Planning II
PROF LIM KWAN HUI
50.021 ARTIFICIAL INTELLIGENCE - PLANNING 1
50.021 Artificial Intelligence
2021 - Term 8
The following notes are compiled from various sources such as textbooks, lecture materials, Web resources and are shared for
academic purposes only, intended for use by students registered for a specific course. In the interest of brevity, every source is not cited.
The compiler of these notes gratefully acknowledges all such sources.
Planning Domain Definition
Language (PDDL)
o A language to describe planning problems that can be used as input to
planner software.
◦ Used by planning researchers as a standard language for defining classical
planning problems
o PDDL and STRIPS
◦ PDDL includes STRIPS as special case along with more advanced features
◦ PDDL includes some simple additional features, such as type specification for
objects, negated preconditions, conditional add/del effects
◦ Some more advanced features include allowing numeric variables and
durative actions
2021 - Term 8 50.021 ARTIFICIAL INTELLIGENCE - PLANNING 2
Components of a PDDL task
o Objects: Things in the world that interest us.
o Predicates: Properties of objects that we are interested in; can be true
or false
o Initial state: The state of the world that we start in.
o Goal specification: Things that we want to be true.
o Actions/Operators: Ways of changing the state of the world.
2021 - Term 8 50.021 ARTIFICIAL INTELLIGENCE - PLANNING 3
PDDL Task Specifications
o Planning tasks specified in PDDL are separated into two files:
◦ A problem file for objects, initial state and goal specification.
◦ A domain file for predicates (= facts) and actions.
o We will use Malte Helmert’s slides for specific examples
2021 - Term 8 50.021 ARTIFICIAL INTELLIGENCE - PLANNING 4
An Introduction to PDDL
1/15Malte Helmert October 16th, AI Planning
What is PDDL?
2/15
PDDL = Planning Domain Definition Language
~ standard encoding language for “classical” planning tasks
Components of a PDDL planning task:
• Objects: Things in the world that interest us.
• Predicates: Properties of objects that we are interested in; can be true or false.
• Initial state: The state of the world that we start in.
• Goal specification: Things that we want to be true.
• Actions/Operators: Ways of changing the state of the world.
Malte Helmert October 16th, AI Planning
3/15
How to Put the Pieces Together
Planning tasks specified in PDDL are separated into two files:
1. A domain file for predicates and actions.
2. A problem file for objects, initial state and goal specification.
Malte Helmert October 16th, AI Planning
4/15
Domain Files
Domain files look like this:
(define (domain )


[...]

)
is a string that identifies the planning domain, e.g. gripper.
Example on the web: gripper.pddl.
Malte Helmert October 16th, AI Planning
5/15
Problem Files
Problem files look like this:
(define (problem )
(:domain )



