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331 lines
8.2 KiB
Markdown
331 lines
8.2 KiB
Markdown
---
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title: "Disjunctive Goals in PDDL"
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date: 2024-04-16T11:26:28-04:00
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draft: false
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tags: ["Automated Planning"]
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math: true
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medium_enabled: false
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---
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Classical AI planning tries to find a sequence of actions that takes an agent from their initial state to a state that satisfies some goal.
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Let's say, for example, that you want to deliver a package that's currently sitting at location `A`. The recipient said that you can drop it off at either their workplace `B` or their home `C`.
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If you drop it off at a some location, then people will be nice enough to let you retrieve the package and place it back at location `A`. Graphically, we can represent it as follows:
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A state in classical planning is a set of atomic formulas. For our problem it will look like:
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```lisp
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(:init
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(at-package A)
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; Delivery Paths
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(CONNECTED A B)
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(CONNECTED A C)
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(CONNECTED A D)
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; Retrieval paths
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(CONNECTED B A)
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(CONNECTED C A)
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(CONNECTED D A)
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)
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```
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The goal in classical planning is a set of ground atomic formulas and the negations of ground atomic formulas. That means, the following isn't a "valid" goal in the classical planning model.
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```lisp
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(:goal (or (at-package B) (at-package C)))
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```
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I put valid in quotation marks since if you use the [Fast Downward](https://www.fast-downward.org/) planner, it will behind the scenes compile it to a valid planning problem. But what if you're not fortunate enough to have a planner automatically do that for you? We'll discuss three different techniques for handling disjunctive goals.
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## (1) Plan for each Disjunct
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A plan that delivers a package to `B` is valid for the goal of delivering it to either `B` or `C`. The same goes for delivering it to `C`. Therefore, the set of valid plans for the disjunctive goal is the union of all the plans that satisfy either of the disjuncts.
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Domain File:
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```lisp
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(define (domain test-disjunct)
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(:requirements :typing)
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(:types location - object)
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(:predicates (at-package ?l - location) (CONNECTED ?l1 ?l2 - location)
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(:action move-package
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:parameters (?l1 ?l2 - location)
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:precondition (and
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(at-package ?l1)
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(CONNECTED ?l1 ?l2)
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)
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:effect (and
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(at-package ?l2)
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(not (at-package ?l1))
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)
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)
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)
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```
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Problem File:
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```lisp
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(define (problem test-disjunct)
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(:domain test-disjunct)
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(:requirements :typing)
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(:objects
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A B C D - location
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)
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(:init
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(at-package A)
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(CONNECTED A B)
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(CONNECTED A C)
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(CONNECTED A D)
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(CONNECTED B A)
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(CONNECTED C A)
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(CONNECTED D A)
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)
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(:goal (at-package B))
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; (:goal (at-package C))
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)
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```
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Call Planner:
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```bash
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./fast-downward.sif --alias lama-first domain-disjunct.pddl problem-disjunct.pddl
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```
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Result:
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```
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move-package a b
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```
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## (2) Derived Predicates (Axioms)
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Axioms or derived predicates are atomic ground formula that can only appear in the precondition of actions and the goal. That is, it cannot appear in the effect.
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We can create a new derived predicate `done` which when true means that we have satisfied the goal.
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```lisp
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(:derived (done) (or (at-package B) (at-package C)))
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```
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Domain File:
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```lisp
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(define (domain test-derived)
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(:requirements :derived-predicates :typing )
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(:types location - object)
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(:predicates (at-package ?l - location) (CONNECTED ?l1 ?l2 - location) (done))
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(:derived (done) (or (at-package B) (at-package C)))
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(:action move-package
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:parameters (?l1 ?l2 - location)
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:precondition (and
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(at-package ?l1)
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(CONNECTED ?l1 ?l2)
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)
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:effect (and
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(at-package ?l2)
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(not (at-package ?l1))
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)
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)
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)
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```
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Problem File:
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```lisp
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(define (problem test-derived)
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(:domain test-derived)
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(:requirements :typing)
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(:objects
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A B C D - location
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)
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(:init
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(at-package A)
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(CONNECTED A B)
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(CONNECTED A C)
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(CONNECTED A D)
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(CONNECTED B A)
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(CONNECTED C A)
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(CONNECTED D A)
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)
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(:goal (done))
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)
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```
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Call Planner:
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```bash
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./fast-downward.sif benchmarks/domain-derived.pddl benchmarks/problem-derived.pddl \
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--search "astar(blind())"
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```
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Result:
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```
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move-package a b
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```
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**Note:** Not all heuristics in FastDownward support axioms. In fact this problem is not limited to FastDownward. The planner call above uses the blind heuristic which supports axioms and is safe.
