Planning in a Single Agent

Transcription

1 What is Planning Planning in a Single gent Sattiraju Prabhakar Sources: Multi-agent Systems Michael Wooldridge I a modern approach, 2 nd Edition Stuart Russell and Peter Norvig Generate sequences of actions to perform tasks and achieve objectives. States, actions and goals Search for solution over abstract space of plans. ssists humans in practical applications design and manufacturing military operations games space exploration 9/25/2005 MS_Planning 2 goal/ intention/ task state of environment planner possible action 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 DL plan to achieve goal 9/25/2005 MS_Planning 3 9/25/2005 MS_Planning 4 1

2 Planning The Blocks World Question: How do we represent... goal to be achieved state of environment actions available to agent plan itself B Contains a robot arm, 3 blocks (, B, and C) of equal size, and a table-top C 9/25/2005 MS_Planning 5 9/25/2005 MS_Planning 6 The Blocks World Ontology The Blocks World To represent this environment, need an ontology On(x, y) obj x on top of obj y OnTable(x) obj x is on the table Clear(x) nothing is on top of obj x Holding(x) arm is holding x Here is a representation of the blocks world described above: Clear() On(, B) OnTable(B) OnTable(C) B C Use the closed world assumption: anything not stated is assumed to be false 9/25/2005 MS_Planning 7 9/25/2005 MS_Planning 8 2

3 The Blocks World goal is a state (or a sequence of states) of the environment represented as a set of formulae Here is a goal: OnTable() OnTable(B) OnTable(C) B C The Blocks World Operators B Example 1: The stack action occurs when the robot arm places the object x it is holding is placed on top of object y. Stack(x, y) pre Clear(y) Holding(x) del Clear(y) Holding(x) add rmempty On(x, y) 9/25/2005 MS_Planning 9 9/25/2005 MS_Planning 10 The Blocks World Operators Example 2: The unstack action occurs when the robot arm picks an object x up from on top of another object y. UnStack(x, y) pre On(x, y) Clear(x) rmempty del On(x, y) rmempty add Holding(x) Clear(y) Stack and UnStack are inverses of one-another. B 9/25/2005 MS_Planning 11 The Blocks World Operators Example 3: The pickup action occurs when the arm picks up an object x from the table. Pickup(x) pre Clear(x) OnTable(x) rmempty del OnTable(x) rmempty add Holding(x) Example 4: The putdown action occurs when the arm places the object x onto the table. pre del add Putdown(x) Holding(x) Holding(x) Clear(x) OnTable(x) rmempty 9/25/2005 MS_Planning 12 3

4 Example: Blocks world Init(On(, Table) On(B,Table) On(C,Table) Block() Block(B) Block(C) Clear() Clear(B) Clear(C)) Goal(On(,B) On(B,C)) ction(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)) ction(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) The Blocks World ctions are represented using a technique that was developed in the STRIPS planner Each action has: a name which may have arguments a pre-condition list list of facts which must be true for action to be executed a delete list list of facts that are no longer true after action is performed an add list list of facts made true by executing the action Each of these may contain variables 9/25/2005 MS_Planning 13 9/25/2005 MS_Planning 14 General language features General language features Representation of states Decompose the world in logical conditions and represent a state as a conjunction of positive literals. Propositional literals: Poor Unknown FO-literals (grounded and function-free): t(plane1, Melbourne) t(plane2, Sydney) Closed world assumption Representation of goals Partially specified state and represented as a conjunction of positive ground literals goal is satisfied if the state contains all literals in goal. Representations of actions ction = PRECOND + EFFECT ction(fly(p,from, to), PRECOND: t(p,from) Plane(p) irport(from) irport(to) EFFECT: T(p,from) t(p,to)) = action schema (p, from, to need to be instantiated) ction name and parameter list Precondition (conj. of function-free literals) Effect (conj of function-free literals and P is True and not P is false) dd-list vs delete-list in Effect 9/25/2005 MS_Planning 15 9/25/2005 MS_Planning 16 4

