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Planning

Planning. Module THREE: Planning, Production Systems,Expert Systems, Uncertainty. Dr M M Awais. What is Planning. Generate sequences of actions to perform tasks and achieve objectives. States, actions and goals Search for solution over abstract space of plans.

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Planning

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  1. Planning Module THREE: Planning, Production Systems,Expert Systems, Uncertainty Dr M M Awais

  2. What is Planning • Generate sequences of actions to perform tasks and achieve objectives. • States, actions and goals • Search for solution over abstract space of plans. • Assists humans in practical applications • design and manufacturing • military operations • games • space exploration CS 331/531 Dr M M Awais

  3. BASIC CONCEPT CS 331/531 Dr M M Awais

  4. Definitions: Summary Planning: The problem of finding some action to achieve some goal System’s Plan: The sequence of such actions is called System’s Plan

  5. Means – Ends Analysis (MEA) • MEA is a simple planning method in AI. • “It is a technique which, rather than blindly searching through all possible actions, focuses on actions that reduce the difference between the current state and the target state” CS 331/531 Dr M M Awais

  6. Algorithm: • To find-plan (initial state, Target state) • If all the goals in target state are true in initial state then succeed • Otherwise • Select an unresolved target state • Find an action that adds goal to the current-state • Enable action by finding a plan (PREPLAN) that actives its pre-conditions i.e., find-plan (initial state, pre-conditions.) Let Mid-state 1 be the result of applying that pre-plan to initial state. • Apply action to Mid state 1 to give Mid state 2 • Find a plan (post plan) from Mid state 2 to target state • Return a plan consisting of Preplan, Action, and Post Plan CS 331/531 Dr M M Awais

  7. Essential Components of a Plan: Preplan, Action, Post Plan. Always choose Action that takes you close to the goal CS 331/531 Dr M M Awais

  8. Goal: G Actions: A1 A2 A3 A4 A5 States: P1 P2 P3 B1 B2 B3 B4 Sequence of Action that take us to the G are A3, followed by A4 and then A5 B3 – B4 – B5, this leads to states: B3, B4 and B4 Rules: P1  B1 P2  B2 P3  B3 B3  B4 B4  G A1 A2 A3 A4 A5 CS 331/531 Dr M M Awais

  9. • Preplan: A1 Post plan: None Cannot proceed further Initial State P3 B1 • Post plan: A4 Preplan: A3 Initial State P3 • B3 Pre plan: A4 Post plan: A5 B4 • Pre plan: A5 G Wrong Choice How can we change CS 331/531 Dr M M Awais

  10. • Preplan: A1 Post plan: None Cannot proceed further Initial State P3 B1 • Post plan: A4 Preplan: A3 Initial State P3 • B3 Pre plan: A4 Post plan: A5 B4 • Pre plan: A5 G How can we change CS 331/531 Dr M M Awais

  11. • Preplan: A1 Post plan: None Cannot proceed further Initial State P3 B1 • Post plan: A4 Preplan: A3 Initial State P3 • B3 Pre plan: A4 Post plan: A5 B4 • Pre plan: A5 G How can we change CS 331/531 Dr M M Awais

  12. • Preplan: A1 Post plan: None Cannot proceed further Initial State P3 B1 • Post plan: A4 Preplan: A3 Initial State P3 • B3 Pre plan: A4 Post plan: A5 B4 • Pre plan: A5 G How can we change CS 331/531 Dr M M Awais

  13. • Preplan: A1 Post plan: None Cannot proceed further Initial State P3 B1 • Post plan: A4 Preplan: A3 Initial State P3 • B3 Pre plan: A4 Post plan: A5 B4 • Pre plan: A5 G How can we change CS 331/531 Dr M M Awais

  14. • Preplan: A1 Post plan: None Cannot proceed further Initial State P3 B1 • Post plan: A4 Preplan: A3 Initial State P3 • B3 Pre plan: A4 Post plan: A5 B4 • Pre plan: A5 G How can we change CS 331/531 Dr M M Awais

