1. Summer School 2002 Planning History and Overview Susanne Biundo University of Ulm Germany

2. Summer School 2002, S. Biundo2 Artificial Intelligence Planning I The field of AI Planning and Scheduling is concerned with all aspects of the system-supported synthesis and execution of plans of action The history of the field dates back to 1967, when Cordell Green presented the first approach.

3. Summer School 2002, S. Biundo3 Artificial Intelligence Planning II actions plans states goals Enable intelligent goal-directed behaviour General aim Basic entities

4. Summer School 2002, S. Biundo4 Actions I Actions perform state changes u actions as to be executed by autonomous systems or virtual agents system control

5. Summer School 2002, S. Biundo5 Actions II u activities as to be pursued in business and production processes process control production of physical goods workflow management

6. Summer School 2002, S. Biundo6 Actions III u tasks as to be performed in management and organisation processes project planning mission planning

7. Summer School 2002, S. Biundo7 Artificial Intelligence Planning The field of AI Planning and Scheduling is concerned with all aspects of the system-supported synthesis and execution of plans They range over a variety of functions

8. Summer School 2002, S. Biundo8 Dealing with Plans n Synthesis of plans u plan generation n Inspection of plans u plan validation u plan verification n Modification of plans u plan repair u plan merging n Scheduling fully automated interactive

9. Summer School 2002, S. Biundo9 States, Actions, and Plans states of the world actions initial state goal state a2a2 a1a1 a n-1 anan Plans Courses of actions “programs”

10. Summer School 2002, S. Biundo10 Planning vs. Scheduling n Planning  initial state I  goal state G  operators O find a sequence of operator instances from O to transform I into G select appropriate actions arrange the actions consider causalities n Scheduling  a set of actions A  a set of resources R  a set of constraints C n find an optimal schedule arrange the actions assign the resources satisfy the constraints such that the schedule is (close to) optimal

11. Summer School 2002, S. Biundo11 Outline n Representations of planning domains u actions, states, and planning problems n Classical planning u state-space, plan-space, and graph-based approaches n Logic-based planning u satisfiability testing and deduction n Hierarchical planning u task decomposition and hybrid approaches n Applications n Historical remarks

12. Summer School 2002, S. Biundo12 Application Domain Characteristics n static vs. dynamic n finite vs. infinite n deterministic vs. non-deterministic n completely vs. partially observable n hierarchically structured vs. flat n instantaneous vs. durative actions n simple vs. complex plans u action sequences u “programs” u “policies”

13. Summer School 2002, S. Biundo13 Domain Modelling Requirements n state and operator descriptions n planning problems: initial and goal states, intermediate states n actions as elementary state transitions and elementary constituents of plans n resources (time, costs, material, personnel) n domain structure n type of orderings on actions n plan structure

14. Summer School 2002, S. Biundo14 An Example Domain n Objects: trucks, locations, cargo (barrels, boxes) n Actions: move, load, unload loc 1 loc 2 loc 3 loc 4

15. Summer School 2002, S. Biundo15 State Descriptions n first-order language comprising u a finite set of predicate symbols, like {At, On, Colour,...}, with arities u a finite set of constant symbols, like {loc 1, loc 2,...,truck, ba 1,...} u an enumerable set of variable symbols, like {x, l, t,...}  connectives  n states are represented by sets (conjunctions) of ground literals adapted from STRIPS (Fikes & Nilsson 1971)

16. Summer School 2002, S. Biundo16 States n states    are interpretations n they assign truth values to ground atoms and ground formulae according to u  I=  iff  (  )  true, if  atomic   I=   iff not  I=    I=  1   2 iff  I=  1 and  I=  2

17. Summer School 2002, S. Biundo17 Operator Descriptions n Operators have three components u an operator symbol o  O (name) of arity n and a list of terms t1,..., tn (arguments), which occur in the preconditions and effects of the operator u a set (conjunction) of literals prec(o), the preconditions of the operator u a set (conjunction) of literals eff(o), the effects of the operator

18. Summer School 2002, S. Biundo18 Operator Application I n effects of operators are often described by two disjoint sets u add(o) = {l | l  eff(o), l atom} (add list)  del(o) = {l |  l  eff(o) } (delete list) n a set S of ground literals describes a set of states n a ground instance a of an operator, i.e. an action, is applicable to S iff u prec(a)  S

