temporal planning

Temporal Planning

action models Using PDDL2.1 standard

how to model the search Progression; Regression; PO planning

how to extract good heuristics

Done

eo,s,es,L

A [d]s eo

s e

Essence of Temporal Planning

http://www.asu.edu/

No Temporal Gap Classical + Scheduling

Forbidding temporal gap implies All effects at one time Before-conditions meet effects After-conditions meet effects

Unique transition per actionA [d] *

pre

eff


A *

B *

C*D*

http://www.asu.edu/

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)

Temporal Planning via Plan Space Planning

Instead of constraints w.r.t steps (s<s’ or P@s), we will have constraints on time points (t – t’ = 4 etc.).

(: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)

)

at_fuse_box@G}

(: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)))

)

Cross_cellar GI

At_fusebox

Have_light@<t1,t2>

t1

t2

t2-t1 =10t1 < tGtI < t1

Have_light@t1




)

at_fuse_box@G}




)

Cross_cellar GI

At_fusebox

Have_light@<t1,t2>

t1

t2

t2-t1 =10t1 < tGtI < t1T4<tGT4-t3=15T3<t1T4<t3 V t1<t4

Have_light@t1

Burn_matcht3 t4

~have-light

The ~have_light effect at t4 can violate the <have_light, t3,t1> causal link! Resolve by Adding T4<t3 V t1<t4




)

at_fuse_box@G}




)

Cross_cellar GI

At_fusebox

Have_light@<t1,t2>

t1

t2t2-t1 =10t1 < tGtI < t1t4<tGt4-t3=15t3<t1t4<t3 V t1<t4t3<t2t4<t3 V t2<t4

Have_light@t1

Burn_matcht3 t4

~have-light

To work on have_light@<t1,t2>, we can either --support the whole interval directly by adding a causal link <have-light, t3,<t1,t2>> --or first split <t1,t2> to two subintervals <t1,t’> <t’,t2> and work on supporting have-light on both intervals

Notice that zenoallows arbitraryslack betweenthe two actions

PO (Partial Order) Search

[Zeno; 1994]

Split theInterval intoMultiple overlappingintervals

Involves Posting temporal Constraints, andDurative goals

Involves LPsolving overLinear constraints(temporal constraintsAre linear too);Waits for nonlinear constraintsTo become linear.

More on Temporal planningby plan-space planners (Zeno)

The “accommodation” to complexity that Zeno makes by refusing to handle nonlinear constraints (waiting instead until they become linear) is sort of hilarious given it doesn’t care much about heuristic control otherwise Basically Zeno is trying to keep the “per-node” cost of the search down (and if

you do nonlinear constraint consistency check, even that is quite hard) Of course, we know now that there is no obvious reason to believe that reducing the

per-node cost will, ipso facto, also lead to reduction in overall search. The idea of “goal reduction” by splitting a temporal subgoal to multiple sub-

intervals is used only in Zeno, and helps it support a temporal goal over a long duration with multiple actions. Neat idea.

Zeno doesn’t have much of a problem handling arbitrary concurrency—since we are only posting constraints on temporal variables denoting the start points of the various actions. In particular, Zeno does not force either right or left alignment of actions.

In addition to Zeno, IxTeT is another influential metric temporal planner that uses plan-space planning idea.

Temporal Planning with Progression?

All the progression planners we looked at were able to produce sequential plans.

Can progression be used to produce concurrent plans? Sub Question: Can progression be used to produce

parallel plans?

Producing parallel plans with progression? The naïve idea is to project over subsets of non-interfering actions (rather than single

actions). Problem: Exponential branching factor

A better idea: Consider “fattening” as well as “lengthening” the current partial plan as two options. We start by representing the state of a partial plan prefix as [S, {A1…Ak}] where S is the

current state, and {A1..Ak} are the mutually non-interfering actions that we have already committed to applying at S.

