Introduction to Artificial Intelligence. Planning

Transcription

1 Introduction to Artificial Intelligence Planning Bernhard Beckert UNIVERSITÄT KOBLENZ-LANDAU Wintersemester 2003/2004 B. Beckert: Einführung in die KI / KI für IM p.1

2 Outline Search vs. planning STRIPS operators Partial-order planning The real world Conditional planning Monitoring and replanning B. Beckert: Einführung in die KI / KI für IM p.2

3 Search vs. Planning Consider the following task Get milk, bananas, and a cordless drill Standard search algorithms seem to fail miserably Talk to Parrot Go To Pet Store Buy a Dog Go To School Go To Class Start Go To Supermarket Buy Tuna Fish Go To Sleep Buy Arugula Read A Book Buy Milk... Finish Sit in Chair Sit Some More Etc. Etc Read A Book B. Beckert: Einführung in die KI / KI für IM p.3

4 Search vs. Planning Actions have requirements & consequences that should constrain applicability in a given state stronger interaction between actions and states needed B. Beckert: Einführung in die KI / KI für IM p.4

5 Search vs. Planning Actions have requirements & consequences that should constrain applicability in a given state stronger interaction between actions and states needed Most parts of the world are independent of most other parts solve subgoals independently B. Beckert: Einführung in die KI / KI für IM p.4

6 Search vs. Planning Actions have requirements & consequences that should constrain applicability in a given state stronger interaction between actions and states needed Most parts of the world are independent of most other parts solve subgoals independently Human beings plan goal-directed; they construct important intermediate solutions first flexible sequence for construction of solution B. Beckert: Einführung in die KI / KI für IM p.4

7 Search vs. Planning Planning systems do the following Unify action and goal representation to allow selection (use logical language for both) Divide-and-conquer by subgoaling Relax requirement for sequential construction of solutions B. Beckert: Einführung in die KI / KI für IM p.5

8 STRIPS STRIPS STandford Research Institute Problem Solver Tidily arranged actions descriptions Restricted language (function-free literals) Efficient algorithms B. Beckert: Einführung in die KI / KI für IM p.6

9 STRIPS: States States represented by: Conjunction of ground (function-free) atoms Example At(Home), Have(Bread) B. Beckert: Einführung in die KI / KI für IM p.7

10 STRIPS: States States represented by: Conjunction of ground (function-free) atoms Example At(Home), Have(Bread) Closed world assumption Atoms that are not present are assumed to be false Example State: Implicitly: At(Home), Have(Bread) Have(Milk), Have(Bananas), Have(Drill) B. Beckert: Einführung in die KI / KI für IM p.7

11 STRIPS: Operators Operator description consists of: Action name Positive literal Buy(Milk) Precondition Conjunction of positive literals At(Shop) Sells(Shop, Milk) Effect Conjunction of literals Have(Milk) B. Beckert: Einführung in die KI / KI für IM p.8

12 STRIPS: Operators Operator description consists of: Action name Positive literal Buy(Milk) Precondition Conjunction of positive literals At(Shop) Sells(Shop, Milk) Effect Conjunction of literals Have(Milk) Operator schema Operator containing variables At(p) Sells(p,x) Buy(x) Have(x) B. Beckert: Einführung in die KI / KI für IM p.8

13 STRIPS: Operator Application Operator applicability Operator o applicable in state s if: there is substitution Subst of the free variables such that Subst(precond(o)) s B. Beckert: Einführung in die KI / KI für IM p.9

14 STRIPS: Operator Application Operator applicability Operator o applicable in state s if: there is substitution Subst of the free variables such that Subst(precond(o)) s Example Buy(x) is applicable in state At(Shop) Sells(Shop, Milk) Have(Bread) with substitution Subst = { p/shop, x/milk } At(p) Sells(p,x) Buy(x) Have(x) B. Beckert: Einführung in die KI / KI für IM p.9

15 STRIPS: Operator Application Resulting state Computed from old state and literals in Subst(effect) Positive literals are added to the state Negative literals are removed from the state All other literals remain unchanged (avoids the frame problem) B. Beckert: Einführung in die KI / KI für IM p.10