  15. • Preplan: A1 Post plan: None Cannot proceed further Initial State P3 B1 • Post plan: A4 Preplan: A3 Initial State P3 • B3 Pre plan: A4 Post plan: A5 B4 • Pre plan: A5 G So MEA will choose A3 always How can we change CS 331/531 Dr M M Awais

  16. Difficulty of real world problems • Assume a problem-solving agent using some search method … • Which actions are relevant? • Exhaustive search vs. backward search • What is a good heuristic functions? • Good estimate of the cost of the state? • Problem-dependent vs, -independent • How to decompose the problem? • Most real-world problems are nearly decomposable. CS 331/531 Dr M M Awais

  17. Implementation Methods CS 331/531 Dr M M Awais

  18. Planning language • What is a good language? • Expressive enough to describe a wide variety of problems. • Restrictive enough to allow efficient algorithms to operate on it. • Planning algorithm should be able to take advantage of the logical structure of the problem. • STRIPS and • Action Description Language (ADL) CS 331/531 Dr M M Awais

  19. General language features • Representation of states • Decompose the world in logical conditions and represent a state as a conjunction of positive literals. • Closed world assumption • Representation of goals • Partially specified state and represented as a conjunction of positive ground literals • A goal is satisfied if the state contains all literals in goal. • Representation of Actions CS 331/531 Dr M M Awais

  20. General language features • Representation of states/goals • Propositional literals: poor  unknown • FO-literals (grounded and function-free): at(plane1, lahore)  at(plane2, karachi) CS 331/531 Dr M M Awais

  21. General language features • Representations of actions • Action = PRECOND + EFFECT Action(fly(P,From, To), PRECOND:at(P,from)  plane(P)  airport(From)  airport(To) EFFECT:¬at(P,From)  at(P,To)) = action schema (P, From, Toneed to be instantiated) • Action name and parameter list • Precondition (conj. of function-free literals) • Effect (conj of literals and P is True and not P is false) • Add-list vs delete-list in Effect • Literal in ADD list if true else in DELETE list CS 331/531 Dr M M Awais

  22. Language semantics? • How do actions affect states? • Action:Applied in any state if PRECOND: satisfied. • Action Applied after finding substitution  for the variables in the PRECOND. CS 331/531 Dr M M Awais

  23. Language semantics? Given Facts: at(p1,lhr)  at(p2,khi)  plane(p1)  plane(p2)  airport(lhr)  airport(khi) Satisfies : at(P,From)  plane(P)  airport(From)  airport(To) With:  ={p1/P, lhr/From, khi/To} CS 331/531 Dr M M Awais

  24. Strips: Advancement • STRIPS is simplified • function-free literals (only propositional representation) • Function symbols lead to infinitely many states and actions • Recent extension:Action Description language (ADL) Action(fly(P:plane, From: airport, To: airport), PRECOND: at(P,From)  (From  To) EFFECT: ¬at(P,From)  at(P,To)) Planning domain definition language (PDDL) CS 331/531 Dr M M Awais

  25. Example: air cargo transport Init(at(c1, khi)  at(c2,lhr)  at(p1,khi)  at(P2,lhr)  cargo(C1)  cargo(c2)  plane(p1)  plane(p2)  airport(lhr)  airport(khi)) Goal(at(c1,lhr)  at(c2,khi)) Action(load(C,P,A) PRECOND: at(C,A)  at(P,A)  cargo(C)  plane(P)  airport(A) EFFECT: ¬at(C,A)  in(C,P)) Action(Unload(C,P,A) PRECOND: in(C,P)  at(P,A)  cargo(C)  plane(P)  airport(A) EFFECT: at(C,A)  ¬in(C,P)) Action(Fly(P,From,To) PRECOND: at(P,From)  plane(P)  airport(From)  airport(To) EFFECT: ¬ at(P,From)  at(P,To)) Can any action be applied?, under what substitutions? [load(c1,p1,khi), fly(p1,khi,lhr), load(c2,p2,lhr), fly(p2,lhr,khi)] CS 331/531 Dr M M Awais