Notice that this is just a generalization of the normal progression state, in which the action set {A1..Ak} will be a singleton

Given a state [S,{A1..Ak}] to expand, we have (backtrackable) choices: Fatten: Consider applying another action B in state S [One branch for each possible action B]

For this to be feasible, B should be applicable in Si and B should not be interfering with A1..Ak. The resulting state will be {S; {A1…Ak}+B}

Advance: Consider advancing the state. If S’ is the state resulting from application of {A1..Ak} to S, then generate the state {S’; {}}

Notice that Fattening is only done at the current state (once advancing is done, the current state changes. So

any new fattening will be done at the new state. Normal progression does an automatic advance after each fatten (which means you will have only

one action at each step)

Generating concurrent plans is similar to generating parallel plans…almost..

We will continue to consider fattening at the current state, and advancing to the next state

Several issues: Actions have durations. So the state information should

include the actions we committed to (but haven’t completed) How much do we advance?

Worst case: Advance time to the “next time point” (could be bad news if we have dense time!)

Clever idea: Advance time to the “next happening” –where the state changes

State-Space Search:Search is through time-stamped states

Search states should have information about -- what conditions hold at the current time slice (P,M below) -- what actions have we already committed to put into the plan (,Q below)

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

Set <pi,ti> of predicates pi and thetime of their last achievement ti < t.

Set of functions represent resource values.

Set of protectedpersistent conditions(could be binary or resource conds).

Event queue (contains resource as wellas binary fluent events).

Time stamp of S.

In the initial state, P,M, non-empty Q non-empty if we have exogenous events

Search Algorithm (cont.) Goal Satisfaction: S=(P,M,,Q,t) G if <pi,ti> G either:

<pi,tj> P, tj < ti and no event in Q deletes pi. e Q that adds pi at time te < ti.

Action Application: Action A is applicable in S if:

All instantaneous preconditions of A are satisfied by P and M.

A’s effects do not interfere with and Q. No event in Q interferes with persistent

preconditions of A. A does not lead to concurrent resource change

When A is applied to S: P is updated according to A’s instantaneous

effects. Persistent preconditions of A are put in Delayed effects of A are put in Q.

Flying

(in-city ?airplane ?city1)

(fuel ?airplane) > 0

(in-city ?airplane ?city1) (in-city ?airplane ?city2)

consume (fuel ?airplane)

Flying

(in-city ?airplane ?city1)

(fuel ?airplane) > 0

(in-city ?airplane ?city1) (in-city ?airplane ?city2)

consume (fuel ?airplane)

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

Search: Pick a state S from the queue. If S satisfies the goals, endElse non-deterministically do one of

--Advance the clock (by executing the earliest event in Qs

--Apply one of the applicable actions to S

[TLplan; Sapa; 2001—talk given 9/12/01]

Decision Epochs: Limiting the places where clock can be advanced

To support concurrency, we need to consider advancing the clock

How far to advance the clock? One popular strategy is to advance the clock to the

time of the next earliest event in the event queue; since this is the least advance needed to make changes to P and M of S.

At this point, all the events happening at that time point are transferred from Q to P and M (to signify that they have happened)Light-match

Cross-cellar

~have-light

1510

In the cellar plan above, the clock,If advanced, will be advanced to 15,Where an event (~have-light will occur)This means cross-cellar can either be doneAt 0 or 15 (and the latter makes no sense)

Cross-cellar

Interference

Clearly an overkill




)

Let current state S be P:{have_light@0; at_steps@0}; Q:{~have_light@15} t: 0(presumably after doing the light-candle action) Applying cross_cellar to this state gives

S’= P:{have_light@0; crossing@0}; :{have_light,<0,10>} Q:{at_fuse-box@10;~have_light@15} t: 0




)

Light-match

Light-match

Cross-cellar

1510

Time-stamp

Short matches

No epoch available “middle of

nowhere” Decision Epoch

Planning is incomplete!

!!!

Wow!

http://www.asu.edu/

Decision Epoch Planning: DEP Only start actions after events Choose

Start an action Advance epoch

Temporally Simple Complete, suboptimal

Temporally Expressive Incomplete, suboptimal

Salvaging DEP

A [3]21 GG

B [2]

2G

light-match [8]ML L

M

fix-fuse [4]L

F

http://www.asu.edu/

Generalized DEP: DEP+ Also end actions after events Choose

Start an action End an action Advance epoch

Temporally Simple Complete, optimal

Temporally Expressive Incomplete, suboptimal

Salvaging DEP

A [3]21 GG

B [2]

2G

http://www.asu.edu/

Wow! Temporally Simple

Classical + Scheduling

Winners incomplete for all Temporally Expressive

Languages

Most/all benchmarks are classical!