16 STRIPS: Operator Application Resulting state Computed from old state and literals in Subst(effect) Positive literals are added to the state Negative literals are removed from the state All other literals remain unchanged (avoids the frame problem) Formally s = (s {P P a positive atom, P Subst(effect(o))}) \ {P P a positive atom, P Subst(effect(o))} B. Beckert: Einführung in die KI / KI für IM p.10

17 STRIPS: Operator Application Example Application of Drive(a, b) precond: At(a), Road(a, b) effect: At(b), At(a) B. Beckert: Einführung in die KI / KI für IM p.11

18 STRIPS: Operator Application Example Application of Drive(a, b) precond: At(a), Road(a, b) effect: At(b), At(a) to state At(Koblenz), Road(Koblenz, Landau) B. Beckert: Einführung in die KI / KI für IM p.11

19 STRIPS: Operator Application Example Application of Drive(a, b) precond: At(a), Road(a, b) effect: At(b), At(a) to state At(Koblenz), Road(Koblenz, Landau) results in At(Landau), Road(Koblenz, Landau) B. Beckert: Einführung in die KI / KI für IM p.11

20 State Space vs. Plan Space Planning problem Find a sequence of actions that make instance of the goal true B. Beckert: Einführung in die KI / KI für IM p.12

21 State Space vs. Plan Space Planning problem Find a sequence of actions that make instance of the goal true Nodes in search space Standard search: Planning search: node = concrete world state node = partial plan B. Beckert: Einführung in die KI / KI für IM p.12

22 State Space vs. Plan Space Planning problem Find a sequence of actions that make instance of the goal true Nodes in search space Standard search: Planning search: node = concrete world state node = partial plan (Partial) Plan consists of Set of operator applications S i Partial (temporal) order constraints Causal links S i c S j S i S j Meaning: S i achieves c precond(s j ) (record purpose of steps) B. Beckert: Einführung in die KI / KI für IM p.12

23 State Space vs. Plan Space Operators on partial plans add an action and a causal link to achieve an open condition add a causal link from an existing action to an open condition add an order constraint to order one step w.r.t. another Open condition A precondition of an action not yet causally linked B. Beckert: Einführung in die KI / KI für IM p.13

24 State Space vs. Plan Space Operators on partial plans add an action and a causal link to achieve an open condition add a causal link from an existing action to an open condition add an order constraint to order one step w.r.t. another Open condition A precondition of an action not yet causally linked Note We move from incomplete/vague plans to complete, correct plans B. Beckert: Einführung in die KI / KI für IM p.13

25 Partially Ordered Plans Start Start Left Sock Right Sock LeftShoeOn, RightShoeOn Finish LeftSockOn Left Shoe RightSockOn Right Shoe LeftShoeOn, RightShoeOn Special steps with empty action Finish Start Finish no precond, initial assumptions as effect) goal as precond, no effect B. Beckert: Einführung in die KI / KI für IM p.14

26 Partially Ordered Plans Start Start Left Sock Right Sock LeftShoeOn, RightShoeOn Finish LeftSockOn Left Shoe RightSockOn Right Shoe LeftShoeOn, RightShoeOn Special steps with empty action Finish Start Finish no precond, initial assumptions as effect) goal as precond, no effect Note Different paths in partial plan are not alternative plans, but alternative sequences of actions B. Beckert: Einführung in die KI / KI für IM p.14

27 Partially Ordered Plans Complete plan A plan is complete iff every precondition is achieved B. Beckert: Einführung in die KI / KI für IM p.15

28 Partially Ordered Plans Complete plan A plan is complete iff every precondition is achieved A precondition c of a step S j is achieved (by S i ) if S i S j c effect(s i ) there is no S k with S i S k S j and c effect(s k ) (otherwise S k is called a clobberer or threat) B. Beckert: Einführung in die KI / KI für IM p.15

29 Partially Ordered Plans Complete plan A plan is complete iff every precondition is achieved A precondition c of a step S j is achieved (by S i ) if S i S j c effect(s i ) there is no S k with S i S k S j and c effect(s k ) (otherwise S k is called a clobberer or threat) Clobberer / threat A potentially intervening step that destroys the condition achieved by a causal link B. Beckert: Einführung in die KI / KI für IM p.15

