vals progress val's progress: the automatic validation tool for pddl2.1 used in the...

VAL’s Progress

VAL's Progress:VAL's Progress:The Automatic Validation The Automatic Validation Tool for PDDL2.1 used in Tool for PDDL2.1 used in the International Planning the International Planning CompetitionCompetition

Richard Howey and Derek Long

University of Durham

VAL’s Progress

IntroductionIntroduction

• VAL was the validation tool used in the 3rd IPC.

• VAL is evolving along side PDDL to validate plans written in PDDL.

• The latest development is to extend VAL to validate plans with continuous effects.

• Validating plans with continuous effects is an important first step to developing planners capable of handling continuous effects.

VAL’s Progress

Validation Example: Validation Example: Generator and Generator and

TanksTanks

Initial State and Problem:Initial State and Problem:

• A generator must run continuously for 100 time units.A generator must run continuously for 100 time units.

• The generator has a capacity of 60 fuel units, using 1 fuel The generator has a capacity of 60 fuel units, using 1 fuel unit for every 1 time unit to generate.unit for every 1 time unit to generate.

• Two fuel tanks with 25 fuel units each can refuel the Two fuel tanks with 25 fuel units each can refuel the generator while it is generating.generator while it is generating.

• The generator starts with a full tank of fuel.The generator starts with a full tank of fuel.

VAL’s Progress

Durative ActionsDurative Actions

Generate:Generate:

• DurationDuration: must be 100 time units.: must be 100 time units.

• Invariant conditionInvariant condition: fuel-level of generator must be greater : fuel-level of generator must be greater than zero.than zero.

• Continuous EffectContinuous Effect: :

Refuel:Refuel:

• DurationDuration: less or equal to time to empty tank.: less or equal to time to empty tank.

• Invariant conditionInvariant condition: fuel-level of generator must be less than : fuel-level of generator must be less than the capacity of the generator.the capacity of the generator.

• Continuous EffectsContinuous Effects:: dr/dt = 1

df/dt = 2 k(f) ( k(f) r – f(0) )

dg/dt = 2 k(f) ( f(0) – k(f) r )

dg/dt = – 1 t = time since durative action began

g = fuel-level of generator

f = fuel-level of a tank

k(f) = flow constant of tank f

VAL’s Progress

Possible PlanPossible Plan

1: (generate generator) [100]1: (generate generator) [100]

20: (refuel generator tank1) [25]20: (refuel generator tank1) [25]

80: (refuel generator tank2) [12.5]80: (refuel generator tank2) [12.5]

generate

refuel 1 refuel 2

VAL’s Progress

Plan to ValidatePlan to Validate

1: 1: (generate generator) - (generate generator) - start

20: 20: Invariant for (generate generator) (generate generator)20: 20: Update of Continuously Changing Primitive Numerical Expressions20: 20: (refuel generator tank1) - (refuel generator tank1) - start

45: 45: Invariant for (generate generator) (generate generator) Invariant for (refuel generator tank1) (refuel generator tank1)45: 45: Update of Continuously Changing Primitive Numerical Expressions45: 45: (refuel generator tank1) - (refuel generator tank1) - end

101: 101: Invariant for (generate generator) (generate generator)101: 101: Update of Continuously Changing Primitive Numerical Expressions101: 101: (generate generator) - (generate generator) - end

VAL’s Progress

Time 1 upto 20Time 1 upto 20

1: 1: (generate generator) - (generate generator) - start

20: 20: Invariant for (generate generator) (generate generator)20: 20: Update of Continuously Changing Primitive Numerical Expressions

t = time since last simple action


g(t) = – t + 60 for t in [0,19)

InvariantInvariantg(t) > 0

for t in (0,19)

UpdateUpdate Generator fuel-level:g(19) = –19 + 60 = 41

dg/dt = – 1

– t + 60 > 0

for t in (0,19)