!!!

http://www.asu.edu/

State of the Art: Incomplete or Slow Metric-FF, MIPS, SGPlan, SAPA,

TP4, TPG, HSP*, ... Guarantees only for temporally

simple languages Can solve some concurrent problems

Light-match, but not short-match Difficult to detect

ZENO, IxTeT, VHPOP, LPGP, ... Complete Slow

!!!

http://www.asu.edu/

Interleaving-Space: TEMPO Delay dispatch decisions until afterwards Choose

Start an action End an action Make a scheduling decision

Solve temporal constraints

Temporally Simple Complete, Optimal

Temporally Expressive Complete, Optimal

Salvaging State-space Temporal Planning

light

fix

match

fuse

fix

fix light

fusefix light

matchfusefix light

http://www.asu.edu/

Slides beyond this not explicitly discussed in the class

http://www.asu.edu/

Regression Search is similar…

In the case of regression over durative actions too, the main generalization we need is differentiating the “advancement of clock” and “application of a relevant action”

Can use same state representation S=(P,M,,Q,t) with the semantics that P and M are binary and resource

subgoals needed at current time point Q are the subgoals needed at earlier

time points are subgoals to be protected over

specific intervals We can either add an action to support

something in P or Q, or push the clock backward before considering subgoals

If we push the clock backward, we push it to the time of the latest subgoal in Q

TP4 uses a slightly different representation (with State and Action information)

[TP4; 1999]

A2:X

A3:W

A1:Y

QRWXy

We can either workOn R at tinf or R and QAt tinf-D(A3)

To work on have_light@<t1,t2>, we can either --support the whole interval directly with one action --or first split <t1,t2> to two subintervals <t1,t’> <t’,t2> and work on supporting have-light on both intervals




)

Let current state S be P:{at_fuse_box@0} t: 0

Regressing cross_cellar over this state gives

S’= P:{}; :{have_light,< 0 , -10>} Q:{have_light@ -10;at_stairs@-10} t: 0




)

Cross_cellar

Have_light

Notice that in contrast to progression,Regression will align the end points of Concurrent actions…(e.g. when we put inLight-match to support have-light)




)

S’= P:{}; :{have_light,< 0 , -10>} Q:{have_light@-10;at_stairs@-10} t: 0

If we now decide to support the subgoal in QUsing light-match

S’’=P:{} Q:{have-match@-15;at_stairs@-10} :{have_light,<0 , -10>} t: 0




)

Cross_cellar

Have_light

Notice that in contrast to progression,Regression will align the end points of Concurrent actions…(e.g. when we put inLight-match to support have-light)

Cross_cellar

Have_light

Light-match

Tradeoffs: Progression/Regression/PO Planning for metric/temporal planning

Compared to PO, both progression and regression do a less than complete job of handling concurrency (e.g. slacks may have to be handled through post-processing).

Progression planners have the advantage that the exact amount of a resource is known at any given state. So, complex resource constraints are easier to verify. PO (and to some extent regression), will have to verify this by posting and then verifying resource constraints.

Currently, SAPA (a progression planner) does better than TP4 (a regression planner). Both do oodles better than Zeno/IxTET. However TP4 could be possibly improved significantly by giving up the insistence

on admissible heuristics Zeno (and IxTET) could benefit by adapting ideas from RePOP.

When is Temporal Planning Really Temporal?

William CushingSubbarao Kambhampati

Special thanks to: J. Benton, Menkes van den

Briel

MausamDaniel Weld

http://www.asu.edu/

http://rakaposhi.eas.asu.edu/yochan.html

Temporal Planning

Plan-space Extended planning graph Reduction to ILP State-space

Competition winners Reachability heuristics

Infinite number of time points Decision Epochs

Restrict start times to events

Introduction

name [duration]start-pre end-preover-pre

start-eff end-eff

light-match [8]ML L

M

fix-fuse [4]L

F

M - matchL - lightF - fuse

http://www.asu.edu/

Troubling Questions What do/should the

IPCs measure?

