Planning with Unknown Object Quantities and Properties - AAIR Lab · 2020-06-29 · Siddharth Srivastava Planning with Unknown Object Quantities and Properties. IntroductionFrameworkPlanning

Introduction Framework Planning Algorithms Results

Planning with Unknown Object Quantities andProperties

Siddharth SrivastavaJoint work with Neil Immerman and Shlomo Zilberstein

University of Massachusetts, Amherst

Eighth Symposium on Abstraction, Reformulation andApproximation

7− 10 July, 2009

Siddharth Srivastava Planning with Unknown Object Quantities and Properties


Overview

Introduction

FrameworkConcrete RepresentationAbstract Representation for Belief StatesActions on Belief States

Planning AlgorithmsPlan GeneralizationPlan MergingPreconditions

Results


Introduction Framework Planning Algorithms Results Conditional Planning

Conditional Planning

pick Next

paper glass

Test Type

pick Next

glasspaper

Test Type

collect In PaperContainer collect In GlassContainercollect In PaperContainer

Test Type

paper glass




Need to merge, maintain history




glass paper

Test Type

Pick Next Pick Next

collect In PaperContainer collect In GlassContainercollect In PaperContainer

Need to merge, maintain history

Progress and termination of loops


Introduction Framework Planning Algorithms Results Concrete Representation Abstraction Actions on Belief States

Concrete States as First-Order Structures

V = {object1, bin1, isGlass1, isPaper1, in2, empty1, collected1, forGlass1, forPaper1}

[[object(2)]] =1

[[isGlass(2)]] = 1

[[bin(1)]] = 1

[[in(2,1)]] = 1

in

bin

isGlass

object

1

2

S1

S2

in

bin

isPaper

object

1

2

[[object(2)]] =1

[[isPaper(2)]] = 1

[[bin(1)]] = 1

[[in(2,1)]] = 1



Action Operators

Precondition: formula in FO.Predicate updates

p′(x̄) =

tuples added to p

(¬p(x̄) ∧∆+p (x̄)) ∨

tuples retained in p

(p(x̄) ∧ ¬∆−p (x̄))

Use formula evaluation to compute action effect.

Frame axioms/successor state axioms (situation calculus) using adouble vocabulary.



Example: The Collect Action

Collect(o,c)

object(o) ∧ container(c) ∧ (isGlass(o)↔ forGlass(c)) ∧∃b(bin(b) ∧ in(o, b) ∧ robotAt(b))

in′(u, v) := (in(u, v) ∧ u 6= o) ∨(¬in(u, v) ∧ u = o ∧ v = c)

empty′(u) := (empty(u) ∧ u 6= c) ∨ in(o, u)collected′(u) := collected(u) ∨ o = u

c container, forPaper, empty

objectin

bin

isPaper

b

o

b c container, forPaper

object, collected

isPaper

o

in

bin, empty

Collect(o,c)



Abstraction Using 3-Valued Logic

in

bin

isGlass

object

1

2

in

bin

isPaper isGlass

object

1

2

= 1/2

in

bin

isPaper

object

1

2

Use 3−Valued logic to abstract as:

TVLA: [Sagiv et al., 2002]




in

bin

isGlass

object

1

2

in

bin

isPaper isGlass

object

1

2

in

bin

isPaper

object

1

2

Focus and coerce w.r.t {isPaper(x)}

Objects are either paper or glass

Integrity Constraint:

Implementation of “sensing” actions




in

bin

isPaper isGlass

object

1

2

in

bin

isPaper isGlass

object4

in

bin

isPaper isGlass

object

5

6

3




in

bin

isPaper isGlass

object

1

2

V

U

in

bin

isPaper isGlass

object4

in

bin

isPaper isGlass

object

5

6

3

in

bin

object

isGlassisPaper

Canonical Abstraction

= Summary element




U

V

in

bin

isPaper isGlass

object

1

2

in

bin

isPaper isGlass

object

3

4

in

bin

object

isGlassisPaper

in

bin

isPaper isGlass

object2n

2n−1

Concretization

Integrity Constraint:

Each bin has a unique object



Abstraction Using 3-Valued Logic: Summary

TVLA [Sagiv et al., 2002]: Three Valued Logic Analysis

Abstraction predicates: unary predicates.

Element’s role = set of abstraction predicates satisfied

Collapse elements of a role into summary elements.

Use integrity constraints to retreive concrete states.