  26. Example: Spare tire problem Init(At(Flat, Axle)  At(Spare,trunk)) Goal(At(Spare,Axle)) Action(Remove(Spare,Trunk) PRECOND: At(Spare,Trunk) EFFECT: ¬At(Spare,Trunk)  At(Spare,Ground)) Action(Remove(Flat,Axle) PRECOND: At(Flat,Axle) EFFECT: ¬At(Flat,Axle)  At(Flat,Ground)) Action(PutOn(Spare,Axle) PRECOND: At(Spare,Groundp) ¬At(Flat,Axle) EFFECT: At(Spare,Axle)  ¬Ar(Spare,Ground)) Action(LeaveOvernight) PRECOND: EFFECT: ¬ At(Spare,Ground)  ¬ At(Spare,Axle)  ¬ At(Spare,trunk)  ¬ At(Flat,Ground)  ¬ At(Flat,Axle) ) This example goes beyond STRIPS: negative literal in pre-condition (ADL description) CS 331/531 Dr M M Awais

  27. Example: Blocks world Init(On(A, Table)  On(B,Table)  On(C,Table)  Block(A)  Block(B)  Block(C)  Clear(A)  Clear(B)  Clear(C)) Goal(On(A,B)  On(B,C)) Action(Move(b,x,y) PRECOND: On(b,x)  Clear(b)  Clear(y)  Block(b)  (b x)  (b y)  (x y) EFFECT: On(b,y)  Clear(x)  ¬ On(b,x)  ¬ Clear(y)) Action(MoveToTable(b,x) PRECOND: On(b,x)  Clear(b)  Block(b)  (b x) EFFECT: On(b,Table)  Clear(x)  ¬ On(b,x)) Spurious actions are possible: Move(B,C,C) CS 331/531 Dr M M Awais

  28. Example: Blocks world:Alternative Representation CS 331/531 Dr M M Awais

  29. Triangle Table: Effective Representation Pre-cond gripping() clear(X) on(X,Y) Unstack (X,Y) Effects gripping(X) clear(Y) CS 331/531 Dr M M Awais

  30. Triangle Table: Effective Representation gripping() clear(X) on(X,Y) unstack (X,Y) gripping(X) clear(Y) putdown (X) gripping() ontable(X) clear(X) CS 331/531 Dr M M Awais

  31. Triangle Table: Effective Representation gripping() clear(X) on(X,Y) unstack (X,Y) gripping(X) clear(Y) putdown (X) ontable(Y) gripping() ontable(X) clear(X) pickup (Y) CS 331/531 Dr M M Awais

  32. Triangle Table: Effective Representation gripping() clear(X) on(X,Y) unstack (X,Y) gripping(X) clear(Y) putdown (X) ontable(Y) gripping() ontable(X) clear(X) ????? pickup (Y) CS 331/531 Dr M M Awais

  33. Triangle Table: Effective Representation By doing this clear (Y) is still the Effect of unstack(X,Y) (same column) gripping() clear(X) on(X,Y) unstack (X,Y) gripping(X) putdown (X) ontable(Y) gripping() ontable(X) clear(X) clear(Y) pickup (Y) CS 331/531 Dr M M Awais

  34. Triangle Table: Effective Representation Are these the pre-cond of pickup(Y): NO You can shift it anywhere in the column gripping() clear(X) on(X,Y) unstack (X,Y) gripping(X) putdown (X) ontable(Y) gripping() ontable(X) clear(X) clear(Y) pickup (Y) CS 331/531 Dr M M Awais

  35. ????? Triangle Table: Effective Representation gripping() clear(X) on(X,Y) unstack (X,Y) gripping(X) putdown (X) ontable(Y) gripping() clear(Y) pickup (Y) ontable(X) clear(X) gripping(Y) pickup (X) CS 331/531 Dr M M Awais

