planning in fol systems sequences of actions to achieve goals

Planning in FOL Systems

sequences of actions to achieve goals

D Goforth - COSC 4117, fall 2006 2

Planning Example: Blocks world objects: blocks on a table actions: move blocks ‘on’ one object

to ‘on’ another object goals: configurations of blocks plan: sequence of actions to achieve

goals

TA B CD


Classical Planning - STRIPS STanford Research Institute Problem

Solver Closed world assumption

facts not in KB are assumed false Predicates in KB must refer to specific

objects (no variables, no functions) Goal – conjunction of positive literals No ‘situation calculus’ – current state

only


Classical Planning - STRIPS actions:

preconditions – predicates that must be in KB

effect – some predicates added to KB and some predicates removed (‘negated’)

plan – sequence of actions to get goal predicates into KB

Blocks world objects: A, B, C, D, T KB:On(A,T)Ôn(B,T)Ôn(C,T)Ôn(D,C)^Block(A)^Block(B)^Block(C)^Block(D)^Clear(A) ^Clear(B )^Clear(D) ^Clear(T)*

Goal: On(A,B)Ôn(B,C)

TA B CD

* Clear(x) means “there is space on x for a block”

Blocks world actions:Move(b,x,y) // move b from x to y

PRE:On(b,x)^Clear(b)^Clear(y)^Block(b)^Block(y)EFFECT:On(b,x)^Clear(y)^Clear(x)^On(b,y)

MoveToTable(b,x) // move b from x to tablePRE:On(b,x)^Clear(b) ^Block(b) ^Block(x)EFFECT:On(b,x)^Clear(x)^On(b,T)

// remove from KB; add to KB

TA B CD


STRIPS requirements need ‘Clear’ because Clear cannot be

inferred from the ‘On’ predicates need two Move actions to manage the

‘clear table’ problemunsolved problem:can’t avoid ‘repeated literal’ problemMove(B,C,C)


Planning – state space search current KB is current state applying an action is an edge revised KB is next state from current KB, search for path of

actions to state containing goal

Blocks worldKB:On(A,T)Ôn(B,T)Ôn(C,T)Ôn(D,C)^Block(A)^Block(B)^Block(C)^Block(D)^Clear(A)^Clear(B) ^Clear(D) ^Clear(T)TA B C

D

KB:On(A,D)Ôn(B,T)Ôn(C,T)Ôn(D,C)^Block(A)^Block(B)^Block(C)^Block(D)^Clear(A) ^Clear(B) ^Clear(T)T

A

B CD

Move(A,T,D)


Forward search irrelevant action problem: actions that

are possible lead to large branching needs good heuristic to be efficient

(breaks FOL domain independence)


Backward search actions with goal state as ‘effect’ are

‘regressed’ focus on ‘relevant’ actions avoid actions that undo goal state

predicates

goal state predicates

previous state predicates undo action

effects

add preconditions

Blocks world – preconditions matchGoal: On(A,B)Ôn(B,C)

T

AB C

D

On(A,T)Ôn(B,T)Ôn(C,T)Ôn(D,C)^Block(A)^Block(B)^Block(C)^Block(D)^Clear(A) ^Clear(B) ^Clear(T)

TA B CD

Move(A,x,B){T/x}

Preconditions for Move(A,T,B)

Blocks world – preconditions not matchGoal: On(A,B)Ôn(B,C)

TA

BD

On(A,T)Ôn(B,T)Ôn(C,T)Ôn(D,C)^Block(A)^Block(B)^Block(C)^Block(D)^Clear(A) ^Clear(B)^Clear(D)^Clear(T)

TA B

C

D

Move(B,x,C){T/x}

C

On(B,T)^Block(B)^Block(C)^Clear(C) ^Clear(B)A B DC

TMoveToTable(y,C)

{D/y}


State space search algorithms heuristics:

admissible (don’t overestimate path cost) generic heuristics not domain dependent

relaxed problem – reduce preconditions, remove negative effects

independent subgoals – achieve goal predicates one at a time: assume one goal does not help or prevent another

Blocks world - heuristicsMove(b,x,y)

PRE:On(b,x)^Clear(b)^Clear(y)^Block(b)^Block(y)EFFECT:On(b,x)^Clear(y)^Clear(x)^On(b,y)

MoveToTable(b,x)PRE:On(b,x)^Clear(b)^Block(b)EFFECT:On(b,x)^Clear(x)^On(b,T)

For example goal On(A,B) On(B,C):Heuristic “independent subgoals” On(A,B) and On(B,C)simplifies because On(A,B) interferes with On(B,C)Heuristic “relaxed problem” remove preconditions,

negatives

TA B CD


Partial Order Planning since GPS (General Problem Solver),

understood getting the major steps in place first

improves planning e.g. car trip including a ferry crossing

plans built in mixed order, not just forward or backward


Partial Order Planning in many plans, order of some steps

does not matter if parts of goal are independent, does not

matter which goal is achieved first

TA B C DGoal: On(A,B)^On(C,D)


Partial Order Planning planning takes place in ‘plan space’

of partial plans a partial plan contains:

1. actions, A, B, C, ...,Start, Finish2. ordering constraint between some

actions: A must be done before B: A B 3. causal links: A produces a precondition

for B:4. set of unachieved preconditions (empty

in final plan)


The empty plan (root of plan search space tree)

Action: StartPRE: noneEFFECT: start state of space

Action: FinishPRE: goal predicatesEFFECT: none

T

AB C

D

AB

D

On(A,B)On(B,T)On(D,C)On(C,T)

On(A,B)On(B,C)On(C,D)

C

open{On(B,C),On(C,D)}

Start Finish

NOTE: some predicates not shown – Clear in KB

A partial planAction: StartPRE: noneEFFECT: On(A,B),On(B,T),On(D,C),On(C,T)

Action: FinishPRE: On(A,B),On(B,C),On(C,D) EFFECT: none

T

AB C

D

AB

DC

open{On(C,D)}

Action: M(B,T,C)PRE: Clear(B),Clear(C)EFFECT: On(B,C)

Start M

causal On(B,C)

A partial planAction: StartPRE: noneEFFECT: On(A,B),On(B,T),On(D,C),On(C,T)

Action: FinishPRE: On(A,B),On(B,C),On(C,D) EFFECT: none

T

AB C

D

AB

DC

open{On(A,B),On(C,D)}

Action: M(B,T,C)PRE: Clear(B),Clear(C)EFFECT: On(B,C)

Action: MT(A,B)PRE: Clear(A)EFFECT: On(A,T),Clear(B)

The complete partially ordered plan Action: Start

Action: FinishPRE: goal

AB C

D

AB

D

On(A,B)On(B,T)On(D,C)On(C,T)

On(A,B)On(B,C)On(C,D)

C

Action: MT(A,B) Action: MT(D,C)

Action: M(C,T,D)

Action: M(B,T,C)

Action: M(A,T,B)

open{}

The total order plans Action: Start


Action: MT(A,B)

Action: MT(D,C)

Action: M(C,T,D)

Action: M(B,T,C)

Action: M(A,T,B)

Action: Start


Action: MT(D,C)

Action: MT(A,B)

Action: M(C,T,D)

Action: M(B,T,C)

Action: M(A,T,B)


Heuristics for partial order plans size of open precondition set

number of unachieved goal predicates overestimates remaining actions if

some actions achieve multiple goals underestimates remaining actions if

some actions will undo preconditions(e.g. taking A off B)

planning in fol systems sequences of actions to achieve goals

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