30 Clobbering and Promotion/Demotion Example Go(Home) clobbers At(HWS) Go(HWS) DEMOTION Demotion Put before Go(HWS) At(HWS) Buy(Drill) Go(Home) At(Home) Promotion Put after Buy(Drill) PROMOTION At(Home) Finish B. Beckert: Einführung in die KI / KI für IM p.16

31 Example: Blocks world "Sussman anomaly" problem A B C A B C Start State Goal State Clear(x) On(x,z) Clear(y) PutOn(x,y) ~On(x,z) ~Clear(y) Clear(z) On(x,y) Clear(x) On(x,z) PutOnTable(x) ~On(x,z) Clear(z) On(x,Table) + several inequality constraints B. Beckert: Einführung in die KI / KI für IM p.17

32 Example: Blocks World START On(C,A) On(A,Table) Cl(B) On(B,Table) Cl(C) B C A On(A,B) On(B,C) FINISH A B C B. Beckert: Einführung in die KI / KI für IM p.18

33 Example: Blocks World START On(C,A) On(A,Table) Cl(B) On(B,Table) Cl(C) B C A Cl(B) On(B,z) Cl(C) PutOn(B,C) On(A,B) On(B,C) FINISH A B C B. Beckert: Einführung in die KI / KI für IM p.18

34 Example: Blocks World START On(C,A) On(A,Table) Cl(B) On(B,Table) Cl(C) B C A PutOn(A,B) clobbers Cl(B) => order after PutOn(B,C) Cl(A) On(A,z) Cl(B) PutOn(A,B) Cl(B) On(B,z) Cl(C) PutOn(B,C) On(A,B) On(B,C) FINISH A B C B. Beckert: Einführung in die KI / KI für IM p.18

35 Example: Blocks World START On(C,A) On(A,Table) Cl(B) On(B,Table) Cl(C) B C A On(C,z) Cl(C) PutOnTable(C) Cl(A) On(A,z) Cl(B) PutOn(A,B) Cl(B) On(B,z) Cl(C) PutOn(B,C) PutOn(A,B) clobbers Cl(B) => order after PutOn(B,C) PutOn(B,C) clobbers Cl(C) => order after PutOnTable(C) On(A,B) On(B,C) FINISH A B C B. Beckert: Einführung in die KI / KI für IM p.18

36 POP (Partial Order Planner) Algorithm Sketch function POP(initial, goal, operators) returns plan plan MAKE-MINIMAL-PLAN(initial, goal) loop do if SOLUTION?( plan) then return plan % complete and consistent end S need, c SELECT-SUBGOAL( plan) CHOOSE-OPERATOR( plan, operators, S need, c) RESOLVE-THREATS( plan) 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 B. Beckert: Einführung in die KI / KI für IM p.19

37 POP Algorithm (Cont d) 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 Finish to ORDERINGS( plan) B. Beckert: Einführung in die KI / KI für IM p.20

38 POP Algorithm (Cont d) procedure RESOLVE-THREATS(plan) for each S threat that threatens a link S i end choose either c S j in LINKS( plan) do Demotion: Add S threat S i to ORDERINGS( plan) Promotion: Add S j S threat to ORDERINGS( plan) if not CONSISTENT( plan) then fail B. Beckert: Einführung in die KI / KI für IM p.21

39 Properties of POP Non-deterministic search for plan, backtracks over choicepoints on failure: choice of S add to achieve S need choice of promotion or demotion for clobberer B. Beckert: Einführung in die KI / KI für IM p.22

40 Properties of POP Non-deterministic search for plan, backtracks over choicepoints on failure: choice of S add to achieve S need choice of promotion or demotion for clobberer Sound and complete B. Beckert: Einführung in die KI / KI für IM p.22

41 Properties of POP Non-deterministic search for plan, backtracks over choicepoints on failure: choice of S add to achieve S need choice of promotion or demotion for clobberer Sound and complete There are extensions for: disjunction, universal quantification, negation, conditionals B. Beckert: Einführung in die KI / KI für IM p.22