  36. ????? Triangle Table: Effective Representation gripping() clear(X) on(X,Y) unstack (X,Y) gripping(X) putdown (X) ontable(Y) gripping() clear(Y) pickup (Y) ontable(X) clear(X) gripping(Y) pickup (X) stack (Y,Z) CS 331/531 Dr M M Awais

  37. gripping(Y) Triangle Table: Effective Representation gripping() clear(X) on(X,Y) unstack (X,Y) gripping(X) putdown (X) ontable(Y) gripping() clear(Y) pickup (Y) ontable(X) clear(X) pickup (X) clear(Z) stack (Y,Z) CS 331/531 Dr M M Awais

  38. Triangle Table: Effective Representation FIRST KERNEL Everything that Should be true For unstack including some additional predictes gripping() clear(X) on(X,Y) unstack (X,Y) gripping(X) putdown (X) ontable(Y) gripping() clear(Y) pickup (Y) ontable(X) clear(X) pickup (X) clear(Z) gripping(Y) stack (Y,Z) CS 331/531 Dr M M Awais

  39. Triangle Table: Effective Representation gripping() clear(X) on(X,Y) unstack (X,Y) gripping(X) SECOND KERNEL putdown (X) ontable(Y) gripping() clear(Y) pickup (Y) ontable(X) clear(X) pickup (X) clear(Z) gripping(Y) stack (Y,Z) CS 331/531 Dr M M Awais

  40. Triangle Table: Effective Representation gripping() clear(X) on(X,Y) unstack (X,Y) gripping(X) putdown (X) THIRD KERNEL ontable(Y) gripping() clear(Y) pickup (Y) ontable(X) clear(X) pickup (X) clear(Z) gripping(Y) stack (Y,Z) CS 331/531 Dr M M Awais

  41. Planning with state-space search • Both forward and backward search possible • Forward Chaining:Progression planners • forward state-space search • Consider the effect of all possible actions in a given state • Backward Chaining:Regression planners • backward state-space search • To achieve a goal, what must have been true in the previous state. CS 331/531 Dr M M Awais

  42. Progression and regression CS 331/531 Dr M M Awais

  43. Progression algorithm • Formulation as state-space search problem: • Initial state = initial state of the planning problem • Literals not appearing are false • Actions = those whose preconditions are satisfied • Add positive effects, delete negative • Goal test = does the state satisfy the goal • Step cost = each action costs 1 • No functions … any graph search that is complete is a complete planning algorithm. • Inefficient: (1) irrelevant action problem (2) good heuristic required for efficient search CS 331/531 Dr M M Awais

  44. Regression algorithm • How to determine predecessors? • What are the states from which applying a given action leads to the goal? Goal state = At(C1, B)  At(C2, B)  …  At(C20, B) Relevant action for first conjunct: Unload(C1,p,B) Works only if pre-conditions are satisfied. Previous state=In(C1, p)  At(p, B) At(C2, B)  …  At(C20, B) Subgoal At(C1,B) should not be present in this state. • Actions must not undo desired literals (consistent) • Main advantage: only relevant actions are considered. • Often much lower branching factor than forward search. CS 331/531 Dr M M Awais

  45. Regression algorithm • General process for predecessor construction • Give a goal description G • Let A be an action that is relevant and consistent • The predecessors is as follows: • Any positive effects of A that appear in G are deleted. • Each precondition literal of A is added , unless it already appears. • Any standard search algorithm can be added to perform the search. • Termination when predecessor satisfied by initial state. • In FO case, satisfaction might require a substitution. CS 331/531 Dr M M Awais

  46. Heuristics for state-space search • Neither progression or regression are very efficient without a good heuristic. • How many actions are needed to achieve the goal? • Exact solution is NP hard, find a good estimate • Two approaches to find admissible heuristic: • The optimal solution to the relaxed problem. • Remove all preconditions from actions • The subgoal independence assumptio: The cost of solving a conjunction of subgoals is approximated by the sum of the costs of solving the subproblems independently. CS 331/531 Dr M M Awais

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