Planning. Philipp Koehn. 30 March 2017

Transcription

1 Planning Philipp Koehn 30 March 2017

2 Outline 1 Search vs. planning STRIPS operators Partial-order planning The real world Conditional planning Monitoring and replanning

3 2 search vs. planning

4 Search vs. Planning 3 Consider the task get milk, bananas, and a cordless drill Standard search algorithms seem to fail miserably: After-the-fact heuristic/goal test inadequate

5 Search vs. Planning 4 Planning systems do the following 1. improve action and goal representation to allow selection 2. divide-and-conquer by subgoaling 3. relax requirement for sequential construction of solutions Differences Search Planning States Data structures Logical sentences Actions Program code Preconditions/outcomes Goal Program code Logical sentence (conjunction) Plan Sequence from S 0 Constraints on actions

6 5 strips operators

7 STRIPS Operators 6 Tidily arranged actions descriptions, restricted language ACTION: Buy(x) PRECONDITION: At(p), Sells(p, x) EFFECT: Have(x) Note: this abstracts away many important details! Restricted language efficient algorithm Precondition: conjunction of positive literals Effect: conjunction of literals

8 7 partial-order planning

9 Partially Ordered Plans 8 Partially ordered collection of steps with Start step has the initial state description as its effect F inish step has the goal description as its precondition causal links from outcome of one step to precondition of another temporal ordering between pairs of steps Open condition = precondition of a step not yet causally linked A plan is complete iff every precondition is achieved A precondition is achieved iff it is the effect of an earlier step and no possibly intervening step undoes it

10 Example 9

11 Example 10

12 Example 11

13 Example 12

14 Example 13

15 Planning Process 14 Operators on partial plans add a link from an existing action to an open condition add a step to fulfill an open condition order one step wrt another to remove possible conflicts Gradually move from incomplete/vague plans to complete, correct plans Backtrack if an open condition is unachievable or if a conflict is unresolvable

16 Partially Ordered Plans Algorithm 15 function POP(initial, goal, operators) returns plan plan MAKE-MINIMAL-PLAN(initial, goal) loop do if SOLUTION?( plan) then return plan S need, c SELECT-SUBGOAL( plan) CHOOSE-OPERATOR( plan, operators, S need, c) RESOLVE-THREATS( plan) end function SELECT-SUBGOAL( plan) returns S need, c pick a plan step S need from STEPS( plan) with a precondition c that has not been achieved return S need, c

17 Partially Ordered Plans Algorithm 16 procedure CHOOSE-OPERATOR(plan, operators, S need, c) choose a step S add from operators or STEPS( plan) that has c as an effect if there is no such step then fail c add the causal link S add S need to LINKS( plan) add the ordering constraint S add S need to ORDERINGS( plan) if S add is a newly added step from operators then add S add to STEPS( plan) add Start S add F inish to ORDERINGS( plan) procedure RESOLVE-THREATS(plan) c for each S threat that threatens a link S i S j in LINKS( plan) do choose either Demotion: Add S threat S i to ORDERINGS( plan) Promotion: Add S j S threat to ORDERINGS( plan) if not CONSISTENT( plan) then fail end

18 Clobbering and Promotion/Demotion 17 A clobberer is a potentially intervening step that destroys the condition achieved by a causal link. E.g., Go(Home) clobbers At(Supermarket): Demotion: put before Go(Supermarket) Promotion: put after Buy(Milk)

19 Properties of Partially Ordered Plans 18 Nondeterministic algorithm: backtracks at choice points on failure choice of S add to achieve S need choice of demotion or promotion for clobberer selection of S need is irrevocable Partially Ordered Plans is sound, complete, and systematic (no repetition) Extensions for disjunction, universals, negation, conditionals Can be made efficient with good heuristics derived from problem description Particularly good for problems with many loosely related subgoals

20 Example: Blocks World 19

21 Example 20

22 Example 21

23 Example 22

24 Example 23

25 24 the real world

26 The Real World 25

27 Things Go Wrong 26 Incomplete information Unknown preconditions, e.g., Intact(Spare)? Disjunctive effects, e.g., Inf late(x) causes Inf lated(x) SlowHiss(x) Burst(x) BrokenP ump... Incorrect information Current state incorrect, e.g., spare NOT intact Missing/incorrect postconditions in operators Qualification problem can never finish listing all required preconditions of actions possible conditional outcomes of actions

28 Solutions 27 Conformant or sensorless planning Devise a plan that works regardless of state or outcome Such plans may not exist Conditional planning Plan to obtain information (observation actions) Subplan for each contingency, e.g., [Check(T ire1), if Intact(T ire1) then Inflate(T ire1) else CallAAA] Expensive because it plans for many unlikely cases Monitoring/Replanning Assume normal states, outcomes Check progress during execution, replan if necessary Unanticipated outcomes may lead to failure (e.g., no AAA card) Really need a combination; plan for likely/serious eventualities, deal with others when they arise, as they must eventually.

29 Conformant Planning 28 Search in space of belief states (sets of possible actual states)

30 29 conditional planning

31 Conditional Planning 30 If the world is nondeterministic or partially observable then percepts usually provide information, i.e., split up the belief state

32 Conditional Planning 31 Conditional plans check (any consequence of KB +) percept [..., if C then P lan A else P lan B,...] Execution: check C against current KB, execute then or else Need some plan for every possible percept game playing: some response for every opponent move backward chaining: some rule such that every premise satisfied AND OR tree search (very similar to backward chaining algorithm)

33 Example 32 Double Murphy: sucking or arriving may dirty a clean square

34 33 monitoring and replanning

35 Execution Monitoring 34 Plan with Partially Ordered Plans algorithms Process plan, one step at a time Validate planned conditions against perceived reality Failure = preconditions of remaining plan not met Preconditions of remaining plan = all preconditions of remaining steps not achieved by remaining steps = all causal links crossing current time point

36 Responding to Failure 35 Run Partially Ordered Plans algorithms again Resume Partially Ordered Plans to achieve open conditions from current state IPEM (Integrated Planning, Execution, and Monitoring) keep updating Start to match current state links from actions replaced by links from Start when done

37 Example 36

38 Example 37

39 Example 38

40 Example 39

41 Example 40

42 Example 41

43 Emergent Behavior 42

44 Emergent Behavior 43

45 Emergent Behavior 44 Loop until success behavior emerges from interaction between monitor/replan agent design and uncooperative environment

46 Summary 45 Planning break down problem into subgoals search for plans for subgoals merge sub-plans Defined actions in terms of preconditions and effects Partially Ordered Plans algorithm Clobbering: need to deal with steps that destroy clausal link in plan Real world: incomplete and incorrect information conformant or conditional planning, monitoring and replanning