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We will use the Logistics domain to illustrate how to represent a planning task in PDDL. In logistics, there are trucks and airplanes that can move packages between different airports and cities. We assume that in the initial state there is a truck in Paris airport. An airplane and two packages are in London airport. Paris has two places: south and north. The goal is to have one package in the north location and the other one in the south location.

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Defining the Domain

Let’s start by defining in the file logistics.pddl the domain and its components:
  • The requirements
  • The types
  • The predicates
  • The actions or operators
First, we define the name of the domain:
logistics.pddl
(define (domain logistics)

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Requirements

The requirements for this logistics example are:
  • strips: The actions will only use positive preconditions (predicates that must be true in the current state to trigger actions) and deterministic effects (effects that necessarily follow action triggering).
  • typing: We will use “types” like in OO programming to represent sets of objects in the world.
logistics.pddl
(:requirements :strips :typing)

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Types

We will use the following types:
  • Places, cities and physical objects are considered as objects
  • Packages and vehicles are physical objects
  • Trucks and airplanes are vehicles
  • Airports and locations are places
logistics.pddl
(:types city place physobj - object
        package vehicle - physobj
        truck airplane - vehicle
        airport location - place
)

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Predicates

We will use the following predicates:
  • in-city(loc, city) - true iff a place loc is in the city city
  • at(obj, loc) - true iff a physical object obj is at place loc
  • in(pkg, veh) - true iff a package pkg is in a vehicle veh
In PDDL, question marks are used for variables:
logistics.pddl
(:predicates
    (in-city ?loc - place ?city - city)
    (at ?obj - physobj ?loc - place)
    (in ?pkg - package ?veh - vehicle)
)

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Operators

We define the operators (actions) of the logistics domain. The domain has 6 operators: load-truck, load-airplane, unload-truck, unload-airplane, drive-truck and fly-airplane.

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Load Truck

To load a truck, we need a package and a truck at the same place. The effect is that the package is now in the truck and no longer at the location.
logistics.pddl
(:action load-truck
    :parameters (?pkg - package ?truck - truck ?loc - place)
    :precondition (and (at ?truck ?loc) (at ?pkg ?loc))
    :effect (and (not (at ?pkg ?loc)) (in ?pkg ?truck))
)

​
Load Airplane

logistics.pddl
(:action load-airplane
    :parameters (?pkg - package ?airplane - airplane ?loc - place)
    :precondition (and (at ?pkg ?loc) (at ?airplane ?loc))
    :effect (and (not (at ?pkg ?loc)) (in ?pkg ?airplane))
)

​
Unload Truck

logistics.pddl
(:action unload-truck
    :parameters (?pkg - package ?truck - truck ?loc - place)
    :precondition (and (at ?truck ?loc) (in ?pkg ?truck))
    :effect (and (not (in ?pkg ?truck)) (at ?pkg ?loc))
)

​
Unload Airplane

logistics.pddl
(:action unload-airplane
    :parameters (?pkg - package ?airplane - airplane ?loc - place)
    :precondition (and (in ?pkg ?airplane) (at ?airplane ?loc))
    :effect (and (not (in ?pkg ?airplane)) (at ?pkg ?loc))
)

​
Fly Airplane

logistics.pddl
(:action fly-airplane
    :parameters (?airplane - airplane ?loc-from - airport ?loc-to - airport)
    :precondition (at ?airplane ?loc-from)
    :effect (and (not (at ?airplane ?loc-from)) (at ?airplane ?loc-to))
)

​
Drive Truck

logistics.pddl
(:action drive-truck
    :parameters (?truck - truck ?loc-from - place ?loc-to - place ?city - city)
    :precondition (and (at ?truck ?loc-from)
                       (in-city ?loc-from ?city)
                       (in-city ?loc-to ?city))
    :effect (and (not (at ?truck ?loc-from)) (at ?truck ?loc-to))
)
Action preconditions and effects can be more complex:
  • Quantified: (forall (?v1 ... ?vn) <effect>) requires the :adl requirement
  • Conditional: (when <condition> <effect>)
  • Actions can also have costs, duration, and time constraints

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Defining the Problem

Now let’s define in the file problem.pddl the problem instance:
problem.pddl
(define (problem p01)
    (:domain logistics)

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Objects

problem.pddl
(:objects
    plane - airplane
    truck - truck
    cdg lhr - airport
    south north - location
    paris london - city
    p1 p2 - package
)

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Initial State

The initial state is a set of ground predicates (all variables bound to objects). Facts not listed are assumed false:
problem.pddl
(:init
    (in-city cdg paris)
    (in-city lhr london)
    (in-city north paris)
    (in-city south paris)
    (at plane lhr)
    (at truck cdg)
    (at p1 lhr)
    (at p2 lhr)
)

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Goal Description

The goal is to have package p1 at north and package p2 at south:
problem.pddl
(:goal (and (at p1 north)
            (at p2 south))
)

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Solution

Running a PDDL planner produces the following plan:
Plan Output
00: (load-airplane p1 plane lhr) [1]
01: (load-airplane p2 plane lhr) [1]
02: (fly-airplane plane lhr cdg) [1]
03: (unload-airplane p1 plane cdg) [1]
04: (unload-airplane p2 plane cdg) [1]
05: (load-truck p1 truck cdg) [1]
06: (load-truck p2 truck cdg) [1]
07: (drive-truck truck cdg south paris) [1]
08: (unload-truck p2 truck south) [1]
09: (drive-truck truck south north paris) [1]
10: (unload-truck p1 truck north) [1]

Plan total cost: 11.00
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