Artificial Intelligence. Planning

Transcription

1 Artificial Intelligence Planning

2 Planning Planning agent Similar to previous problem solving agents Constructs plans that achieve its goals, then executes them Differs in way it represents and searches for solutions STRIPS Action schema Actions, preconditions, effects Partial-order planning Sub-goaling 2

3 Search vs. Planning Consider shopping task: Get milk, bananas, and a cordless drill Standard search algorithms seem to fail miserably LARGE branching factor Talk to Parrot Go to Pet Store Buy a Dog Go to School Go to Class start Go to Supermarket Go to Sleep Buy Tuna Fish Buy Arugula Read a Book Buy Milk finish Sit in Chair Sit some More Etc. Read a Book 3

4 Search vs. Planning Planning systems do the following: Relax requirement for sequential construction of solutions Add actions to plan wherever needed, rather than an incremental sequence starting at initial state No connection between order of planning and order of execution *** Most parts of world are independent of most other parts Divide-and-conquer by sub-goaling Easier to solve several small sub-problems rather than one big problem However, can be difficult to put sub-plans together 4

5 STRIPS Planning Classical representation language of planners (STRIPS) STanford Research Institute Problem Solver 5

6 Language of Planning Representation of states Decompose world into logical conditions as conjunction of positive literals At(P1, Columbus) At(P2, Boston) Representation of goals Partially specified state as conjunction of positive ground literals At(P2, Miami) Representation of actions Specified in terms of preconditions that must hold before action can be executed, and the effects after execution ACTION(Fly(p, from, to)) Precondition: Effect: 6

7 Action Schema An action schema consists of 3 parts: Action name and parameter list: Fly(p, from, to) Preconditions as conjunction of positive literals stating what must be true before action can be executed Precondition: At(p, from) Plane(p) Airport(from) Airport(to) Effects as conjunction of positive or negative literals describing how the state changes when action is executed Effect: At(p, from) At(p, to) 7

8 Semantics An action is applicable in any state that satisfies the precondition Otherwise the action has no effect Establishing applicability involves a substitution for the precondition variables 8

9 Semantics Consider current state defined by At(P1, JFK) At(P2, SFO) Plane(P1) Plane(P2) Airport(JFK) Airport(SFO) This state satisfies precondition At(p, from) Plane(p) Airport(from) Airport(to) with substitution {p/p1, from/jfk, to/sfo} Thus action Fly(P1, JFK, SFO) is applicable 9

10 Frame Problem What changes and what does not change in the world when execute actions? Consider robot hand picking up an object Does change: location of object, robot hand now holding object Does NOT change: the locations of all other objects Frame Problem: How does one determine and keep track of what changes and what stays the same when an operator/action is applied in a particular state? 10

11 Dealing with Frame Problem in STRIPS Being in state s, the result after executing action a is state s The new state s is same as s, except any positive literal P in the effect of a is added to s and any negative literal P is removed from s Current state (before action): At(P1, JFK) At(P2, SFO) Plane(P1) Plane(P2) Airport(JFK) Airport(SFO) Action: Fly(p, from, to) has effect At(p, from) At(p, to) Current (new) state (after action): At(P1, SFO) At(P2, SFO) Plane(P1) Plane(P2) Airport(JFK) Airport(SFO) Removed At(P1, JFK) and added At(P1, SFO) (Notice Airport(JFK) still included) 11

12 Dealing with Frame Problem in STRIPS If positive effect is already in state s (before executing action), then it is not added twice If negative effect is not in s, then that part of the effect is ignored STRIPS assumption: Every literal not mentioned in the effect remains unchanged e.g., Airport(JFK) 12

13 Planning Algorithms Most straightforward approach is state-space search Forward Forward from initial state or Backward from the goal At(P1, A) At(P2, A) Fly(P1, A, B) Fly(P2, A, B) At(P1, B) At(P2, A) At(P1, A) At(P2, B) Backward At(P1, A) At(P2, B) At(P1, B) At(P2, A) Fly(P1, A, B) Fly(P2, A, B) At(P1, B) At(P2, B) 13

