ~ ~Holding, ~Dry, Clean, ~ Dry-It Dry ~Dry Dry ~Dry Dry Pickup ~Dry Holding Holding Paint Holding ~Holding ~Clean ~Clean Holding & Clean & Finish p > 0.85 Planning, Execution & Learning: Conditional 11

12 p=0.7 ~Holding, Dry, Clean, ~ Confronting a Threat Start p=0.3 ~Holding, ~Dry, Clean, ~ Dry Pickup ~Dry Holding Holding Paint Holding ~Holding ~Clean ~Clean Holding & Clean & Finish p > 0.85 Planning, Execution & Learning: Conditional 12

13 Assessing the Plan Initial: {(Dry, ~Holding, Clean, ), 0.7) Goal: pr(holding & Clean & ) > 0.85 (~Dry, ~Holding, Clean, ), 0.3)} Paint: {(Dry, ~Holding, Clean, ), 0.63) (Dry, ~Holding, ~Clean, ), 0.07) (~Dry, ~Holding, Clean, ), 0.27) (~Dry, ~Holding, ~Clean, ), 0.03)} Dry-It: {(Dry, ~Holding, Clean, ), 0.63) (Dry, ~Holding, ~Clean, ), 0.07) (Dry, ~Holding, Clean, ), 0.216) (~Dry, ~Holding, Clean, ), 0.054) (Dry, ~Holding, ~Clean, ), 0.024) (~Dry, ~Holding, ~Clean, ), 0.006)} Pickup: {(Dry, Holding, Clean, ), ) (Dry, ~Holding, Clean, ), ) (Dry, Holding, ~Clean, ), ) (Dry, ~Holding, ~Clean, ), ) (~Dry, Holding, Clean, ), ) (~Dry, ~Holding, Clean, ), ) (~Dry, Holding, ~Clean, ), ) (~Dry, ~Holding, ~Clean, ), )} {(Dry, ~Holding, Clean, ), 0.846) (Dry, ~Holding, ~Clean, ), 0.094) (~Dry, ~Holding, Clean, ), 0.054) (~Dry, ~Holding, ~Clean, ), 0.006)} Planning, Execution & Learning: Conditional 13

14 Buridan Summary Handles Probabilistic Actions Outcomes conditioned on current state and random chance Different Notion of Plan Success Probability of achieving goal greater than threshold Adds multiple actions to increase probability No Observational Actions Not a conditional planner Planning, Execution & Learning: Conditional 14

15 C-Buridan (Draper, 1994) Conditional, Partial-Order Planner Extensions to Buridan Representation: Observation labels on actions Clear distinction between effects and observations Models noisy sensors Algorithm: Conditioning (branching) to remove threats Add observation actions to separate contexts Propagate context labels Planning, Execution & Learning: Conditional 15

16 Branches can Rejoin Differences from CNLP Plans are DAG s Branch Added Only to Remove Threat Not really planning to observe No a priori Relationship Between Observation Labels and Propositions Planner must discover correlations Planning, Execution & Learning: Conditional 16

17 Conditionally Processing Widgets (I) p=0.7 ~Flawed, ~Blemished, ~, ~ Start p=0.3 Flawed, Blemished, ~, ~ Ship Paint ~ ~Blemished ~, ~, Flawed ~Flawed & Finish p > 0.85 Planning, Execution & Learning: Conditional 17

18 Conditionally Processing Widgets (II) p=0.7 ~Flawed, ~Blemished, ~, ~ Start p=0.3 Flawed, Blemished, ~, ~ Paint ~ ~Blemished Ship ~, ~, Flawed ~Flawed Reject ~, ~, Flawed ~Flawed & Finish p > 0.85 Planning, Execution & Learning: Conditional 18

19 Conditionally Processing Widgets (III) p=0.7 ~Flawed, ~Blemished, ~, ~ Start p=0.3 Flawed, Blemished, ~, ~ Ship Paint ~ ~Blemished Inspect ~Blemished Blemished a 1 a 2 ~, Reject ~, Flawedc: {a ~, 1 } c: {a ~Flawed 2 } ~, Flawed ~Flawed & Finish p > 0.85 c: {a 1, a 2 } Planning, Execution & Learning: Conditional 19