AI Planning References: - Russell and Norvig, Artificial Intelligence: A modern approach, 2nd ed. Prentice Hall, 2003 - PRODIGY4.0: The Manual and Tutorial by the Prodigy Research Group, Dept. of Computer Science, Carnegie Mellon University, Technical Report CMU-CS-92-150, 1992. 1
Outline Introduction Search vs. Planning Representation of a planning domain / problem Linear planning with STRIPS
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Introduction
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Who plans? Business people: creation of business plans Lawyers: plan a client’s defense Industry: plan robot movements for production Architects: design plans for buildings Computer scientists: plan a system’s development
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Who plans? Telecommunications: plan connection setting Army: create plans for attack, defense, troop deployment Transportation logistics: plan moving objects/persons between locations
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What do they have in common? Search in a state space State: a snapshot of the world Action or operator: transformation of a state into the next
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What do they have in common? Initial state: starting point Goal: conditions for termination of the process Plan: sequence of operators that transform the initial state into a state that meets the goal Heuristics: knowledge to guide the search to make it more efficient
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Tourist example State person’s
location, time and money constraints, … airline (and other) ticket prices, schedules and availability
Operators fly
on a given flight travel on a given train take a cab stay in a bed & breakfast, 8
Tourist example Initial state we
are in Madrid (home)
Goal spend
one week in Pittsburgh
Plan takeCab
(Home, BarajasAirport), takeFlight(MAD,PIT), takeCab(PIT,___Hotel), ...
Heuristics make
a reservation, prefer airlines with frequentflyer membership 9
Search vs. Planning
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Search vs. planning Consider the task get milk, bananas, and a cordless drill Standard search algorithms seem to fail miserably: why?
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Search vs. planning
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Search vs. planning Search
Planning
States
Lisp data structures
Logical sentences
Actions
Lisp code
Preconditions/effects
Goal
Lisp code
Logical sentence (conjunction)
Plan
Sequence from S0
Sequence of actions (linear) Constraints on actions (partial order)
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Representation of a Planning Domain / Problem
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An example of a planning domain blocksworld
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Blocksworld Problem: build one or more stacks specified in terms of what blocks are on top of other blocks
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Blocksworld Underlying hypotheses:
Set of cube-shaped blocks sitting on a table All blocks are equal except for the name The table is unlimited in size Block position on table does not matter A robot arm can pick one block at a time (only if block has nothing on top) Blocks can be stacked, but only one block fits on top of another 17
Blocksworld Actions Blocks
are picked up and put down by the arm Arm can hold only one block at a time
Goal Build
towers of blocks (size, order, etc)
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Representing the blocksworld Objects Blocks:
A, B, C Table: Table
States Conjunctions
of ground literals On(A, B), OnTable(C), Clear(B), ArmEmpty, Holding(C)
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Representing the blocksworld Actions Operator
schemas with variables e.g.: PickUp(x), PutDown(x, y)
Domain Axioms “At
most one block on top of another” “Hand (i.e. the robot arm) must be initially empty and block must be clear to pick it up”
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Representation First order logic is the most frequent representation formalism for states, actions, etc. It
is expressive enough to describe a wide variety of problems It is restrictive enough to design efficient algorithms
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State representation Let us consider predicate schemata (i.e., predicates that have free variables) Examples: HasMoney(x,y) FlightReservation(x,
flight, date) FlightInfo(number, origin, destination, departuretime, arrival-time) ...
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State representation A state is represented by a conjunction of instantiated (i.e. “ground”) predicates; e.g.: HasMoney(Mary,1000), FlightReservation(Mary,
AA304, 3-Nov-99) FlightInfo(AA304, Madrid, NewYork,12:05,12:30)
Instantiated predicates are function free We assume that what is not explicitly represented as part of the state is false (closed world assumption) 23
STRIPS operators Tidily arranged actions descriptions, restricted language Abstracting away many important details! Restricted language ⇒ efficient algorithm
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STRIPS operators An action schema has three parts: Action
name (with parameter list) Precondition: Conjunction of function-free positive literals stating what must be true in the state before the action can be executed Effect: conjunction of function-free literals describing state changes
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STRIPS operators - ADD list: asserted to be true in An action schema has three parts: state
the new
DEL asserted to be name-state (withlist:parameter list)false in the new Precondition: Conjunction of function-free positive literals stating what must be true in the state before the action can be executed Effect: conjunction of function-free literals describing state changes