Action Application on Belief States

U

V

in

bin

object

isGlassisPaper

in

bin

isPaper isGlass

object

1

2

in

bin

isPaper isGlass

object

3

4

in

bin

isPaper isGlass

object2n

2n−1

Axn: CollectAnObject()



Action Application on Belief States

A simpler case: only paper objects and containers

container, forPaper, empty

isPaper

object

binb c

o

b

isPaper

oCollect(o,c)

in

bin

empty

object

container, forPaper

collected

in

c

in

Underspecified action application



Drawing Out Action Arguments

Rolei

φ

S0

Rolei Role

iRolei

Rolei

φφ

S SS1 2 3

Rolei

φφ

Rolei

Rolei

S S1 2

Focus

Coerce

φ constrained to be unique and satisfiable



Drawing Out Action Arguments

Rolei

φ

S0

Rolei

φφ

Rolei

Rolei

S S1 2

Draw

out an element labelled

φ

φ constrained to be unique and satisfiable



Summary of Action Application

Draw-out action arguments prior to application

Use focus and coerce to create cases for properties of drawnout of objects.Branches caused:

Classifiable, e.g #R{S} > 1Unpredictable at planning-time, e.g. “object type=paper”


Introduction Framework Planning Algorithms Results Plan Generalization Plan Merging Preconditions

Plan Generalization

Use abstract structures to recognize loop invariants in example concrete plans.

Example Execution

goToNextBin()S 0#

S 1# senseType() S 2

# preProc−Paper() S 3# collectPaper()

S 4#

2 objects of each type collected;

2 bins remaining

Tracing

S 0 S 2preProc−Paper() S 3S 1

S 5 S 7

{bin}# (S ) > 10

S 0

senseType()

#{object, isPaper}:+1#{object}: −1

goToNextBin()

#{bin}: −1#{bin, visited}: +1

Not role−count classifiable

collectPaper()

#{object, isPaper}: −1

#{object, isPaper,

#{container, forPaper}: +1

empty}: −1#{container, forPaper

collected}: +1

#{bin,visited}: −1

#{bin,visited,empty}: +1

Developed for completely observable settings [Srivastava et al., 2008]



Merging Generalized Plans

Find Loops

S 0goToNextBin() senseType()

S 2preProc−Paper()

S 3S 1

goToNextBin() S 6senseType()S 5

S 7

S 8

collectPaper()

Plan for Unhandled StructurepreProc−Glass() collectGlass() goToNextBin()

S 7#

S 9#

S 10#

S 11#

Generalize and Merge

S 0goToNextBin() senseType()

S 2preProc−Paper()

S 3S 1S 5 goToNextBin()

S 8

S 6

S 7 S 9preProc−Glass() collectGlass()

S 10S 12

collectPaper()

senseType()

senseType()

goToNextBin()

A single plan may not explore all possibilities.

Construct problem instances from unsolved belief states.

Solve them using classical planners.



Finding Preconditions

Branches solve only some members of abstract structures.

Classify branches using role counts; propagate backwards.

Need for doing this constrains predicate update formulas.



Example ResultsInitial: p0 = ‖{paper, collected}‖; pc0 = ‖{empty,container,forPaper}‖;g0, gc0 : similar for glass; b0 = ‖{bin}‖

Loop 1goToNextBin()

senseType()

apply−PaperPreProc(obj)

senseType()


collect−PaperCont(obj)

collect−Paper−Cont(obj)

paper

paper

Final: p0 + l1; pc0 − l1; b0 − l1

Solves 1 instance out of every2n

Loops 1 & 2goToNextBin()

senseType()


apply−GlassPreProc(obj)

senseType()


collect−PaperCont(obj)

goToNextBin()

collect−Glass−Cont(obj)


paper

2

Final: p0 + l1; pc0 − l1; g0 +l2; gc0 − l2; b0 − l1 − l2

2n−1 + 1 out of every 2n



Transport Domain



Transport Domain: Results

Initial undelivered counts:m0 = ‖{monitor, atD2}‖; s0 = ‖{server, atD1}‖

Loop 1

load(server, T2)

mv(T2, D3)

load(server, T1)

unload(T2) mv(T2, L)

mv(T2, D2)

mv(T1, L) unload(T1)

mv(T1,D1)

load(LCD, T2)

mv(T2,L)

server present

Final: mo − l1; s0 − l1

Loops 1 & 2

load(server, T2)

mv(T2, D3)

load(server, T1)

unload(T2) mv(T2, L)

mv(T2, D2)

mv(T1, L) unload(T1)

mv(T1,D1)

load(LCD, T2)

mv(T2,L)load(server,T2)mv(T2, D1)

mv(T2,L)

server lost

Final: m0− l1; so− l1−k1



Solutions: Recycling and Transport

goToNextBin()

senseType()



senseType()


collect−PaperCont(obj)collect−Glass−Cont(obj)


goToNextBin()

collect−Glass−Cont(obj)


