1. Planning II CSE 573

2. © Daniel S. Weld 2 Logistics Reading for Wed Ch 18 thru 18.3 Office Hours No Office Hour Today

3. © Daniel S. Weld 3 573 Topics Agency Problem Spaces Search Knowledge Representation & Inference Planning Supervised Learning Logic-BasedProbabilistic Reinforcement Learning

4. © Daniel S. Weld 4 Planning Description of initial state of world E.g., Set of propositions: ((block a) (block b) (block c) (on-table a) (on- table b) (clear a) (clear b) (clear c) (arm-empty)) Description of goal: i.e. set of worlds or… E.g., Logical conjunction Any world satisfying conjunction is a goal (and (on a b) (on b c))) Description of available actions Sequence of Actions Input: Output:

5. © Daniel S. Weld 5 STRIPS Representation Simplifying assumptions Atomic time Agent is omniscient (no sensing necessary). Agent is sole cause of change Actions have deterministic effects STRIPS representation World = set of true propositions Actions: Precondition: (conjunction of literals) Effects (conjunction of literals)

6. © Daniel S. Weld 6 Action Schemata (:operator pick-up :parameters ((block ?ob1)) :precondition (and (clear ?ob1) (on-table ?ob1) (arm-empty)) :effect (and (not (clear ?ob1)) (not (on-table ?ob1)) (not (arm-empty)) (holding ?ob1))) Instead of defining: pickup-A and pickup-B and … Define a schema: Note: strips doesn’t allow derived effects; you must be complete! }

7. © Daniel S. Weld 7 Planning Outline The planning problem Representation Compilation to SAT Searching world states Regression Heuristics Graphplan Reachability analysis & heuristics Planning under uncertainty

8. © Daniel S. Weld 8 Planning as Search Nodes Arcs Initial State Goal State World states Action executions The state satisfying the complete description of the initial conds Any state satisfying the goal propositions

9. © Daniel S. Weld 9 Forward-Chaining World-Space Search A C B C B A Initial State Goal State

10. © Daniel S. Weld 10 Backward-Chaining Search Thru Space of Partial World-States D C B A E D C B A E D C B A E * * * Problem: Many possible goal states are equally acceptable. From which one does one search? A C B Initial State is completely defined D E

11. © Daniel S. Weld 11 Planning as Search - Backward Nodes Arcs Initial State Goal State A conjunctive goal (“set of goals”) Regression of goal through action defn The goal of the planning problem A set of goals  the planning problem’s initial description

12. © Daniel S. Weld 12 Regression Regressing a goal, G, thru an action, A Yields the weakest precondition G’ Such that: if G’ is true before A is executed G is guaranteed to be true afterwards A G precond effect G’ Represents a set of world states

13. © Daniel S. Weld 13 Regression Example pick-up :parameters ((block ?ob1)) :precondition (and (clear ?ob1) (on-table ?ob1) (arm-empty)) :effect (and (not (clear ?ob1)) (not (on-table ?ob1)) (not (arm-empty)) (holding ?ob1))) A G precond effect G’ (and (holding C) (on A B)) (and (clear C) (on-table C) (arm-empty) (on A B)) Disjunction  preconditions

14. © Daniel S. Weld 14 Conditional Effects

15. © Daniel S. Weld 15 Regressing Conditional Effects A G precond effect G’ (and (at keys home) (at paycheck bank)) (and (at briefcase bank) (in keys briefcase) (not (in paycheck briefcase)) (at paycheck bank)) bank home

16. © Daniel S. Weld 16 Heuristics Raise issue Defer until…

17. © Daniel S. Weld 17 Planning Outline The planning problem Representation Compilation to SAT Searching world states Regression Heuristics Graphplan Reachability analysis & heuristics Planning under uncertainty

18. © Daniel S. Weld 18 Graphplan Phase 1 - Graph Expansion Necessary (insufficient) conditions for plan existence Local consistency of plan-as-CSP Phase 2 - Solution Extraction Variables action execution at a time point Constraints goals, subgoals achieved no side-effects between actions

19. © Daniel S. Weld 19 The Plan Graph … … … level 0level 2level 4level 6 level 1level 3level 5 propositions actions propositions actions

