1. 3/25: Leaving STRIPS Planning and going to Sapa

2. Administrivia 3/25  Homework 4 due next class  Midterm soon after that  Will be take home  Will have a “Shock and Awe” flavor  You can be an “embedded exam taker” by suggesting problems  Today:  Metric/Temporal planning (MTP)  Representation issues  Modeling MTP in Progression and Regression  And Graphplan and PO planning etc. etc.

3. Metric Temporal Planning  Time: Durative actions; Temporal constraints on goals (deadlines; inter-goal constraints – eg. Make sure to be in airport 2 hours before you are in the plane); Exogenous events  Durations may be static or “dynamic”  duration depends on the context—eg. Time to fill your gas tank depends on how empty the tank is to begin with  Advanced issues: Uncertain durations…  Modeling issues: When are preconditions needed? How long will they persist? When are effects given?  A default assumption is to say that all preconditions are needed at the beginning and must hold during the entire action’s duration. And that all effects will be available at the end of the action  E.g Consider “Grading homeworks” action—when are the homeworks needed? When are the grades available? What does your teacher tell you?  Planning issues: How to support concurrency?(see next slide) How to support multi- objective (cost/make-span/robustness) optimization  Resources: Actions may consume/produce (continuous quantity) “resources”  Modeling issues: How to model resource availability (especially over the duration of an action)  Planning issues: How to efficiently reason with continuous quantities during planning Special cases: TP: Temporal planning RP: Resource Planning

4. Concurrency  Suppose I tell you that a plan P contains actions A1… A10, each with duration d1…d10, then what is the makespan (execution duration) of P?  Makespan(P) >= max(d1…d10)  If Makespan(P) = Sum(d1…d10), then it is a strictly serial plan  If Makespan(P) > Sum(d1..d10), then there is idle-time in the plan  Actions don’t need to start right after the preceding action  Think of the bank teller gossiping with his colleague in between servicing each customer  Planned idle/slack time may not always be a bad thing—it can sometimes improve the robustness of the plan  Think of three travel plans involving connections in Minneapolis: Plan 1 schedules 5 min for connection time; plan 2 schedules 1 hour; plan 3 schedules 2 days. Which one is better (all else being equal).

5. Some Brand Names  Planners that can handle similar types of temporal and resource constraints:  TLPlan, HSTS, IxTexT, Zeno, SAPA  TlPlan, SAPA are progression-based planners  HSTS,IxTET,Zeno are partial-order-based planners  TlPlan,HSTS are domain-customized planners; the rest are domain independent  Planners that can handle a subset of constraints:  Only temporal: TGP, TPG, LPGP  Only resources: LPSAT, GRT-R, Kautz-Walser  Subset of temporal and resource constraints: TP4, Resource-IPP  LPGP and LPSAT are “loosely-coupled” systems. LPSAT connects SAT and LP solvers; LPGP connects Graphplan and LPsolver  Issues of how “tight” is the loose-connection.  TGP,TPG,LPGP are Graphplan-based  LPSAT is based on SAT encodings being sent to LP solvers  Kautz-Walser is based solely on LP encodings

6. Approaches for MTP  In theory, pretty much every one of the approaches we saw for classical planning can be (and have been) extended to MTP (with varying degrees of scalability)  There are some interesting tradeoffs  PO planners are easiest to extend to support the concurrency needed for durative actions  Have harder time handling resources (because resource consumption depends on exactly what actions occurred before this time point)  Progression planners easiest to extend to support resource consuming actions  But harder time handling concurrency (need to consider “advancing clock” as a separate option in addition to applying one of the actions)

7. 3/27: Our Road Map  Will focus on conjunctive planning approaches— with special attention to Sapa  action models  Using PDDL2.1 standard  how to model the search  Progression; Regression; PO planning  how to extract good heuristics

8. Action Representation Flying (in-city ?airplane ?city1) (fuel ?airplane) > 0  (in-city ?airplane ?city1) (in-city ?airplane ?city2) consume (fuel ?airplane) Durative with E A = S A + D A Instantaneous effects e at time t e = S A + d, 0  d  D A Preconditions need to be true at the starting point, and protected during a period of time d, 0  d  D A Action can consume or produce continuous amount of some resource Action Conflicts: Consuming the same resource One action’s effect conflicting with other’s precondition or effect