14 Forward State-Space Search Similar to past problem solving approach Start with initial state, considering sequences of actions until find sequence reaching goal state Initial state Set of positive ground literals Actions Applicable to state only if preconditions satisfied Adding positive and removing negative effects Goal test Checks if state satisfies planning goal Step cost Seldom addressed in STRIPS Typically each is 1 14

15 Backward State-Space Search Sometimes called regression planning Advantage is that consider only relevant actions Those actions that achieve one of the conjuncts of the goal *** Typically much lower branching factor than forward search *** 15

16 Backward Planning Process Given a goal G, let action A be relevant The corresponding predecessor Any positive effects of A in G are deleted Each precondition of A is added (unless already appears) Must insist that actions not undo any desired literals Use standard search algorithms to carry out search Terminate when predecessor is satisfied by the initial state 16

17 Total-Order Planning Start Forward and backward search are particular forms of totally ordered plan search Make decisions on linear sequences of actions, rather than work on each sub-problem separately Right Sock Left Sock Right Shoe Left Shoe Finish 17

18 Interleaving Planners in early 1970 s worked with totally ordered action sequences Computed subplan for each subgoal, and then string subplans together in some order However, not work for even some simple problems Sussman Anomaly 18

19 Sussman Anomaly B C A A B C Start State Goal State Final state requires On(A,B) and On(B, C) Try to focus on backward subgoal On(B,C) first Now trying to put A on top of B cannot be done without undoing On(B, C) Or try to focus on subgoal On(A, B) first But now trying to put B on top of C would cause On(A,B) to be undone Need interleaving of actions from different subplans! 19

20 Partial-Order Planning Prefer approach that works on several sub-goals independently, solves with sub-plans, and then combines the sub-plans Any planning algorithm that can place two actions into a plan without specifying which comes first is called a partial-order planner (Note that a partial-order plan can be linearized into total-order plans) 20

21 Partially-Ordered Plan Totallyordered plans Start Right Sock Left Sock Right Shoe Start Left Sock Right Sock Right Shoe Partial-order plan: Left Sock LeftSockOn Left Shoe Start Right Sock RightSockOn Right Shoe LeftShoeOn, RightShoeOn Left Shoe Left Shoe Finish Finish Finish 21

22 Partial-Order Planner Partial-order planner has 4 components First two define steps of the plan Last two serve as bookkeeping to extend plan 1: Set of actions that make up steps of plan 2: Set of ordering constraints ( A before B ) 3: Set of causal links ( A achieves p for B ) (A=RightSock),(B=RightShoe),(p=RightSockOn) 4: Set of open preconditions (not achieved by some action in the plan) Planners work to reduce this to the empty set A p B 22

23 Partial-Order Planning Initial plan Start, Finish (Start before Finish) No causal links All preconditions of Finish are open Successor function A Pick an open precondition p i for B/Finish Choose action A that achieves p i for B p 1, p 2 Resolve any conflicts (promotion or demotion) B Goal test Exit if no more open preconditions, else generate new successor 23

24 Promotion/Demotion A clobberer is potentially intervening step that destroys a condition achieved by causal link: Go(Home) clobbers At(Store) S 3 c S 1 S 1 S 1 c S 2 S 3 c c S 2 c S 2 S 3 threatens condition c Demotion of S 3 Promotion of S 3 S 3 c 24

25 Example: Blocks World B C A A B C Start State Goal State STRIPS Actions: 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) 25

26 Example: Blocks World Start On(C,A), On(A,Table), Clear(B), On(B,Table), Clear(C) B C A On(A,B), On(B,C) Finish A B C 26