Essence of Temporal Planning Required Concurrency Temporally Simple Temporally Expressive

Can Decision Epoch Planning be fixed?

No. But! DEP+

“Less” incomplete TEMPO

Reachability heuristics

Overview

≈ Classical ≈

Harder

http://www.asu.edu/

Required Concurrency Temporally Simple Languages

Concurrency never necessary …but can be exploited for quality

Temporally Expressive Languages Can specify problems such that

concurrency is needed


http://www.asu.edu/

Temporal Action Languages

eo,s,es,Lname [duration]

Start-pre End-preOver-pre

Start-eff End-eff


oeLname [duration]

Over-pre

End-eff

http://www.asu.edu/

Temporal Action Languages Temporally Simple

Rescheduling is possible MIPS, SGPlan, LPG, …

Sequential planning is complete – “optimal” ? TGP, yes In general, yes

Temporally Expressive

Temporal Gap

A [d]s eo

s eeo,s,

es,L

Les Ls

eLs,e


http://www.asu.edu/

(Minimal) Temporally Expressive Languages

Temporal Gap Before-condition and effect After-condition and effect Two effects

Temporally Simple No Temporal Gap


http://www.asu.edu/

No Temporal Gap Classical + Scheduling

Forbidding temporal gap implies All effects at one time Before-conditions meet effects After-conditions meet effects

Unique transition per action

Theorem: Every concurrent plan is an O(n) rescheduling of a sequential plan And vice versa

A [d] *pre

eff


A *

B *

C*D*

http://www.asu.edu/

Conclusions Required concurrency is the essence of temporal

planning Otherwise classical planner + O(n) scheduling

suffices Simple test for required concurrency: Temporal gap

Decision epoch planning is fundamentally incomplete But DEP+ may solve most real-world problems

Complete state-space temporal planning: TEMPO Allows leveraging of state-based reachability

heuristics !!!!!

http://www.asu.edu/

Evaluating Temporal Planning Domains

William CushingSubbarao Kambhampati

Kartik Talamadupula

Daniel WeldMausam

http://www.asu.edu/

http://rakaposhi.eas.asu.edu/yochan.html

Competition winners are incomplete

fix-fuse

light-match

L

FM

L -M^ -L

How incomplete? What should the IPC measure?

Epoch A time at which an event

happens Decision Epoch Planning

Only start actions after epochs

Temporal Planning

Required Concurrency

http://www.asu.edu/

How deep is the problem?

Required Concurrency

Languages Incomplete for

temporally expressive languages

Complete for temporally simple languages

http://www.asu.edu/

(Minimal) Temporally Expressive Languages

Temporal Gap Before-condition and effect After-condition and effect Two effects

Temporally Simple No Temporal Gap

http://www.asu.edu/

Required Concurrency Inherently sequential is easy

Timestamps (with support for arithmetic) Loose integration with a PERT scheduler TGP, LPG-td, SGPlan, MIPS, …

Required concurrency is hard The plan space is larger The scheduling sub-problem is harder

Sub-problem optimality principle State of the art is VHPOP, LPGP, CRIKEY

TEMPO, reduction to CSP

http://www.asu.edu/

The International Planning Competition

Benchmarks must not require (much) concurrency

How much? None at all

How do we show it? Use temporal gap?

Problem: “every” action has temporal gap

http://www.asu.edu/

Solution: Decompile temporal gap (navigate ?rover ?alpha ?omega)

Pre: (at start (at ?rover ?alpha)) Eff: (and

(at start (not (at ?rover ?alpha))) (at end (at ?rover ?omega)))

(navigate ?rover ?alpha ?omega) (over all (=> (at ?rover) ?alpha ?

omega))

http://www.asu.edu/

Causal Structure and Concurrency

A *

B

D *

C*

light-matchML L

M

fix-fuseL

F

light-match

fix-fuseA B C D

*

Inherently Sequential Inherently Concurrent

http://www.asu.edu/

Navigate’s sequential structure

navigateS D

S

communicateS

navigateD

??S

??D

http://www.asu.edu/

Technique: Start-time Sequentialization

light-matchML L

M

fix-fuseL

F

AL

BLL

AL

BLL

Do not want to enumerate plans! Nor every sequentialization!