9. (:durative-action burn_match :parameters () :duration (= ?duration 15) :condition: (and (at start have_match) (at start have_strikepad)) :effect (and (at start have_light) (at end (not have_light)) ) have_match, have strikepad have_light ~have_light (dur: 15) (:durative-action cross_cellar :parameters () :duration (= ?duration 10) :condition (and (at start have_light) (over all have_light) (at start at_steps)) :effect (and (at start (not at_steps)) (at start crossing)(at end at_fuse_box) ) have_light (dur: 10) have_light, at_steps at_fuse_box ~at_steps, crossing PDDL 2.1 (Level 2) Pure Durative Actions

10. PDDL 2.1 Level 3: Durative actions and numeric quantities (but discrete effects) The entire energy to be consumed is “encumbered” at the very beginning (even though it gets consumed Slowly over the full duration.

11. PDDL 2.1 Level 4: Durative actions and numeric quantities (with continuous effects: )

12. Issues in modeling continuous change by discrete vs. continuous effects  Consider the action of boiling a pan of water  The quantity “temperature of water” changes continuously over the duration of the action  We can ignore continuous effects by specifying that temperature is 100 0 C at the end  Easy to handle; can only access the temperature at the end of the action; Reduces concurrency (what if we also put a blow torch to the pan to “hasten” the process?)  Or we can specify that the temperature of the water raises at a linear rate until it becomes 100  Harder to handle; but allows more concurrency (the total rate of increase is summation of all the individual rates of increase)

13. PDDL 2.1 Standard: Summary  Durations  Static and dynamic durations allowed  Also allows duration inequalities  Preconditions  Can be “at start” or “over all” (throughout the duration)  Doesn’t model preconditions being needed for arbitrary durations in the middle  Effects  Can be “at start” or “at end”  This makes effects “discrete”  Numeric quantities  Can be present in the preconditions or effects  Presence in the effects can be “discrete” (“at start”/”at end”) or continuous  Continuous change specified by giving a “rate” at which the quantity changes  Non-linear rate harder

14. State of the Art (as of IPC2002)  At IPC 2002; PDDL 2.1 standard had three levels  Level 1: STRIPS/ADL  Level 2: +Durative Actions  FF, LPG, SAPA….  Level 3: +Numeric quantities discrete change  Sapa, LPG  Level 4: +Continuous change  None at IPC  Some planners can handle it “in theory” but none are scalable

15. Problem Representation  Achievement Goals are specified as a list where pi needs to hold by time t i  ti is the deadline by which G must hold. It can be metric time (e.g. make clear(b) true by 2pm.)  If ti is omitted we will assume that G is a non-deadline goal (must be true by the time the plan is done.  “Persist Goals” are specified as a condition and an interval over which it must hold  A persist goal may be supported by different actions for the different parts of the duration ( “goal reduction” a la ZENO )  E.g. striking multiple matches to have light over a duration

16. Plan representation A1 A2 A3 Drive(cityA,cityB) Q At(truck,B) An executable plan must provide -- the actions that need to be executed -- the start times for each of the actions  Or a set of simple temporal constraints on the set of actions (S.T.C. are generalization of partial orders) E.g. A1—[4,5]  A2 (means 4 <= ST(A2) – ST(A1) <= 5 ) Plan views: Pert and Gantt charts GANTT Chart is what is shown on the right PERT shows the Causal links

18. Plan Quality Measures  Makespan: Clock time for the execution of the plan (more concurrency  lower makespan)  Slack: The difference between the deadline for a goal and the time by which the plan achieves it  Tardiness is negative slack  Optimize max/min/average slack/tardiness measures  Cost: Sum of costs of all the actions  Can be split into multiple dimensions, one corresponding to each resource A1 A2 A3 Drive(cityA,cityB) Q At(truck,B) Can two plans with same make-span have different slack measures?