42 Properties of POP Non-deterministic search for plan, backtracks over choicepoints on failure: choice of S add to achieve S need choice of promotion or demotion for clobberer Sound and complete There are extensions for: disjunction, universal quantification, negation, conditionals Efficient with good heuristics from problem description But: very sensitive to subgoal ordering B. Beckert: Einführung in die KI / KI für IM p.22

43 Properties of POP Non-deterministic search for plan, backtracks over choicepoints on failure: choice of S add to achieve S need choice of promotion or demotion for clobberer Sound and complete There are extensions for: disjunction, universal quantification, negation, conditionals Efficient with good heuristics from problem description But: very sensitive to subgoal ordering Good for problems with loosely related subgoals B. Beckert: Einführung in die KI / KI für IM p.22

44 The Real World On(x) ~Flat(x) START FINISH ~Flat(Spare) Intact(Spare) Off(Spare) On(Tire1) Flat(Tire1) On(x) Remove(x) Off(x) ClearHub Off(x) ClearHub Puton(x) On(x) ~ClearHub Intact(x) Flat(x) Inflate(x) ~Flat(x) B. Beckert: Einführung in die KI / KI für IM p.23

45 Things Go Wrong Incomplete information Unknown preconditions Example: Intact(Spare)? Disjunctive effects Example: Inflate(x) causes Inflated(x) SlowHiss(x) Burst(x) BrokenPump... B. Beckert: Einführung in die KI / KI für IM p.24

46 Things Go Wrong Incomplete information Unknown preconditions Example: Intact(Spare)? Disjunctive effects Example: Incorrect information Inflate(x) causes Inflated(x) SlowHiss(x) Burst(x) BrokenPump... Current state incorrect Example: spare NOT intact Missing/incorrect postconditions in operators B. Beckert: Einführung in die KI / KI für IM p.24

47 Things Go Wrong Incomplete information Unknown preconditions Example: Intact(Spare)? Disjunctive effects Example: Incorrect information Inflate(x) causes Inflated(x) SlowHiss(x) Burst(x) BrokenPump... Current state incorrect Example: spare NOT intact Missing/incorrect postconditions in operators Qualification problem Can never finish listing all the required preconditions and possible conditional outcomes of actions B. Beckert: Einführung in die KI / KI für IM p.24

48 Solutions Conditional planning Plan to obtain information (observation actions) Subplan for each contingency Example: [Check(Tire1), If(Intact(Tire1),[Inflate(Tire1)],[CallHelp])] Disadvantage: Expensive because it plans for many unlikely cases B. Beckert: Einführung in die KI / KI für IM p.25

49 Solutions Conditional planning Plan to obtain information (observation actions) Subplan for each contingency Example: [Check(Tire1), If(Intact(Tire1),[Inflate(Tire1)],[CallHelp])] Disadvantage: Expensive because it plans for many unlikely cases Monitoring/Replanning Assume normal states / outcomes Check progress during execution, replan if necessary Disadvantage: Unanticipated outcomes may lead to failure B. Beckert: Einführung in die KI / KI für IM p.25

50 Conditional Planning Execution of conditional plan [...,If(p,[thenPlan],[elsePlan]),...] Check p against current knowledge base, execute thenplan or elseplan B. Beckert: Einführung in die KI / KI für IM p.26

51 Conditional Planning Execution of conditional plan [...,If(p,[thenPlan],[elsePlan]),...] Check p against current knowledge base, execute thenplan or elseplan Conditional planning Just like POP except: If an open condition can be established by observation action add the action to the plan complete plan for each possible observation outcome insert conditional step with these subplans CheckTire(x) KnowsIf(Intact(x)) B. Beckert: Einführung in die KI / KI für IM p.26

52 Conditional Planning Example Start On(Tire1) Flat(Tire1) Inflated(Spare) On( x ) Inflated( x ) Finish (True) B. Beckert: Einführung in die KI / KI für IM p.27

53 Conditional Planning Example Start On(Tire1) Flat(Tire1) Inflated(Spare) Flat(Tire1) Intact(Tire1) Inflate(Tire1) (Intact(Tire1)) Tire1 On( x ) Tire1 Inflated( x ) Finish (True) B. Beckert: Einführung in die KI / KI für IM p.27