19. Summer School 2002, S. Biundo19 Operator Application II n the application of a to S results in a set of literals T = (S - del(a) - {  l | l  add(a) })  eff(a) n T describes the set of possible successor states to S w.r.t a (T = succ (S, a)) n simplification u CWA : S contains only atoms u prec(a) contains only atoms u T = succ(S, a) = (S - del(a))  add(a), if prec(a)  S

20. Summer School 2002, S. Biundo20 Planning Problems n a planning problem (plan specification) P = (init, goal, O) u init and goal : sets of literals describing the initial and goal states of the problem u O : set of operators n a sequence a 1... a m of operator ground instances (actions) is a plan iff u a 1 is applicable to some state description S u a i is applicable to each state description resulting from the application of a i-1 ( 1  i  m ) to the resp. predecessor

21. Summer School 2002, S. Biundo21 Solutions to Planning Problems n a sequence a 1... a m of actions is a solution to a planning problem P = (init, goal, O) iff u a 1... a m is a plan u a 1 is applicable to init u each goal-literal is in the successor state description of a m n a 1... a m is a linear (total-order) plan

22. Summer School 2002, S. Biundo22 Semantic Properties n an action is sound iff there exist states ,  '   such that  I= prec(a) and  ' I= eff(a) n a sound action specifies a state transition n if an action a is applicable to a state description S and  I= S for a state   , then  I= prec(a) n if  I= S and a is applicable to S and T is the successor state description to S w.r.t. a, then there exists  '   with  'I= T

23. Summer School 2002, S. Biundo23 Correctness of Plans n a plan that is a solution to a planning problem P = (init, goal, O) specifies a set of state transitions from each state satisfying init to a state satisfying goal n such a plan is correct w.r.t. the given problem (plan specification)

24. Summer School 2002, S. Biundo24 State description At (truck, loc 1 ), On (truck, b 3 ), On(truck, b 4 ),..., At (truck, loc 1 ), At (b 3, loc 1 ),..., At (b 1, loc 4 ),..., Connected (loc 1, loc 2 ),... Example I loc 1 loc 2 loc 3 loc 4 b3b3 b4b4 c1c1 b5b5 b2b2 b1b1 c3c3 c2c2

25. Summer School 2002, S. Biundo25 Operator descriptions n move (t: truck, l 1, l 2 : location) prec: At (t, l 1 ), Connected (l 1, l 2 ) add: At (t, l 2 ) del: At (t, l 1 ) n unload (t: truck, l: location, c: cargo) prec: At (t, l), On (t, c) add: At (c, l) del: On (t, c) Example II n load (t: truck,...) prec:...

26. Summer School 2002, S. Biundo26 Planning Problem Example III loc 1 loc 2 loc 3 loc 4 b3b3 b4b4 c1c1 b5b5 b2b2 b1b1 c3c3 c2c2 loc 3 c1c1 ?? goal: At(c 1, loc 3 ) init: At (truck, loc 1 ), On (truck, c 1 ),....

27. Summer School 2002, S. Biundo27 Example IV loc 1 loc 2 loc 3 loc 4 b3b3 b4b4 b5b5 b2b2 b1b1 c3c3 c2c2 plan b3b3 c1c1 c1c1 loc 1 loc 2 loc 3 b4b4 b5b5 loc 4 b2b2 b1b1 c3c3 c2c2 move (truck, loc 1, loc 2 ) ; move (truck, loc 2, loc 3 ) ; unload (truck, loc 3, c 1 )

28. Summer School 2002, S. Biundo28 How to find a plan n state-space search u search space subset of state space u nodes states u edges actions n find a path from the initial state to a goal state

29. Summer School 2002, S. Biundo29 Forward Search progression-planning (init, goal, O) S :  init p :   repeat repeat ifthenreturn if goal  S then return p A :  { a | prec(a)  S and a ground instance of some o  O} ifthenfail if A =  then fail choose choose a  A S :  succ (S, a) p :  p;a

30. Summer School 2002, S. Biundo30 Backward Search regression-planning (init, goal, O) S :  goal p :   repeat repeat ifthenreturn if S  init then return p A :  { a | (eff(a)  S)   and a ground instance of some o  O} ifthenfail if A =  then fail choose choose a  A S :  wp (S, a) = (S - eff(a))  eff(a) p :  a;p