20. © Daniel S. Weld 20 Graph Expansion Proposition level 0 initial conditions Action level i no-op for each proposition at level i-1 action for each operator instance whose preconditions exist at level i-1 Proposition level i effects of each no-op and action at level i … … … … i-1ii+10

21. © Daniel S. Weld 21 Constructing the planning graph… Initial proposition layer Just the initial conditions Action layer i If all of an action’s preconds are in i-1 Then add action to layer I Nop actions have P as precond and effect Proposition layer i+1 For each action at layer i Add all its effects at layer i+1

22. © Daniel S. Weld 22

23. © Daniel S. Weld 23 Mutual Exclusion Two actions are mutex if one clobbers the other’s effects or preconditions they have mutex preconditions Two proposition are mutex if all ways of achieving them are mutex

24. © Daniel S. Weld 24 Mutual Exclusion Actions A,B exclusive (at a level) if A deletes B’s precond, or B deletes A’s precond, or A & B have inconsistent preconds Propositions P,Q inconsistent (at a level) if all ways to achieve P exclude all ways to achieve Q

25. © Daniel S. Weld 25 Graphplan Create level 0 in planning graph Loop If goal  contents of highest level (nonmutex) Then search graph for solution If find a solution then return and terminate Else extend graph one more level A kind of double search: forward direction checks necessary (but insufficient) conditions for a solution,... Backward search verifies...

26. © Daniel S. Weld 26 Searching for a Solution For each goal G at time t For each action A making G true @t Select A unless mutex with previously chosen action If no actions work, backup to last G (breadth first search) Recurse on preconditions of actions selected, t-1 Proposition Init State Action Time 1 Proposition Time 1 Action Time 2

27. © Daniel S. Weld 27 Searching for a solution If goals are present & non-mutex: Choose action to achieve each goal Add preconditions to next goal set Recurse!

28. © Daniel S. Weld 28 Dinner Date Initial Conditions: (:and (cleanHands) (quiet)) Goal: (:and (noGarbage) (dinner) (present)) Actions: (:operator carry :precondition :effect (:and (noGarbage) (:not (cleanHands))) (:operator dolly :precondition :effect (:and (noGarbage) (:not (quiet))) (:operator cook :precondition (cleanHands) :effect (dinner)) (:operator wrap :precondition (quiet) :effect (present))

29. © Daniel S. Weld 29 Planning Graph noGarb cleanH quiet dinner present carry dolly cook wrap cleanH quiet 0 Prop 1 Action 2 Prop 3 Action 4 Prop

30. © Daniel S. Weld 30 Are there any exclusions? noGarb cleanH quiet dinner present carry dolly cook wrap cleanH quiet 0 Prop 1 Action 2 Prop 3 Action 4 Prop

31. © Daniel S. Weld 31 Do we have a solution? noGarb cleanH quiet dinner present carry dolly cook wrap cleanH quiet 0 Prop 1 Action 2 Prop 3 Action 4 Prop

32. © Daniel S. Weld 32 Extend the Planning Graph noGarb cleanH quiet dinner present carry dolly cook wrap carry dolly cook wrap cleanH quiet noGarb cleanH quiet dinner present 0 Prop 1 Action 2 Prop 3 Action 4 Prop

33. © Daniel S. Weld 33 Searching Backwards noGarb cleanH quiet dinner present carry dolly cook wrap carry dolly cook wrap cleanH quiet noGarb cleanH quiet dinner present 0 Prop 1 Action 2 Prop 3 Action 4 Prop

34. © Daniel S. Weld 34 One (of 4) Possibilities noGarb cleanH quiet dinner present carry dolly cook wrap carry dolly cook wrap cleanH quiet noGarb cleanH quiet dinner present 0 Prop 1 Action 2 Prop 3 Action 4 Prop

35. © Daniel S. Weld 35 Graphplan Solution Extraction as a Constraint Network Present@4 NoGarb@4 Dinner@4 Not carry & cook Not dolly & wrap Vars = Domain = Constraints = Goals@t Actions@t-1

36. © Daniel S. Weld 36 Review: Arc- & Path-Consistency Connect with graph construction What is k?

37. © Daniel S. Weld 37 Blackbox SAT Encoding … … … level 0level 2level 4level 6 level 1level 3level 5 propositions actions propositions actions

38. © Daniel S. Weld 38 Heuristics for Regression Planning