Recycling

forkLift(kind1, T1)

forkLift(kind1, T2)

mv(T1, L)

mv(T2, L)

load(kind1, T1)

unload(T1) mv(T1,D1)

mv(T2,L)

load(kind1, T2)

mv(T2, D3)

load(kind2, T2)

mv(T2, D2)

unload(T2)

load(kind1,T2)

forkLift(kind1, T2)

mv(T2, D1)

mv(T2,L)

Transport

2

3

4

2

2

3

4



Conclusions

An approach for representing unknown quantities forplanning.

Methods for finding generalized plans with branches andloops.

Automatic computation of preconditions for many kinds ofnested loops in a broad class of domains.



Example Results: Domain Coverage

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25 30 35

Cov

erag

e (D

)

Max Number of Bins (n)

D(n>=8) = 1

D(n>=8) = 0.5

D(n>=8) = 0.25

CFF-soln7Gen(Eg 1)

Gen(Eg 1+2)Gen(Eg 1..3)Gen(Eg 1..4)

Dπ(n) = |Sπ(n)|/|T (n)|



Merging Generalized Plans: Algorithm

Input: Existing plan Π, eg trace tracei

Output: Extension of Πif Π = ∅ then1

Π← tracei2return Π3

endrepeat4

mpΠ, mpt ← findMergePoint(Π, tracei, bpΠ, bpt)5if mpΠ found and not first iteration then6

attachEdges(Π, tracei, bpt, mpt, mpΠ, bpΠ)7

endif mpΠ found then8

bpΠ, bpt ← findBranchPoint(Π, tracei, mpΠ, mpt)9

enduntil new bpΠ or mpΠ not foundreturn Π10

Algorithm 1: ARANDA-Merge



Related Work

Plans with Loops[Winner and Veloso, 2007]: no preconditions or sensingactions, but use partial ordering.[Levesque, 2005]: single planning parameter, limitedpreconditions.[Cimatti et al., 2003]: “hard” loops.

Planning with unknown quantities:[Milch et al., 2005]: action operators not provided.



Plan Generalization: Example

delivered, Crate

delivered, CrateCrate

Truck

at

Dock

Loc

dest, at

dest, at

Garage

Chosen,Crate Loc

atat

at

dest

destCrate

Crate

delivered, Crate

dest

dest

Garage

Dockat

at

Crate

Chosen

Truck

at

Loc

dest, at

delivered, Crate

dest

dest

Garage

Dockat

at

Crate

Chosen

Truck

at

Loc

dest, at

delivered, Crate

delivered, Crate

delivered, CratedestDock

Loc

dest, at

Garage

Truck

at

at

Chosen,Crate

Crate

dest

Loc

dest, at

Crate

findDest(); Load(); setTarget(destLoc); Drive(); Unload(); Choose(Crate)=



Plan Generalization: Example

Dockat dest

at

Truck

dest, at

Locationcrate

Garagedelivered;crate

Dockat dest

at

Truck

Locationcrate

Garage

Dock

at

Truck

dest, at

Location


destat

chosen;crate

Dockat dest

at

Truck

dest, at

Locationcrate


S1

S2

S3

S4

Choose(crate)



References I

Cimatti, A., Pistore, M., Roveri, M., and Traverso, P. (2003).Weak, strong, and strong cyclic planning via symbolic modelchecking.Artif. Intell., 147(1-2):35–84.

Levesque, H. J. (2005).Planning with loops.In Proc. of IJCAI, pages 509–515.

Milch, B., Marthi, B., Russell, S. J., Sontag, D., Ong, D. L.,and Kolobov, A. (2005).Blog: Probabilistic models with unknown objects.In Proc. of IJCAI, pages 1352–1359.



References II

Sagiv, M., Reps, T., and Wilhelm, R. (2002).Parametric shape analysis via 3-valued logic.ACM Transactions on Programming Languages and Systems,24(3):217–298.

Srivastava, S., Immerman, N., and Zilberstein, S. (2008).Learning generalized plans using abstract counting.In Proc. of AAAI, pages 991–997.

Winner, E. and Veloso, M. (2007).LoopDISTILL: Learning domain-specific planners fromexample plans.In Workshop on AI Planning and Learning, ICAPS.


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Planning with Unknown Object Quantities and Properties - AAIR Lab · 2020-06-29 · Siddharth Srivastava Planning with Unknown Object Quantities and Properties. IntroductionFrameworkPlanning