31. Summer School 2002, S. Biundo31 How to implement efficient planning procedures ? reduction of the search space structuring the search space goal-directed procedures strategies heuristics encodings Guiding the Search

32. Summer School 2002, S. Biundo32 island search means ends analysis STRIPS - Algorithm (Fikes & Nilsson 1971) n select a goal n achieve the goal from initial state n compute new initial state n select next goal n repeat until all goals achieved Example Strategy i g i’

33. Summer School 2002, S. Biundo33 n plan-space search u search space space of partial plans u nodes partial plans u edges plan refinement operations n find a complete and consistent non-linear plan that leads from the initial state to a goal state How to find a plan

34. Summer School 2002, S. Biundo34 Non-linear Plans I np = (PlanSteps, OrderingConstraints, CausalLinks, VariableBindings,...) n PlanSteps : a set of labeled operations n OrderingConstraints : a partial order on PlanSteps n CausalLinks : a set of causal relations between plan steps (ps i ps j ) : ps i establishes the precondition c of ps j n VariableBindings : x  t, x variable, t term c

35. Summer School 2002, S. Biundo35 Non-linear Plans II a non-linear plan np solves a planning problem P = (init, goal, O) iff np is a complete and consistent refinement of the initial plan ({ps , ps  }, {(ps  < ps  )}, ,  ) ps  and ps  are fictive plan steps with eff(ps  ) = init prec(ps  ) = goal

36. Summer School 2002, S. Biundo36 Non-linear Plans III n np is complete iff u each precondition of each plan step is established by a plan step u each linearisation of np is safe, i.e. no step ps k with c  del(ps k ) can occur between ps i and ps j, if ps i establishes a precondition c of ps j n np is consistent iff u its ordering constraints are consistent, i.e. if ps i < ps j then not ps j < ps i u its variable bindings are consistent, i.e. if x  A then not x  B, if A  B u

37. Summer School 2002, S. Biundo37 Example At(c 1, loc 3 ) At(b 5, loc 4 ) At (truck, loc 1 ) ps  ps  On (truck, c 1 ) At (b5, loc 2 )

38. Summer School 2002, S. Biundo38 Example At(c 1, loc 3 ) At(b 5, loc 4 ) At (truck, loc 1 ) ps  ps  unload(c 1, loc 3 ) unload(b 5, loc 4 ) At (truck, loc 3 ) At (c 1, loc 3 ) On (truck, c 1 ) At (b5, loc 2 ) At (b 5, loc 4 ) At (truck, loc 4 ) On (truck, b 5 ) ps 1 ps 2

39. Summer School 2002, S. Biundo39 Example At(c 1, loc 3 ) At(b 5, loc 4 ) At (truck, loc 1 ) ps  ps  move(truck, loc 2, loc 3 ) unload(c 1, loc 3 ) unload(b 5, loc 4 ) At (truck, loc 3 ) At (truck, loc 2 ) At (c 1, loc 3 ) On (truck, c 1 ) At (b5, loc 2 ) At (b 5, loc 4 ) At (truck, loc 4 ) On (truck, b 5 ) ps 3 ps 1 ps 2

40. Summer School 2002, S. Biundo40 Example At(c 1, loc 3 ) At(b 5, loc 4 ) At (truck, loc 1 ) ps  ps  move(truck, loc 2, loc 3 ) unload(c 1, loc 3 ) At (truck, loc 3 ) At (truck, loc 2 ) At (c 1, loc 3 ) On (truck, c 1 ) At (b5, loc 2 ) ps 2 ps 1 move(truck, loc1, loc2) At (truck, loc1) At (truck, loc2) ps3

41. Summer School 2002, S. Biundo41 Example At(c 1, loc 3 ) At(b 5, loc 4 ) At (truck, loc 1 ) ps  ps  move(truck, loc 2, loc 3 ) unload(c 1, loc 3 ) unload(b 5, loc 4 ) At (truck, loc 3 ) At (truck, loc 2 ) At (c 1, loc 3 ) On (truck, c 1 ) At (b5, loc 2 ) At (b 5, loc 4 ) At (truck, loc 4 ) On (truck, b 5 ) ps 2 ps 1 ps 4 ps 3