Action
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STRIPS operators: An example ACTION SCHEMA: Buy(x) PRECONDITION: At(p) ∧ Sells(p,x) EFFECT: Have(x)
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STRIPS operators: An example ACTION SCHEMA: Buy(x) PRECONDITION: At(p) ∧ Sells(p,x) EFFECT: Have(x)
STRIPS assumption: every literal not mentioned in the effect remains unchanged
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STRIPS operators: Another example ACTION SCHEMA: Fly(p,from,to) PRECOND: At(p,from) ∧ Plane(p) ∧ Airport(from) ∧ Airport(to) DEL-LIST: At(p,from) ADD-LIST: At(p,to)
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STRIPS operators: Another example ACTION SCHEMA: Fly(p,from,to) PRECOND: At(p,from) ∧ Plane(p) ∧ Airport(from) ∧ Airport(to) DEL-LIST: At(p,from) ADD-LIST: At(p,to)
Any variable in the precondition and effect lists must also appear in the action’s parameter list 30
Blocksworld (typical) predicates
Initial state
Goal description
On(x,y): block x is on top of block y OnTable (x): block x is on the table Clear(x): block x has nothing on top Holding(x): the robot arm is holding block x ArmFree: the arm is not holding anything 31
Blocksworld (typical) predicates
Initial state
Goal description
Initial state:
On(A,B), On(B,D), OnTable(D), OnTable(C), Clear(A), Clear(C), ArmFree Goal:
OnTable(A),On(C,B) 32
Blocks world (typical) operators - UNSTACK(x, y)
PRE: On(x,y), Clear(x), ArmFree ADD: Holding(x), Clear(y) DEL: On(x,y), ArmFree, Clear(x)
- STACK(x, y)
PRE: Holding(x),Clear(y) ADD: On(x,y),Clear(x), ArmFree DEL: Holding(x), Clear(y)
- PICKUP(x)
PRE: OnTable(x), Clear(x), ArmFree ADD: Holding(x) DEL: OnTable(x), ArmFree, Clear(x)
- PUTDOWN(x)
PRE: Holding(x) ADD: OnTable(x), Clear(x), ArmFree DEL: Holding(x)
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Linear Planning with STRIPS
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A typical generic agent architecture
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How do we plan? Means-ends analysis (MEA) Focusing
on the ends (goals) and the means to achieve them (operators)
Decomposing problems into subproblems ... Hierarchically
(abstraction techniques) Based on previous experience/plans (case-based planning) Reactively (reactive agents / replanning)
Considering other agents Obtaining
the planning capability as an emerging property (in a society of agents) 36
Some difficult issues Our world view may be limited (bounded rationality) The world may be constantly changing (dynamic environment) Action execution takes time (temporal reasoning) Contradictory goals (goal dependencies) Our world model fails (uncertainty) 37
Some difficult issues Plans are not always valid (execution and replanning) Some plans are not good enough (quality of plans) We must find a way to adapt to the world (adaptive capability / learning)
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Linear Planning: STRIPS Precursor: means-ends analysis (GPS 1959) subgoal
based search: given a goal, choose an op to achieve it
STRIPS idea: choose
a goal conjunct (i.e. an element of the conjunction that characterizes the goal) choose an instantiated operator that achieves it operator preconditions become new subgoals (cf backward chaining)
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Linear Planning: STRIPS Frame problem: What happens to the world context when an action is executed? Solution: STRIPS assumption: every literal not mentioned in the operator effect remains unchanged
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Representation Recall terms, predicates, connectives, quantifiers Example: ∀ x,y student(x) ∧ subject(y) ∧ [¬ passed(x,y) ∨ firsttime(x,y)] ⇒ register(x,y) There is no single representation for a domain!
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Linear Planning: STRIPS Search: Nodes: current state + goal-operator stack Root node: initial state and goal conjunction Heuristics: always choose a relevant operator (achieves one of the goal conjuncts)
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Linear Planning: STRIPS Idea: Push into the stack goals and operators to achieve them Pop from stack goals that are true in current state, as well as executed operators
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STRIPS Algorithm repeat until [empty stack] or [no more nodes can be expanded] if [stack top is an instantiated operator] if [instantiated op can be executed] then [execute operator], [pop operator from stack and add it to the plan] else [push operator preconditions into stack] if [stack top is a goal conjunction] if [the conjunction is true in the current state] then [pop it from stack] else [generate as successors all possible orderings of the goals] [choose one of the goals and push into stack] if [stack top is a goal] if [the goal is true in the current state] then [pop it from the stack] else if [there is a goal loop] then [backtrack] else for each [instantiated operator that adds that goal] [create a successor] if [there are successors] then [choose one] else [backtrack], [push the goal into stack] 44
INIT: OnTable(B) On(A,B) Clear(A) ArmFree
PICKUP(A) Holding(A) PUTDOWN(A) OnTable(A)
X
S0
S0
PUTDOWN(A) OnTable(A)
S0
Holding(A) PUTDOWN(A) OnTable(A)
S0
UNSTACK(A,A) Holding(A) PUTDOWN(A) OnTable(A)
S0
goal loop X
S0
A
Initial state S0
UNSTACK(A,B) Holding(A) PUTDOWN(A) OnTable(A)
S0
A
… OnTable(A) Clear(A) ArmFree OnTable(A),Clear(A), ArmFree PICKUP(A)…OnTable(A)
A B
Goal
X
X OnTable(A),Clear(A), ArmFree PICKUP(A) Holding(A) PUTDOWN(A) OnTable(A)
OnTable(A)
X
X
B S1
B S2
A
S0
√ Clear(A),ArmFree,On(A,B)
S0
√ Holding(A)
S1
UNSTACK(A,B) Holding(A) PUTDOWN(A) OnTable(A)
PUTDOWN(A) OnTable(A)
√ OnTable(A)
S 45 2
