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

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

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

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

5. 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

6. 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

7. 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

8. 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)

9. 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 );

10. 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

11. 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}

12. 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

13. 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’)

14. 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

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

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

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

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

19. 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

20. 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

21. 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 ) }

22. 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] }

23. 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

24. 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

25. 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?

26. 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?

27. TP4: Heuristic Functions

28. 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

29. 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

30. 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

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

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

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

34. 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

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

36. Experiments
performance
TGP
TP4
Sapa
ZENO
expressiveness

37. Comments?