27 Example: Blocks World Start On(C,A), On(A,Table), Clear(B), On(B,Table), Clear(C) B C A Clear(B), On(B,z:T), Clear(C) PutOn(B,C) On(B,z:T), Clear(C), Clear(z:T), On(B,C) On(A,B), On(B,C) Finish A B C 27

28 Example: Blocks World Start On(C,A), On(A,Table), Clear(B), On(B,Table), Clear(C) B C A Clear(B), On(B,z:T), Clear(C) PutOn(B,C) PutOn(A,B) clobbers Clear(B), so order after PutOn(B,C) Clear(A), On(A,z:T), Clear(B) PutOn(A,B) On(B,z:T), Clear(C), Clear(z:T), On(B,C) On(A,z:T), Clear(B), Clear(z:T), On(A,B) On(A,B), On(B,C) Finish A B C 28

29 Example: Blocks World Start On(C,A), On(A,Table), Clear(B), On(B,Table), Clear(C) B C A On(C,z:A), Clear(C) PutOnTable(C) On(C,z:A), Clear(z:A), On(C, T) Clear(A), On(A,z:T), Clear(B) PutOn(A,B) Clear(B), On(B,z:T), Clear(C) PutOn(B,C) On(B,z:T), Clear(C), Clear(z:T), On(B,C) PutOn(B,C) clobbers Clear(C), so order after PutOnTable(C) On(A,z:T), Clear(B), Clear(z:T), On(A,B) On(A,B), On(B,C) Finish A B C 29

30 Shakey The original STRIPS program was designed to control the robot Shakey (SRI, s). Shakey s world Four rooms along a corridor with a door and a light switch Move from room to room Push movable objects (like boxes) Climb on and off of rigid objects (like boxes) Turn light switches on and off Shakey was capable of moving, grabbing and pushing things, based on plans created by STRIPS In simulation for climbing on boxes and toggling switches 30

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32 Environment for Shakey Room1 Room2 Room3 Room4 Box4 Box3 Box2 Box1 Shakey ls1 ls2 ls3 ls4 Door1 Door2 Door3 Door4 Corridor 32

33 Strips and Shakey Vocabulary and operators Go from current location to y: Go(y) Precondition At(Shakey,x) establishes the current location x and y must be In the same room: In(x,r) In(y,r) A door between two rooms is In both of them Push an object b from location x to y: Push(b,x,y) Needs the precondition predicate Pushable(b) Climb on a box: Climb(b) Introduce a predicate On and constant Floor and add precondition On(Shakey,Floor) to Go Preconditions of Climb(b) are that Shakey is At the same place as b and that b is Climbable 33

34 Strips and Shakey Vocabulary and operators (con t) Climb down from a box: Down(b) Undo the effects of Climb Turn a light switch on/off: TurnOn(ls), TurnOff(ls) Shakey must be on a box at the light switch location 34

35 OSU Med 35

36 Time, Schedules, and Resources STRIPS talks about what actions do, but not about how long an action takes or when an action occurs (except before/after) Consider package delivery Might like to know when package will arrive, not just that it will arrive Time is of the essence General family of job shop scheduling applications 36

37 Expressiveness and Extensions STRIPS is insufficiently expressive for some real-world domains, thus other variants have been developed Action Description Language (ADL) ACTION(Fly(p:Plane, from:airport, to:airport)) Precondition: At(p, from) (from to) Effect: At(p, from) At(p, to) Not go to itself Easier to read (not expressible in STRIPS) 37

38 Expressiveness and Extensions Both STRIPS and ADL adequate for many real domains However some significant restrictions and unnaturalness For example, if people, packages, etc. are in an airplane, then they too change location when plane flies Could specify each item changes location when flying, but would like to have plane contents change with location of plane Common Sense reasoning? 38

39 Summary STRIPS language Preconditions, action, effects Partial-order planning Divide-and-conquer by sub-goaling Relax requirement for sequential construction of solutions Shakey the robot 39