54 Conditional Planning Example Start On(Tire1) Flat(Tire1) Inflated(Spare) Check(Tire1) Intact(Tire1) Flat(Tire1) Intact(Tire1) Inflate(Tire1) (Intact(Tire1)) Tire1 On( x ) Tire1 Inflated( x ) Finish (True) (Intact(Tire1)) B. Beckert: Einführung in die KI / KI für IM p.27

55 L Conditional Planning Example Start On(Tire1) Flat(Tire1) Inflated(Spare) Check(Tire1) Intact(Tire1) Flat(Tire1) Intact(Tire1) Inflate(Tire1) (Intact(Tire1)) Tire1 On( x ) Tire1 Inflated( x ) Finish (True) (Intact(Tire1)) On( x ) Finish Inflated( x ) ( Intact(Tire1)) B. Beckert: Einführung in die KI / KI für IM p.27

56 L Conditional Planning Example Start On(Tire1) Flat(Tire1) Inflated(Spare) Check(Tire1) Intact(Tire1) Flat(Tire1) Intact(Tire1) Inflate(Tire1) (Intact(Tire1)) Tire1 On( x ) Tire1 Inflated( x ) Finish (True) (Intact(Tire1)) Spare On( x ) Spare Finish Inflated( x ) ( Intact(Tire1)) B. Beckert: Einführung in die KI / KI für IM p.27

57 L L L Conditional Planning Example Start On(Tire1) Flat(Tire1) Inflated(Spare) Check(Tire1) Intact(Tire1) Flat(Tire1) Intact(Tire1) Inflate(Tire1) (Intact(Tire1)) Tire1 On( x ) Tire1 Inflated( x ) Finish (True) (Intact(Tire1)) LIntact(Tire1) Remove(Tire1) ( Intact(Tire1)) Puton(Spare) ( Intact(Tire1)) Spare On( x ) Spare Finish Inflated( x ) ( Intact(Tire1)) B. Beckert: Einführung in die KI / KI für IM p.27

58 Monitoring Execution monitoring Failure: Preconditions of remaining plan not met B. Beckert: Einführung in die KI / KI für IM p.28

59 Monitoring Execution monitoring Failure: Preconditions of remaining plan not met Action monitoring Failure: Preconditions of next action not met (or action itself fails, e.g., robot bump sensor) B. Beckert: Einführung in die KI / KI für IM p.28

60 Monitoring Execution monitoring Failure: Preconditions of remaining plan not met Action monitoring Failure: Preconditions of next action not met (or action itself fails, e.g., robot bump sensor) Consequence of failure Need to replan B. Beckert: Einführung in die KI / KI für IM p.28

61 Preconditions for Remaining Plan Start At(Home) Go(HWS) At(HWS) Sells(HWS,Drill) Buy(Drill) At(HWS) Go(SM) At(SM) Sells(SM,Milk) At(SM) Sells(SM,Ban.) At(HWS) Have(Drill) Sells(SM,Ban.) Sells(SM,Milk) Buy(Milk) Buy(Ban.) At(SM) Go(Home) Have(Milk) At(Home) Have(Ban.) Have(Drill) Finish B. Beckert: Einführung in die KI / KI für IM p.29

62 Replanning Simplest On failure, replan from scratch B. Beckert: Einführung in die KI / KI für IM p.30

63 Replanning Simplest On failure, replan from scratch Better Plan to get back on track by reconnecting to best continuation Failure B. Beckert: Einführung in die KI / KI für IM p.30

64 Replanning: Example PRECONDITIONS FAILURE RESPONSE START Color(Chair,Blue) ~Have(Red) Get(Red) Have(Red) Paint(Red) Color(Chair,Red) FINISH none Have(Red) Color(Chair,Red) N/A Fetch more red Repaint B. Beckert: Einführung in die KI / KI für IM p.31

65 Summary Planning Differs from general problem search; subgoals solved independently STRIPS: restricted format for actions, logic-based Nodes in search space are partial plans POP algorithm Standard planning cannot cope with incomplete/incorrect information Conditional planning with sensing actions to complete information; expensive at planning stage Replanning based on monitoring of plan execution; expensive at execution stage B. Beckert: Einführung in die KI / KI für IM p.32