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Before replacing that evaluator, however, make sure to [read the docs](https://www.fast-downward.org/Doc/Evaluator) to make sure that the heuristic states that it supports axioms, and that it is safe in the presence of them.
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## (3) Compilation
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The core idea of this technique is to push the disjunction onto the search space. As with the last technique we create a new predicate `done`. However, instead of automatically deriving `done` through an axiom, we create an action for every disjunct whose precondition is that disjunct, and whose effect is `done`.
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Example:
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```lisp
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(:action goal-B
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:parameters ()
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:precondition (at-package B)
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:effect (done)
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)
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(:action goal-C
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:parameters ()
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:precondition (at-package C)
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:effect (done)
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)
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```
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Our new goal will be `(:goal (done))`. After you plan using the compiled version of the problem, drop the actions `goal-B` and `goal-C` and you have a plan for the disjunctive problem.
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This technique works great when you're grabbing the first optimal plan, however, there are two considerations that need to be made when you grab more than just one plan[^1].
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[^1]: The field of diverse planning looks at generating multiple plans for a given planning problem. The introduction to ["Reshaping Diverse Planning"](https://ojs.aaai.org/index.php/AAAI/article/view/6543) by Michael Katz and Shirin Sohrabi covers well the motivations behind this.
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(1) There's nothing guarding against an infinite chain of `goal-B` action calls. Hence the following is a valid plan:
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```
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move-package a b
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goal-B
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goal-B
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goal-B
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```
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We can address this by adding `(not (done))` to the preconditions of each of the goal actions.
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(2) We have no effects that remove `done`, so a valid plan can move to a state that satisfies the goal and then move away.
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```
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move-package a b
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move-package b a
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```
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We can address this by adding `(not (done))` to the effect of every action that is not the goal actions.
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Domain File:
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```lisp
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(define (domain test-compile)
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(:requirements :typing)
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(:types location - object)
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(:predicates (at-package ?l - location) (CONNECTED ?l1 ?l2 - location) (done))
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(:action move-package
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:parameters (?l1 ?l2 - location)
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:precondition (and
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(at-package ?l1)
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(CONNECTED ?l1 ?l2)
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)
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:effect (and
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(at-package ?l2)
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(not (at-package ?l1))
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(not (done))
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)
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)
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(:action goal-B
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:parameters ()
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:precondition (and
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(at-package B)
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(not (done))
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)
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:effect (done)
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)
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(:action goal-C
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:parameters ()
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:precondition (and
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(at-package C)
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(not (done))
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)
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:effect (done)
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)
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)
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```
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Problem File:
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```lisp
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(define (problem test-compile)
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(:domain test-compile)
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(:requirements :strips)
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(:objects
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A B C D - location
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)
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(:init
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(at-package A)
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(CONNECTED A B)
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(CONNECTED A C)
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(CONNECTED A D)
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(CONNECTED B A)
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(CONNECTED C A)
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(CONNECTED D A)
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)
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(:goal (done))
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)
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```
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Planner Call:
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To retrieve multiple plans, we can use the [Kstar](https://github.com/IBM/kstar) package by IBM. In particular, I had success with their [Python package](https://pypi.org/project/kstar-planner/).
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```python
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from kstar_planner import planners
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from pathlib import Path
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domain_file = Path("domain-compile.pddl")
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problem_file = Path("problem-compile.pddl")
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plans = planners.plan_topk(
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domain_file=domain_file,
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problem_file=problem_file,
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number_of_plans_bound=3,
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timeout=30
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)
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print(plans)
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```
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Output:
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```
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===
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move-package a b
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goal-b
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===
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move-package a c
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goal-c
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===
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move-package a b
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move-package b a
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move-package a b
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goal-b
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```
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Not sure why you would want to execute the last plan, but at least the package got to its destination at the end :D
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