42. Summer School 2002, S. Biundo42 Example At(c 1, loc 3 ) At(b 5, loc 4 ) At (truck, loc 1 ) ps  ps  move(truck, loc 2, loc 3 ) unload(c 1, loc 3 ) unload(b 5, loc 4 ) At (truck, loc 3 ) At (truck, loc 2 ) At (c 1, loc 3 ) On (truck, c 1 ) At (b5, loc 2 ) At (b 5, loc 4 ) At (truck, loc 4 ) On (truck, b 5 ) ps 2 ps 1 ps 4 ps 3 move(truck, loc3, loc4) At (truck, loc3) At (truck, loc4) ps5

43. Summer School 2002, S. Biundo43 Example At(c 1, loc 3 ) At(b 5, loc 4 ) At (truck, loc 1 ) ps  ps  move(truck, loc 2, loc 3 ) unload(c 1, loc 3 ) unload(b 5, loc 4 ) At (truck, loc 3 ) At (truck, loc 2 ) At (c 1, loc 3 ) On (truck, c 1 ) At (b5, loc 2 ) At (b 5, loc 4 ) At (truck, loc 4 ) On (truck, b 5 ) ps 2 ps 1 ps 4 ps 3 move(truck, loc3, loc4) At (truck, loc3) At (truck, loc4) ps5

44. Summer School 2002, S. Biundo44 Partial-Order Causal-Link Planning SNLP - Algorithm (McAllister & Rosenblitt 1991) np :  initial-plan(init, goal, O) pocl (np) ifthen return fail if np inconsistent then return fail ifthen return if np complete then return np if if there is a causal link (ps i ps j ) ““ “threatened “ by a step ps k, i.e. c  del(ps k ) and ps k possibly inbetween ps i and ps j then choose Promotion : return pocl (np  (ps k < ps i )) Demotion : return pocl (np  (ps j < ps k )) c

45. Summer School 2002, S. Biundo45 Partial-Order Causal-Link Planning ctd. choose choose ps k and c  prec(ps k ) where there is no causal link (ps l ps k ) for some ps l choose choose a. choose ps m from np such that c  eff(ps m ) return return pocl (np  (ps m ps k )) choose b. choose an operator o  O and a variable instantiation  such that c  eff(  (o)) generate a new plan step ps n from  (o) np :  insert (np, ps n ) return return pocl (np  (ps n ps k )) c c c

46. Summer School 2002, S. Biundo46 Plan-space vs. State-space Planning n plan-space-based planning least commitment principle u generation of non-linear plans partial order on actions u least restricting variable bindings u step-wise plan refinement n state-space-based planning u generation of linear plans total order on actions u step-wise plan extension Least commitment w.r.t. variable instantiation

47. Summer School 2002, S. Biundo47 n planning-graph construction u search space compact representation of u the state space u nodes atoms, actions u edges precondition-, add-, delete- relations n find a sequence of sets of actions that represent a complete and consistent non-linear plan leading from the initial state to a goal state How to find a plan

48. Summer School 2002, S. Biundo48 Planning-Graphs F0 : init Fn : goal f 0.1 f 0.2 f 0.3 f 0.p a 1.1 a 1.2 a 1.k f 1.1 f 1.2 f 1.3 f 1.m 0 1 A F

49. Summer School 2002, S. Biundo49 Graph Construction and Analysis I two phases n construction of the planning graph : forward search u generate successive layers of the planning graph, starting from the initial state, until a layer n is reached, which contains the goals n analysis of the planning graph : backward search u construction of a plan GRAPHPLAN (Blum & Furst 1995)

50. Summer School 2002, S. Biundo50 Graph Construction and Analysis II u collect in layer n a set of non-mutex actions that achieve the goals u collect in each layer i a set of independent actions that establish the preconditions of actions collected in layer i+1 (1 < i < n) u F0 (init) contains the preconditions of actions collected in layer 1 n two actions are mutual exclusive (mutex) iff they interact or their preconditions are mutex, i.e. are established by non-mutex actions

51. Summer School 2002, S. Biundo51 Graph Construction and Analysis III n two actions a and b interact iff (prec(a)  add(a))  del(b)   or (prec(b)  add(b))  del(a)  

52. Summer School 2002, S. Biundo52 Properties u graph-based planning approaches rely on ground instances of state descriptions and operators u they combine aspects of linear and non-linear planning u they generate shortest plans in terms of “time steps” u they always terminate

