Archive Notes

2. Planning in PDDL

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Issues with classic planning

Classic planning has some issues which may be difficult or impossible to apply to problems:

  • actions are instantaneous
  • actions don’t define quantity or resources
  • goals cannot define resource constraints

Typing in PDDL

We can declare types in PDDL by adding it to our requirements:

# in domain
(:requirements typing)
(:types vehicle location)
 
(:predicates
	# use a dash to introduce a type
	(at ?v - vehicle ?p - location)
	(accessible ?v - vehicle ?p1 ?p2 - location)
)

Metric Planning

PDDL 2.1 introduces the ability to model numeric values through fluents. Fluents allow us to manage resources.

We can include this by using:

(:requirements fluents)

We can now create functions:

(:functions
	(fuel-level ?v - vehicle)
	(fuel-used ?v - vehicle)
	(fuel-required ?p1 ?p2 - location)
	(total-fuel-used)
)

And use them in our actions:

(:action drive
 :parameters (?v - vehicle ?from ?to - location)
 :precondition (and
   (at ?v ?from)
   (accessible ?v ?from ?to)
   (>= (fuel-level ?v) (fuel-required ?from ?to))
 )
 :effect (and
   (not (at ?v ?from))
   (at ?v t?to)
   (decrease (fuel-level ?v) (fuel-required ?from ?to))
   (increase (total-fuel-used) (fuel-required ?from ?to))
   (increase (fuel-used ?v) (fuel-required ?from ?to))
 )
)

Now let’s try defining a problem:

(:objects
  truck car - vehicle
  Paris Berlin Rome Madrid - location
)
 
(:init
  (at truck Rome)
  (at car Paris)
  
  (= (fuel-level truck) 100)
  (= (fuel-level car) 100)
  
  (accessible car Paris Berlin)
  (accessible car Berlin Rome)
  (accessible car Rome Madrid)
  (accessible truck Rome Paris)
  (accessible truck Rome Berlin)
  (accessible truck Berlin Paris)
  
  (= (fuel-required Paris Berlin) 40)
  (= (fuel-required Berlin Rome) 30)
  (= (fuel-required Rome Madrid) 50)
  (= (fuel-required Rome Paris) 35)
  (= (fuel-required Rome Berlin) 40)
  (= (fuel-required Berlin Paris) 40)
  
  (= (total-fuel-used) 0)
  (= (fuel-used car) 0)
  (= (fuel-used truck) 0)
)
 
(:goal (and
  (at truck Paris)
  (at car Rome)
))
 
(:metric minimize (total-fuel-used))

Temporal Planning

Conditions may hold true at different times.

We can define a durative action which includes a duration:

(:durative-action move-up-slow
 :parameters (?lift - slow-elevator ?f1 - floor ?f2 - floor)
 :duration (= ?duration (travel-slow ?f1 ?f2))
 :condition (and
   (at start (lift-at ?lift ?f1))
   (at start (above ?f1 ?f2))
   (at start (reachable-floor ?lift ?f2))
 )
 :effect (and
   (at start (not (lift-at ?lift ?f1)))
   (at end (lift-at ?lift ?f2))
 )
)

In the problem file we define:

(above f0 f1)
(reachable-floor slow1 f1)
(= (travel-slow f0 f1) 12)

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