heuristic planning with time and resources

Heuristic Planning with Time and Resources

--Sapa, TP4, and others

Quiz1: Expressiveness of Temporal Action

• ZENO

• TGP

• TP4

• Sapa

ts te

ts te

ts te

effectprecondition

Sapa and TP4Sapa TP4

Search Direction

Search Space

Branching Rule

Extension

Concurrency

Path Cost

Heuristic

Integrating resource

Forward chaining Backward chaining

Sapa: search space

S = ( P, M, II, Q, t)

P: set of predicates that are true

M: set of functions representing metric-resources

II: set of persistent conditions that need to be protected for a while

Q: queue containing scheduled future events

t: time stamp

P= {(pi, ti)|ti<t}: set of predicates that are true at t and achieved at ti

Sapa: Search Space

The initial state S0=(P,M,II,Q,t)P= {(pi, ti)|ti<t}: p is true at t and achieved at ti

M: metric-resources

II: persistent conditions

Q: scheduled future events

t: time stamp

--P= (pi, to), piIp

--M given resource constraints--Q empty, II empty

Sapa: Search Space

The state S=(P,M,II,Q,t)entails the goal G if

P= {(pi, ti)|ti<t}: p is true at t and achieved at ti

M: metric-resources



t: time stamp

--(pi, ti)G, (pi, tj)P, tj<=ti, no event in deletes pi

-- eQ adds pi at tj, tj<=ti

Sapa: Action Application

Giving S=(P,M,II,Q,t), an action A is applicable in S if:


M: metric-resources



t: time stamp

-- All instant-pre(A) |= P,M

-- eff(A) not interfere with

II and Q

-- no eQ interferes with

persistent-pre(A)

Sapa: branching rule

Choose an action A applicable in S,if A != no-op

S’ = ApplyInstantaneousUpdates ( S, A )Q’ = AddDelayedEvents ( Q, S, A)

Else S’ = SS’.t = eventTime( Front(Q) )While eventTime(Front(Q)) == S’.t

e = Dequeue(Q);S’ = ApplyEffect(S’, e );

TP4: search space

S = ( E, F, t)

E: set of predicates that are required to be true

t: time stamp

F= {(ai, i)}: action ai is planned to start at t- i

TP4: Search Space

The initial state S0=?• E={pi}: pi is required to be true at t

• F= {(ai, i)}: action ai is planned to start at t- i

• t: time stamp

S0= (G, NULL)

The final state S ?

{S= (E, NULL)|EIp}

TP4: Action Application

S=(E,{(aj,j)},t)

A set of actions SE is applicable in S if

• E={pi}: pi is required to be true at t


• t: time stamp -- every action is compatible with each other;

--pE, aSE, padd(a), a is compatible with bF

TP4: branching rule

Choose a set of actions SE applicable in S,

define: Fnew = { (a, dur(a)| aSE }

adv = min{, a!=no-op}

then’ = {pre(a) | (a,)FFnew}

F’ = { (a, adv)| (a,)FFnew, adv}

S’ = (E’, F’)


Search Direction

Search Space State world & state of search so far

Branching Rule Sound & complete Sound & incomplete

Extension

Concurrency

Path Cost

Heuristic



Quiz 2: Concurrency

qpre(a)

!qdelayed-effect(b)

Quiz 2: Concurrency

qinstant-effect(a)

!qdelayed-effect(b)


Search Direction



Concurrency

(temporal)Proposition lock (“holding”)

Proposition lock

Extension Easy? Limited?

Path Cost

Heuristic




Search Direction



Concurrency


Proposition lock

Extension

Heuristic

Path Cost



Sapa: Extension?


M: metric-resources



t: time stamp

an action A is applicable in S=(P,M,II,Q,t) if:

-- All instant-pre(A) |= P,M

-- eff(A) not interfere with II and Q

-- no eQ interferes with persistent-pre(A)

II = { (prea, t2 ) }

All (pre(a), -t1) |= P, M

TP4: Extension?

A set of actions SE is applicable in S=(E, F, t) if:

-- every action is compatible with each other;

--pE, aSE, padd(a), a is compatible with bF

E={ p| p is true during [t1, t2] }

• E={pi}: pi is required to be true at t


• t: time stamp


Search Direction



Concurrency


Proposition lock


Path Cost

Heuristic




Search Direction



Extension Easy? Limited?Concurrency


Proposition lock

Heuristic

Path Cost



Sapa: Heuristic Function

Relaxed temporal planning graph(RTPG)

-- no delete list

-- no resource consumption

Max-span?

Min-slack?

Max-slack?

Sum-slack?

Sum-action?

Sum-duration?

Sapa: Heuristic Function

Max-span? Min-slack? Max-slack? Sum-slack?

Sum-action? Sum-duration?

TP4: Heuristic Functions

kFa

iFa

kiiikk

apreHFEH

,)(max),(,),(

*

),(

*

,)(),(),(

** Fa

i

ii

apreEHFEH

,max),( *

||,

* EHEHmEEE


Search Direction





Proposition lock

Heuristic RTGP DP

Path Cost depends c(S, S’)=adv



TP4: Incremental Branching

• Estimating the cost of Partial States– Estimate lower bounds on p

• Ordering predicates in a state-- decreasing order of “difficulty”

• Right-shift equivalence-- if an action was applicable but was not used, then it

won’t be used


Search Direction





Proposition lock

Heuristic RTGP DP




Resource Management

• Producible

• Consumable

• Reusable

• Shareable

• Non-shareable

• Limited-capacity

Sapa: resource management

• Producable, consumable, non-shareable

Sum-duration

Sum-action

• Shareable ?

TP4: resource management

• Reusable & Non-shareable?

• Reusable & Limited-capacity?

• Consumable & non-producible?


Search Direction Forward chaining Backward chaining

Search Space S=(P,M,II,Q,t) S=(E,{(aj,j)},t)

Branching Rule Sound complete Sound, incomplete


ConcurrencyProposition lock

Non-shareable resourcesProposition lock (“holding”)


Heuristic RTGP DP


Easy if inadmissible hard

Quiz3: Continuous Change

• ZENO?

• Sapa?

• TGP & TP4?

Experiments

TGP

ZENO

TP4 Sapa

expressiveness

perf

orm

ance

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heuristic planning with time and resources

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