1. Modelling planning problems using PDDL
EH 2750
Modelling planning problems using PDDL
Arshad Saleem
06 Oct, 2014

2. Contents Forward and Backward chaining PDLL Modeling example in PDDL
PDDL modeling exercise

3. Forwards and Backwards Chaining
If <condition> Then <conclusion>
If <condition> Then <conclusion>
If <condition> Then <conclusion>
If <condition> Then <conclusion>
<Goal>

4. Forwards and Backwards Chaining
If <condition> Then <conclusion>
Forwards chaining
Data driven
Backwards chaining
Goal driven

5. Backwards Chaining Match the goal to the conclusions of rules
Set up the premises of the rules that matched as sub-goals
Repeat until:
all sub-goals match directly with known facts (goal is true), or
Some sub-goal fail to match (goal is false)
If <condition> Then <conclusion>
Forwards chaining
Data driven
Backwards chaining
Goal driven

6. Backwards Chaining There may be more than one rule which
conclusion matches the goal (a conflict)
Choose the first rule we find which matches and continue the search by trying to match its premises
If this fails, we backtrack up one or more levels of
rule and try again
Backward chaining is usually implemented as
depth-first search

7. Example: Backwards Chaining
Production rules:
1. if a then b,
2. if (f and k) then i
3. if (b and c) then d,
4. if (d and h) then f,
5. if (k or g) then h,
6. if b then c
Facts: a, k
Goal: f

8. Example: Backwards Chaining
Goal: we want to prove f
rule 4 says that we can prove f if d and h can be proved
Sub-goal: we want to prove d:
rule 3 says that we could prove d if b and c can be proved
(Sub-)sub-goal: we want to prove b:
rule 1 says that we could prove b if a can be proved
but a is a known fact, so we have proven b
(Sub-)sub-goal: we want to prove c:
rule 6 says that we could prove c if b can be proved
but we just proved b so we have also proven c
As we now have proved b and c, we know that d holds
Sub-goal: we want to prove h:
rule 5 says that we could prove h if k or g can be proved
but k is a known fact, so we have proven h
As we now have proved both d and h, we have proven f!

9. Forward-chaining Match the facts in the knowledge base to the
premises of rules
Apply the rules and add
the conclusions as new
(temporary) facts to the
knowledge base
Repeat until
– the goal is achieved, or
– no more rules fire

10. Example: Forwards Chaining
With forward chaining, we usually make all possible
derivations of new facts with each iterations, i. e. we fire all rules which apply
Thus, forward chaining uses a breadth first search
Example: same production rules as above
1. if a then b,
2. if (f and k) then i
3. if (b and c) then d,
4. if (d and h) then f,
5. if (k or g) then h,
6. if b then c
and the same known facts: a, k

11. Example: Forwards Chaining
Pass 0:
facts a,k
Pass 1: using rule 1. We conclude b
facts a,b,k
using rule 5. We conclude h
facts a,b,h,k
using rule 6. We conclude c
facts a,b,c,h,k
Pass 2: using rule 3. We conclude d
facts a,b,c,d,h,k
using rule 4. We conclude f
facts a,b,c,d,f,h,k
Pass 3: using rule 2. We conclude i
facts a,b,c,d,f,h,I,k
Production rules:
1. if a then b,
2. if (f and k) then i
3. if (b and c) then d,
4. if (d and h) then f,
5. if (k or g) then h,
6. if b then c
Facts: a, k
Goal: f

12. PDDL A modeling language for
PDDL = Planning Domain Definition Language
Problems modeled in this language can be executed by a software (JavaFF library in our case)

13. Components of PDDL 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.

14. Two parts of PDDL modelling
Planning tasks specified in PDDL are separated into two files
A domain file for predicates and actions
A problem file for objects, initial state and goal specification

15. Domain file

16. Problem file

17. Gripper 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.

18. Gripper example 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.

19. Gripper example: Objects

20. Gripper example: Predicates

21. Gripper example: Initial state

22. Gripper example: Goal state

23. Gripper example: movement action

24. Gripper example: pickup action

25. Gripper example: drop action

26. PDDL small exercise
Let’s write PDDL for:

27. Questions