53. Summer School 2002, S. Biundo53 A Different View on Planning Give a course at 2nd PLANET Summer School select topicprepare course travel to Thessaloniki give course contact travel agent pack bagplan travel select material prepare slides go by plane go by car go by train

54. Summer School 2002, S. Biundo54 realistic aim solving complex, realistic planning problems project planning mission planning requirements u flexible plan generation u understandable solutions u user interaction and predefined user plans Hierarchical Planning I

55. Summer School 2002, S. Biundo55 n exploiting the inherent hierarchical structure of application domains n relying on pre-defined, pre-structured, abstract solutions u procedural and declarative specifications of abstract operators n considering ordering and causal constraints Hierarchical Planning II

56. Summer School 2002, S. Biundo56 n task net construction u search space the space of task networks u nodes tasks u edges refinement and decomposition operations n find a complete and consistent primitive task network that represents a solution of the initial problem (goal task) How to find a plan

57. Summer School 2002, S. Biundo57 n abstract tasks, compound tasks n goal tasks n primitive tasks n decomposition methods : (t : task, tn : task-network) tn : abstract / primitive task network tn : pre-defined (abstract) partial plan Hierarchical Task Network Planning O-Plan (Drabble, Tate, et al. 1977) UMCP (Erol, Hendler, Nau 1994)

58. Summer School 2002, S. Biundo58 stepwise expansion of abstract task networks through decomposition operations start from the initial goal task select and apply appropriate decomposition methods until a primitive task network is obtained Decomposition Planning I

59. Summer School 2002, S. Biundo59 n consistence and completeness of the primitive task network are guaranteed through the use of correct methods n a method (t, tn) is correct iff tn is a correct implementation of t simplest case: u tn is a complete and consistent (abstract) plan u the preconditions of tasks in tn are established through the preconditions of t or within tn u tn produces the effects of t Decomposition Planning II

60. Summer School 2002, S. Biundo60 combination of state- and operator-based abstraction declarative and procedural task descriptions n preconditions and effects on any level of abstraction n integration of POCL and decomposition planning n well-founded combination of both techniques through the concept of decomposition axioms Hybrid Planning I PANDA (Biundo & Schattenberg 2001)

61. Summer School 2002, S. Biundo61 Hybrid Planning II n decomposition axioms relate preconditions and effects of tasks across abstraction levels decomposition of tasks refinement of preconditions and effects At (u:unit, l:loc)  [ (V-At (u:vehicle, l:loc, r:road) ... )  (A-At (u:aircraft, l:loc, h:height) ... )  (C-At (c:container, l:loc)  In (u:unit, c:... ) ]

62. Summer School 2002, S. Biundo62 Hybrid Planning III formal definition and proof of correctness of methods decomposition steps reasoning about resources on different levels of abstraction Energy-Checked (u:unit)  [ (power-level (u:e-dev) > 300 )  (fuel-level (u:m-dev) > 100) ... ]

63. Summer School 2002, S. Biundo63 Hybrid Planning IV Planning Algorithm n combining POCL planning and task decomposition n extending the range of plan refinement operations u task decomposition u task insertion u causal link identification u variable constraints F (non-) codesignation F sort restriction

64. Summer School 2002, S. Biundo64 n first-order plan specifications existence formulas :  x  y [  (x)   (x, y) ] n planning through theorem proving constructive proofs : y  p(x) n provably correct plans n complex plans conditionals (case analysis) recursion (induction) Deductive Planning Green 1969, Manna & Waldinger 1979 planning as programming

65. Summer School 2002, S. Biundo65 n conditional operators n universally quantified effects n disjunctive preconditions n function expressions in operator descriptions u state transitions through variable assignments u similarity to the state variable concept Extended Representations ADL (Pednault 1986) simplifying domain descriptions

66. Summer School 2002, S. Biundo66 n planning through satisfiability testing n planning via model checking Different Representations

67. Summer School 2002, S. Biundo67 n heuristic search n domain analysis u general u problem dependent n control rules Improving the Efficiency of Planning

68. Summer School 2002, S. Biundo68 n... planning and plan execution n... integrating planning and scheduling n... planning through constraint satisfaction n... probabilistic planning n... planning for information gathering n... planner performance evaluation and comparison I didn’t mention...

69. Summer School 2002, S. Biundo69 The History of Planning

70. Summer School 2002, S. Biundo70 Bibliography