Classical Planning: Limits

Transcription

1 Classical Planning: Limits

2 Spacecraft Domain

3 Spacecraft Domain

4 Extensions Time Resources Constraints Uncertainty Utility

5 Model

6 Temporal Interval Relations

7 Interval Algebra (aka Allen Algebra) [Allen 83] Relation Symbol Inverse Illustration X before Y b bi x y X equal Y = x y X meets Y m mi x y X overlaps Y o oi X during Y d di x y x y X starts Y s si X finishes Y f fi x y y x Topic 60

8 Interval Algebra: Qualitative TN Variables An interval represent an event with some duration Constraints Intervals I, J are related by a binary constraint The constraint is a subset of the 13 basic relations r = { b, m, o, s, d, f, bi, mi, oi, si, di, fi, = } Example: I {r 1,r 2,,r k } J (I r 1 J) (I r 2 J) (I r k J) Enumerate atomic relations between two variables Topic 61

9 Interval Algebra Constraint Network Variables: temporal intervals I and J Domain: set of ordered pairs of real numbers Constraints are subsets of the 13 relations How many distinct relations? A solution is an assignment of a pair of numbers to each variable such that no constraint is violated Topic 62

10 Interval Algebra: Example Story: John was not in the room when I touched the switch to turn on the light but John was in the room later when the light was on. CSP model: Variables: Switch the time of touching the switch Light the light was on Room the time that John was in the room Constraints: Switch overlaps or meets Light: S {o, m} L Switch is before, meets, is met by or after Room: S {b, m, mi, bi} R Light overlaps, starts or is during Room: L {o, s, d} R Light {o, m} {o, s, d} Switch Room {b, m, mi, a} Topic 63

11 The Task: Get the Minimal Network Light Light {o, m} {o, s, d} Constraint Tightening {o, m} {o, s} Switch {b, m, mi, a} Room Switch {b, m} Room A unique network equivalent to original network All constraints are subsets of original constraints Provides a more explicit representation Useful in answering many types of queries Topic 64

12 Temporal Operators

13 Temporal Operators

14 Temporal Operators

15 Temporal Operators

16 Temporal Operators

17 Temporal Planning Problem

18 Consistent Complete Plan

19 CBI-Planning

20 Initial Plan

21 Expansion

22 Expansion

23 Coalescing

24 Coalescing

25 Expansion

26 Coalescing

27 CBI-Algorithm

28 CBI-Planners

29 CBI vs POP CBI is similar to POP because least commitment and partial order But, temporal constraints in CBI Contraints Temporal Network associated with a plan Constraint propagation

30 Planning and Scheduling Scheduling has usually been addressed separately from planning Thus, will give an overview of scheduling algorithms In some cases, cannot decompose planning and scheduling so cleanly

31 Temporal Constraints

32 RAX Example: DS1

33 Temporal Constraints as Inequalities

34 Metric Constraints

35 Temporal Constraint Networks

36 Temporal Constraint Satisfaction Problem

37 Simple Temporal Networks

38 Simple Temporal Networks

39 Simple Temporal Network (STP) A special class of temporal problems Can be solved in polynomial time An edge e ij : i j is labeled by a single interval [a ij, b ij ] [10, 20] i j Constraint (a ij x j - x i b ij ) expressed by (x j - x i b ij ) ( x i - x j -a ij ) Example (x j - x i 20) ( x i - x j -10) Topic 92

40 Distance Graph of an STP The STP is transformed into an all-pairsshortest-paths problem on a distance graph Each constraint is replaced by two edges: one + and one - j i Constraint graph directed cyclic graph Topic 93

41 Solving the Distance Graph of the STP x x1 x x2 x4 Run Floyd-Warshall all pairs shortest path If any pair of nodes has a negative cycle inconsistency If consistent after F-W minimal & decomposable Once d-graph formed, assembling a solution by checking against the previous labeling Total time: F-W O(n 3 ) + Assembling O(n 2 ) = O(n 3 ). Topic 94

42 Eventi: Example

43 Eventi: Example

44 Example Eventi: Floyd-Warshall

45 STN example Start End

46 A Complete CBI-Plan is a STN

47 A Complete CBI-Plan is a STN

48 DS1: Remote Agent

49 Remote Agent Experiment: RAX

50 Remote Agent

51 Remote Agent

52 Mission Manager Remote Agent

53 Constraints: Remote Agent

54 Planner starts Remote Agent

55 Planning Remote Agent

56 Final Plan Remote Agent

57 Constraints Remote Agent

58 Remote Agent Flexible Temporal Plan through least commitment

59 Remote Agent Executive system dispatch tasks

60 Planning Remote Agent

61 Planning to plan Remote Agent

62 Remote Agent Periodic planning and replanning

63 Remote Agent Executive system dispatch tasks

64 Remote Agent The Plan Executor has two duties: Select and Schedule activities for execution Update the network (constraint propagation) after the action execution or execution step (latency) Executor Cycle: Activity Graph (STN) from Planner Propagate with latency Enabled time points = scheduled parents (fixed time points) Select and Schedule enabled time points Propagate constraint network given the new binds

65 Remote Agent Executing Flexible Plans

66 Remote Agent Constraint propagation can be costly

67 Remote Agent Constraint Propagation can be costly

68 Remote Agent Solution: compile temporal constraints to an efficient network

69 Remote Agent Dispatchability Alcuni vincoli non visibili a tempo di esecuzione; Occorre rendere la rete dispatchable aggiungendo vincoli impliciti (e.g. D prima di B) Compilare la rete in forma dispatchable: Introdotti vincoli impliciti Tolti vincoli ridondanti

70 Dispatchability

71 Dispatcher

72 Dispatcher

73 Dispatchability

74 Dispatchability

75 Dispatchability All pair graph Filtered graph

76 Controllability Alcune attività non sono controllabili, ma solo osservabili E.g. after start_turn, end_turn? Quando finisce? Il grafo delle attività STN contiene time point controllabili e non controllabili Le attività non controllabili non possono essere schedulate, ma solo osservate Propagazione??

77 Controllability

78 Gestire eventi non controllabili Es. Se B schedulato prima di X, B vincola X Soluzione Dinamica: B dopo X Controllability Soluzione Forte: B a 99

79 Controllability Weak Controllability: per ogni evento incontrollabile esiste uno scheduling che permette l esecuzione; Strong Controllability: esiste uno scheduling robusto qualunque siano gli eventi non controllabili; Dynamic Controllability: per ogni evento incontrollabile passato esiste uno scheduling che permette l esecuzione.

80 Controllability

81 Controllability

82 Controllability

83 IDEA Architecture Evoluzione del RA: reactive and deliberative planning

84 IDEA Architecture Muti-agent architecture:

85 IDEA Architecture Reactive planning come controllo Interazione deliberative and reactive planning

86 GenoM (LAAS) Functional Layer

87 PRS Controller A procedural controller (vedi dopo )

88 IDEA Architecture Attività pianificate (plan database):

89 IDEA Architecture Reactive Planning

90 IDEA Architecture Reactive and Deliberative planning