Heuristic Planning with Time and Resources --Sapa, TP4, and others

Quiz1: Expressiveness of Temporal Action precondition effect ZENO TGP TP4 Sapa ts te ts te ts te

Sapa and TP4 Sapa TP4 Search Direction Search Space Forward chaining Branching Rule Extension Concurrency Path Cost Heuristic Integrating resource Forward chaining Backward chaining

Sapa and TP4 Sapa TP4 Search Direction Search Space Forward chaining Branching Rule Extension Concurrency Path Cost Heuristic Integrating resource Forward chaining Backward chaining

Sapa: search space S = ( P, M, II, Q, t) t: time stamp P: set of predicates that are true P= {(pi, ti)|ti<t}: set of predicates that are true at t and achieved at ti II: set of persistent conditions that need to be protected for a while Q: queue containing scheduled future events M: set of functions representing metric-resources

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 The initial state S0=(P,M,II,Q,t) --P= (pi, to), piÎIp --M given resource constraints --Q empty, II empty

Sapa: Search Space The state S=(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 The state S=(P,M,II,Q,t) entails the goal G if --(pi, ti)ÎG,  (pi, tj)ÎP, tj<=ti, no event in deletes pi -- eÎQ adds pi at tj, tj<=ti

Sapa: Action Application Giving S=(P,M,II,Q,t), an action A is applicable in S if: 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 -- All instant-pre(A) |= P,M -- eff(A) not interfere with II and Q -- no eÎQ 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’ = S S’.t = eventTime( Front(Q) ) While eventTime(Front(Q)) == S’.t e = Dequeue(Q); S’ = ApplyEffect(S’, e );

TP4: search space S = ( E, F, t) t: time stamp E: set of predicates that are required to be true F= {(ai, di)}: action ai is planned to start at t- di

TP4: Search Space The initial state S0=? S0= (G, NULL) E={pi}: pi is required to be true at t F= {(ai, di)}: action ai is planned to start at t- di t: time stamp The initial state S0=? S0= (G, NULL) The final state S ? {S= (E, NULL)|EIp}

TP4: Action Application E={pi}: pi is required to be true at t F= {(ai, di)}: action ai is planned to start at t- di t: time stamp S=(E,{(aj,dj)},t) A set of actions SE is applicable in S if -- every action is compatible with each other; --pE, aSE, padd(a), a is compatible with bF

TP4: branching rule Choose a set of actions SE applicable in S, define: Fnew = { (a, dur(a)| aSE } dadv = min{d, a!=no-op} then E’ = {pre(a) | (a,d)ÎFÈFnew} F’ = { (a, d-dadv)| (a,d)ÎFÈFnew, d>dadv} S’ = (E’, F’)

Sapa and TP4 Sapa TP4 Search Direction Search Space State world & state of search so far Branching Rule Sound & complete Sound & incomplete Extension Concurrency Path Cost Heuristic Integrating resource Forward chaining Backward chaining

Quiz 2: Concurrency qpre(a) !qdelayed-effect(b) What about ZENO? TGP?

Quiz 2: Concurrency qpre(a) !qdelayed-effect(b) What about ZENO? TGP?

Quiz 2: Concurrency qinstant-effect(a) !qdelayed-effect(b) What about ZENO? TGP?

Quiz 2: Concurrency qinstant-effect(a) !qdelayed-effect(b) What about ZENO? TGP?

Sapa and TP4 Sapa TP4 Easy? Limited? Search Direction Search Space State world & state of search so far Branching Rule Sound & complete Sound & incomplete Concurrency (temporal) Proposition lock (“holding”) Proposition lock Extension Easy? Limited? Path Cost Heuristic Integrating resource Forward chaining Backward chaining

Sapa and TP4 Sapa TP4 Search Direction Search Space State world & state of search so far Branching Rule Sound & complete Sound & incomplete Concurrency (temporal) Proposition lock (“holding”) Proposition lock Extension Heuristic Path Cost Integrating resource Forward chaining Backward chaining

Sapa: Extension? All (pre(a), -t1) |= P, M II = { (prea, t2 ) } 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 All (pre(a), -t1) |= P, M Effect? Delayed event Q Exogenous events? Delayed event Q 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 eÎQ interferes with persistent-pre(A) II = { (prea, t2 ) }

TP4: Extension? E={pi}: pi is required to be true at t F= {(ai, di)}: action ai is planned to start at t- di t: time stamp Effect? ? (which action should choose w/ affect exist partial plan) Exogenous events? (time stamp is relative to the goals) A set of actions SE is applicable in S=(E, F, t) if: -- every action is compatible with each other; --pE, aSE, padd(a), a is compatible with bF E={ p| p is true during [t1, t2] }

Sapa and TP4 Sapa TP4 Easy? Limited? Search Direction Search Space State world & state of search so far Branching Rule Sound & complete Sound & incomplete Concurrency (temporal) Proposition lock (“holding”) Proposition lock Extension Easy? Limited? Path Cost Heuristic Integrating resource Forward chaining Backward chaining

Sapa and TP4 Sapa TP4 Easy? Limited? Search Direction Search Space State world & state of search so far Branching Rule Sound & complete Sound & incomplete Extension Easy? Limited? Concurrency (temporal) Proposition lock (“holding”) Proposition lock Heuristic Path Cost Integrating resource Forward chaining Backward chaining

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? t8 Min-slack? tg-t8 Max-slack? tg-t8 Sum-slack? 2*tg-t8 Sum-action? 5 Max-span? Min-slack? Max-slack? Sum-slack? Sum-action? Sum-duration?

TP4: Heuristic Functions

Sapa and TP4 Sapa TP4 Easy? Limited? Search Direction Search Space State world & state of search so far Branching Rule Sound & complete Sound & incomplete Extension Easy? Limited? Concurrency (temporal) Proposition lock (“holding”) Proposition lock Heuristic RTGP DP Path Cost depends c(S, S’)=dadv Integrating resource Forward chaining Backward chaining

TP4: Incremental Branching Estimating the cost of Partial States Estimate lower bounds on dp 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

Sapa and TP4 Sapa TP4 Easy? Limited? Search Direction Search Space State world & state of search so far Branching Rule Sound & complete Sound & incomplete Extension Easy? Limited? Concurrency (temporal) Proposition lock (“holding”) Proposition lock Heuristic RTGP DP Path Cost depends c(S, S’)=dadv Integrating resource Forward chaining Backward chaining

Resource Management Producible Consumable Reusable Shareable Non-shareable Limited-capacity Check spelling of “producable”

Sapa: resource management Producable, consumable, non-shareable Sum-action Sum-duration Shareable? Not allowed Continuous change? Linear Shareable ?

TP4: resource management Reusable & Non-shareable? Reusable & Limited-capacity? Consumable & non-producible?

Sapa and TP4 Sapa TP4 Search Direction Forward chaining Backward chaining Search Space S=(P,M,II,Q,t) S=(E,{(aj,dj)},t) Branching Rule Sound complete Sound, incomplete Extension Easy? Limited? Concurrency Proposition lock Non-shareable resources Proposition lock (“holding”) Path Cost depends c(S, S’)=dadv Heuristic RTGP DP Integrating resource Easy if inadmissible hard

Quiz3: Continuous Change ZENO? Sapa? TGP & TP4?

Experiments performance TGP TP4 Sapa ZENO expressiveness

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