VAL’s Progress


20: 20: (refuel generator tank1) - (refuel generator tank1) - start

45: 45: Invariant for (generate generator) (generate generator) Invariant for (refuel generator tank1) (refuel generator tank1)45: 45: Update of Continuously Changing Primitive Numerical Expressions45: 45: (refuel generator tank1) - (refuel generator tank1) - end



a = fuel-level of tank 1

dg/dt = – 1

dr/dt = 1

da/dt = 0.08r – 2

dg/dt = – 0.08r + 2

dg/dt = – 0.08t + 1

g(t) = – 0.04t2 + t + 41

for t in [0,25)

r(t) = t for t in [0,25)

a(t) = 0.04t2 – 2t + 25

for t in [0,25)

VAL’s Progress

Time 20Time 20upto 45upto 45

InvariantsInvariants

UpdateUpdate

g(25) = – 0.04252 + 25 + 41 = 41, a(25) = 0

g(t) > 0

for t in [0,25) – 0.04t2 + t + 41 > 0

for t in [0,25)g(t) 60

for t in (0,25)

– 0.04t2 + t + 41 60

for t in (0,25)

0.04t2 – t + 19 0 for t in (0,25)



VAL’s Progress


80: 80: Invariant for (generate generator) (generate generator)80: 80: Update of Continuously Changing Primitive Numerical Expressions


g = fuel-level of generator g(t) = – t + 41

for t in [0,35)

InvariantInvariantg(t) > 0

for t in [0,35)

UpdateUpdate Generator fuel-level:

g(35) = – 35 + 41= 6

dg/dt = – 1

– t + 41 > 0

for t in [0,35)

VAL’s Progress

Time 80 upto 92.5Time 80 upto 92.5

80: 80: (refuel generator tank2) - (refuel generator tank2) - start

92.5: 92.5: Invariant for (generate generator) (generate generator) Invariant for (refuel generator tank2) (refuel generator tank2)92.5: 92.5: Update of Continuously Changing Primitive Numerical Expressions92.5: 92.5: (refuel generator tank2) - (refuel generator tank2) - end



b = fuel-level of tank 2

dg/dt = – 1

dr/dt = 1

db/dt = 0.32r – 4

dg/dt = – 0.32r + 4

dg/dt = – 0.32t + 3

g(t) = – 0.16t2 + 3t + 6

for t in [0,12.5)

r(t) = t for t in [0,12.5)

b(t) = 0.16t2 – 4t + 25

for t in [0,12.5)

VAL’s Progress

Time 80Time 80upto 92.5upto 92.5

InvariantsInvariants

UpdateUpdate Generator and Tank fuel-levels: g(12.5) = 18.5, b(12.5) = 0

g(t) > 0

for t in [0,12.5) – 0.16t2 + 3t + 6 > 0

for t in [0,12.5)

g(t) 60

for t

in (0,12.5)

– 0.16t2 + 3t + 6 60

for t in (0,12.5)

0.16t2 – 3t – 54 0 for t in (0,12.5)



VAL’s Progress

Time 92.5 upto 101Time 92.5 upto 101

101: 101: Invariant for (generate generator) (generate generator)101: 101: Update of Continuously Changing Primitive Numerical

Expressions101: 101: (generate generator) - (generate generator) - end

g(t) = – t + 18.5 for t in [0,8.5)

InvariantInvariant

g(t) > 0

for t in [0,8.5)

UpdateUpdate Generator fuel-level: g(8.5) = – 8.5 + 18.5 = 10

dg/dt = – 1

– t + 18.5 > 0 for t in [0,8.5)

VAL’s Progress

GoalGoal

VAL’s Progress

LaTeX ReportLaTeX Report

• Plan

• Plan to validate

• Plan validation

• Diagrams

• See handouts for generator validation report

VAL’s Progress

Gantt ChartGantt Chart

Actions of different executives can

be displayed on different rows

VAL’s Progress

GraphsGraphsGraphs of the primitive

numerical expressions are

plotted for the duration

of the plan.

VAL’s Progress

ConclusionsConclusions

• Restrictions on types of continuous effects are required to guarantee validation of plans: all continuous effects must be polynomial

• Validating plans with continuous effects is an important first step to developing planners capable of handling continuous effects.

vals progress val's progress: the automatic validation tool for pddl2.1 used in the...

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