)
is a string that identifies the planning task, e.g. gripper-four-balls.
must match the domain name in the corresponding domain file.
Example on the web: gripper-four.pddl.
Malte Helmert October 16th, AI Planning
Malte Helmert October 16th, AI Planning 6/15
Running Example
Gripper task with four balls:
There is a robot that can move between two rooms and pick up or drop balls with either of
his two arms. Initially, all balls and the robot are in the first room. We want the balls to be in
the second room.
• Objects: The two rooms, four balls and two robot arms.
• Predicates: Is x a room? Is x a ball? Is ball x inside room y? Is robot arm x empty? [...]
• Initial state: All balls and the robot are in the first room. All robot arms are empty. [...]
• Goal specification: All balls must be in the second room.
• Actions/Operators: The robot can move between rooms, pick up a ball or drop a ball.
Malte Helmert October 16th, AI Planning 7/15
Gripper task: Objects
Objects:
Rooms: rooma, roomb
Balls: ball1, ball2, ball3, ball4
Robot arms: left, right
In PDDL:
(:objects rooma roomb
ball1 ball2 ball3 ball4
left right)
Malte Helmert October 16th, AI Planning 8/15
Gripper task: Predicates
Predicates:
ROOM(x)
BALL(x)
GRIPPER(x)
at-robby(x)
at-ball(x, y)
free(x)
carry(x, y)
– true iff x is a room
– true iff x is a ball
– true iff x is a gripper (robot arm)
– true iff x is a room and the robot is in x
– true iff x is a ball, y is a room, and x is in y
– true iff x is a gripper and x does not hold a ball
– true iff x is a gripper, y is a ball, and x holds y
In PDDL:
(:predicates (ROOM ?x) (BALL ?x) (GRIPPER ?x)
(at-robby ?x) (at-ball ?x ?y)
(free ?x) (carry ?x ?y))
Malte Helmert October 16th, AI Planning 9/15
Gripper task: Initial state
Initial state:
ROOM(rooma) and ROOM(roomb) are true.
BALL(ball1), ..., BALL(ball4) are true.
GRIPPER(left), GRIPPER(right), free(left) and free(right) are true.
at-robby(rooma), at-ball(ball1, rooma), ..., at-ball(ball4, rooma) are
true. Everything else is false.
In PDDL:
(:init (ROOM rooma) (ROOM roomb)
(BALL ball1) (BALL ball2) (BALL ball3) (BALL ball4)
(GRIPPER left) (GRIPPER right) (free left) (free right)
(at-robby rooma)
(at-ball ball1 rooma) (at-ball ball2 rooma)
(at-ball ball3 rooma) (at-ball ball4 rooma))
Malte Helmert October 16th, AI Planning 10/15
Gripper task: Goal specification
Goal specification:
at-ball(ball1, roomb), ..., at-ball(ball4, roomb) must be true.
Everything else we don’t care about.
In PDDL:
(:goal (and (at-ball ball1 roomb)
(at-ball ball2 roomb)
(at-ball ball3 roomb)
(at-ball ball4 roomb)))
Malte Helmert October 16th, AI Planning 11/15
Gripper task: Movement operator
Action/Operator:
Description:
Precondition:
Effect:
The robot can move from x to y.
ROOM(x), ROOM(y) and at-robby(x) are true.
at-robby(y) becomes true. at-robby(x) becomes false.
Everything else doesn’t change.
In PDDL:
(:action move :parameters (?x ?y)
:precondition (and (ROOM ?x) (ROOM ?y)
(at-robby ?x))
:effect (and (at-robby ?y)
(not (at-robby ?x))))
Malte Helmert October 16th, AI Planning 12/15
Gripper task: Pick-up operator
Action/Operator:
Description:
Precondition:
The robot can pick up x in y with z.
BALL(x), ROOM(y), GRIPPER(z), at-ball(x, y),
at-robby(y) and free(z) are true.
carry(z, x) becomes true. at-ball(x, y) and free(z)
become false. Everything else doesn’t change.
Effect:
In PDDL:
(:action pick-up :parameters (?x ?y ?z)
:precondition (and (BALL ?x) (ROOM ?y) (GRIPPER ?z)
(at-ball ?x ?y) (at-robby ?y) (free ?z))
:effect (and (carry ?z ?x)
(not (at-ball ?x ?y)) (not (free ?z))))
Malte Helmert October 16th, AI Planning 13/15
Gripper task: Drop operator
Action/Operator:
Description: The robot can drop x in y from z.
(Preconditions and effects similar to the pick-up operator.)
In PDDL:
(:action drop :parameters (?x ?y ?z)
:precondition (and (BALL ?x) (ROOM ?y) (GRIPPER ?z)
(carry ?z ?x) (at-robby ?y))
:effect (and (at-ball ?x ?y) (free ?z)
(not (carry ?z ?x))))
Malte Helmert October 16th, AI Planning 14/15
A Note on Action Effects
Action effects can be more complicated than seen so far.
They can be universally quantified:
(forall (?v1 ... ?vn)
)
They can be conditional:
(when
)
Example on the web: crazy-switches.pddl
Malte Helmert October 16th, AI Planning 15/15
Questions?