Start-time sequentialization Fixed attempt Suffices for benchmarks (not necessary)

End-time sequentialization Critical-time sequentialization

Start times of containing actions in same order as all dependencies

http://www.asu.edu/

Element Safety Y < X S(A(Y)) > S(A(X)) Threat-free

X supports Z, Y threatens Z

Interaction-free Z supports Y X threatens Y

Link-free Y supports X

AL

BL

AL

BL

AL

BL

http://www.asu.edu/

Benchmarks never require concurrency

Durative change on m.v. fluents is safe Unbounded resources are safe

“The Perils of Discrete Resource Models” ICAPS workshop on IPC

A few special cases (at end (calibrated ?c ?r))

Document… http://rakaposhi.eas.asu.edu/is-benchmarks.html

Forthcoming

(:durative-action navigate:parameters (?x - rover ?y - waypoint ?z - waypoint):duration (= ?duration 5) :condition (and

;;(at start (at ?x ?y)) ;; MV Fluent ;;(at start (>= (energy ?x) 8)) ;; Resource Consumption (over all (can_traverse ?x ?y ?z)) (at start (available ?x)) (over all (visible ?y ?z)) )

:effect (and ;;(at start (decrease (energy ?x) 8)) ;; Resource Consumption (over all (consume (energy ?x) 8)) ;; Resource Consumption ;;(at start (not (at ?x ?y))) ;; MV Fluent ;;(at end (at ?x ?z)))) ;; MV Fluent (over all (-> (at ?x) ?y ?z)) ;; MV Fluent

))

;;(at ?x - rover ?y - waypoint)

(at ?x - rover ) - waypoint

http://rakaposhi.eas.asu.edu/is-benchmarks.html

http://www.asu.edu/

Only RC due to Modeling Bugs 1: drop 1.1: drop 2.05: sample … (and (full ?s) (empty ?s))

1: recharge 1.1: recharge 1.2: recharge … (>= (energy ?x) (* k (capacity ?x)))

http://www.asu.edu/

Syntactic Sugar for avoiding Errors Action drop (store)

full(store) == true at start full(store) := false at end

Should be at start empty(store) := true at end

Explicit resources amount(store) :consume 1 space(store) :produce 1

Explicit durative change + m.v. fluents amount(store) == full => empty

http://www.asu.edu/

Temporal Machine Shop Benchmarks lack required concurrency

Real world lacks required concurrency? (:durative-action fire-kiln

:parameters (?k - kiln):duration (= ?duration 20):effect (and (over all (lend (firing ?k)))

(over all (–> (ready ?k) true false)) (:durative-action bake-ceramic

:parameters (?p - piece ?k - kiln):duration (= ?duration (bake-time ?p)):condition (and (over all (firing ?k))

(over all (shaped ?p))):effect (over all (–> (baked ?p) false true)))

http://www.asu.edu/

Real world required concurrency (and

(lifted bowl-left) (lifted bowl-right))

Spray-oil (during milling) Heat-beaker (while adding

chemicals) Ventilate-room (while drying glue) …

http://www.asu.edu/

Lessons for the Competition Competitors tune for the benchmarks

Most of the competitors simplify to TGP Either required concurrency is

important Benchmarks should test it

Or it isn’t Language should be inherently sequential

PDDL spec. highlights light-match RC occurs in the real world

Might need processes, continuous effects

http://www.asu.edu/

Conclusion Required Concurrency separates easy and hard

temporal planning The easy case allows offloading to a scheduler

Still an intriguing problem Simplify the language – push the classical track

The hard case forces temporal reasoning by the planner Real world required concurrency is frequent

PDDL 2.1.3 was designed for required concurrency But the benchmarks fell through

Analysis of domains is hard Automatable? Embeddable within a search?

Domain modeling is very hard Durative change Resources

Evaluating Temporal Planning Domains

ICAPS 2007

When is Temporal Planning Really Temporal?IJCAI 2007

The Perils of Discrete Resource Models

ICAPS 2007, IPC workshop

http://www.asu.edu/

temporal planning

Documents