5 Language semantics? Language semantics? How do actions affect states? n action is applicable in any state that satisfies the precondition. For FO action schema applicability involves a substitution θ for the variables in the PRECOND. t(p1,jfk) t(p2,sfo) Plane(P1) Plane(P2) irport(jfk) irport(sfo) Satisfies : t(p,from) Plane(p) irport(from) irport(to) With θ ={p/p1,from/jfk,to/sfo} Thus the action is applicable. The result of executing action a in state s is the state s s is same as s except ny positive literal P in the effect of a is added to s ny negative literal P is removed from s t(p1,sfo) t(p2,sfo) Plane(P1) Plane(P2) irport(jfk) irport(sfo) STRIPS assumption: (avoids representational frame problem) every literal NOT in the effect remains unchanged 9/25/2005 MS_Planning 17 9/25/2005 MS_Planning 18 Expressiveness and extensions Example: air cargo transport STRIPS is simplified Important limit: function-free literals llows for propositional representation Function symbols lead to infinitely many states and actions Recent extension:ction Description language (DL) ction(fly(p:plane, from: irport, to: irport), PRECOND: t(p,from) (from to) EFFECT: t(p,from) t(p,to)) Init(t(C1, SFO) t(c2,jfk) t(p1,sfo) t(p2,jfk) Cargo(C1) Cargo(C2) Plane(P1) Plane(P2) irport(jfk) irport(sfo)) Goal(t(C1,JFK) t(c2,sfo)) ction(load(c,p,a) PRECOND: t(c,a) t(p,a) Cargo(c) Plane(p) irport(a) EFFECT: t(c,a) In(c,p)) ction(unload(c,p,a) PRECOND: In(c,p) t(p,a) Cargo(c) Plane(p) irport(a) EFFECT: t(c,a) In(c,p)) ction(fly(p,from,to) PRECOND: t(p,from) Plane(p) irport(from) irport(to) EFFECT: t(p,from) t(p,to)) [Load(C1,P1,SFO), Fly(P1,SFO,JFK), Load(C2,P2,JFK), Fly(P2,JFK,SFO)] Standardization : Planning domain definition language (PDDL) 9/25/2005 MS_Planning 19 9/25/2005 MS_Planning 20 5

6 Example: Spare tire problem Progression algorithm Init(t(Flat, xle) t(spare,trunk)) Goal(t(Spare,xle)) ction(remove(spare,trunk) PRECOND: t(spare,trunk) EFFECT: t(spare,trunk) t(spare,ground)) ction(remove(flat,xle) PRECOND: t(flat,xle) EFFECT: t(flat,xle) t(flat,ground)) ction(puton(spare,xle) PRECOND: t(spare,groundp) t(flat,xle) EFFECT: t(spare,xle) r(spare,ground)) ction(leaveovernight PRECOND: EFFECT: t(spare,ground) t(spare,xle) t(spare,trunk) t(flat,ground) t(flat,xle) ) This example goes beyond STRIPS: negative literal in pre-condition (DL description) Formulation as state-space search problem: Initial state = initial state of the planning problem Literals not appearing are false ctions = those whose preconditions are satisfied dd 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 9/25/2005 MS_Planning 21 9/25/2005 MS_Planning 22 Regression algorithm Regression algorithm How to determine predecessors? What are the states from which applying a given action leads to the goal? Goal state = t(c1, B) t(c2, B) t(c20, B) Relevant action for first conjunct: Unload(C1,p,B) Works only if pre-conditions are satisfied. Previous state= In(C1, p) t(p, B) t(c2, B) t(c20, B) Subgoal t(c1,b) should not be present in this state. ctions must not undo desired literals (consistent) Main advantage: only relevant actions are considered. Often much lower branching factor than forward search. General process for predecessor construction Give a goal description G Let be an action that is relevant and consistent The predecessors is as follows: ny positive effects of that appear in G are deleted. Each precondition literal of is added, unless it already appears. ny 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. 9/25/2005 MS_Planning 23 9/25/2005 MS_Planning 24 6

7 Planning with state-space search What is Means-End Reasoning? Both forward and backward search possible Progression planners forward state-space search Consider the effect of all possible actions in a given state Regression planners backward state-space search To achieve a goal, what must have been true in the previous state. Basic idea is to give an agent: representation of goal/intention to achieve representation actions it can perform representation of the environment and have it generate a plan to achieve the goal Essentially, this is automatic programming 9/25/2005 MS_Planning 25 9/25/2005 MS_Planning 26 Plan The STRIPS approach a1 I a17 a142 G The original STRIPS system used a goal stack to control its search The system has a database and a goal stack, and it focuses attention on solving the top goal (which may involve solving subgoals, which are then pushed onto the stack, etc.) What is a plan? sequence (list) of actions, with variables replaced by constants. 9/25/2005 MS_Planning 27 9/25/2005 MS_Planning 28 7

8 The Basic STRIPS Idea Place goal on goal stack: Goal1 Considering top Goal1, place onto it its subgoals: GoalS1-2 GoalS1-1 Goal1 Then try to solve subgoal GoalS1-2, and continue 9/25/2005 MS_Planning 29 Stack Manipulation Rules, STRIPS If on top of goal stack: Compound or single goal matching the current state description Compound goal not matching the current state description Single-literal goal not matching the current state description Rule Nothing Then do: Remove it 1. Keep original compound goal on stack 2. List the unsatisfied component goals on the stack in some new order Find rule whose instantiated add-list includes the goal, and 1. Replace the goal with the instantiated rule; 2. Place the rule s instantiated precondition formula on top of stack 1. Remove rule from stack; 2. Update database using rule; 3. Keep track of rule (for solution) Stop Underspecified there are decision branches here within the search tree 9/25/2005 MS_Planning 30 8