Rushabh's Digital Garden

Example Problems on Planning

3 min read

Example 1

Design a planning problem using STRIP for Air cargo transport. It involves loading and unloading cargo onto and of planes and flying it from place. Initial state: At SFO airport, Cargo1, Plane1 and at JFK airport, Cargo2, Plane2 is present. Goal state: At SFO airport Cargo2 and at JFK airport Cargo1 is present.

1. Define Predicates

These describe the facts of the world:

  • At(x, y) – Object x is at location y

  • In(c, p) – Cargo c is inside Plane p

  • Cargo(x) – x is a cargo

  • Plane(x) – x is a plane

  • Airport(x) – x is an airport

2. Initial State

At(Cargo1, SFO)
At(Plane1, SFO)
At(Cargo2, JFK)
At(Plane2, JFK)
Cargo(Cargo1)
Cargo(Cargo2)
Plane(Plane1)
Plane(Plane2)
Airport(SFO)
Airport(JFK)

3. Goal State

At(Cargo1, JFK)
At(Cargo2, SFO)

4. Actions

(a) Load(c, p, a)

Preconditions:
  At(c, a) ∧ At(p, a) ∧ Cargo(c) ∧ Plane(p) ∧ Airport(a)
 
Effects:
  In(c, p) ∧ ¬At(c, a)

(b) Unload(c, p, a)

Preconditions:
  In(c, p) ∧ At(p, a) ∧ Cargo(c) ∧ Plane(p) ∧ Airport(a)
 
Effects:
  At(c, a) ∧ ¬In(c, p)

(c) Fly(p, from, to)

Preconditions:
  At(p, from) ∧ Plane(p) ∧ Airport(from) ∧ Airport(to)
 
Effects:
  At(p, to) ∧ ¬At(p, from)

5. Plan Overview (One Possible Sequence)

To achieve the goal state:

  1. Load(Cargo1, Plane1, SFO)

  2. Fly(Plane1, SFO, JFK)

  3. Unload(Cargo1, Plane1, JFK)

  4. Load(Cargo2, Plane2, JFK)

  5. Fly(Plane2, JFK, SFO)

  6. Unload(Cargo2, Plane2, SFO)

Example 2

Consider problem of changing a flat tire. The goal is to have a good spare tire properly mounted on to the car’s axle, where the initial state has a flat tire on the axle and a good spare tire in the trunk. Give the ADL description for the problem and also discuss the solution.

Problem: Changing a Flat Tire

Initial State

  • On(FlatTire, Axle) – Flat tire is mounted on the axle

  • In(SpareTire, Trunk) – Spare tire is inside the trunk

  • Tire(FlatTire), Tire(SpareTire)

  • Spare(SpareTire)

  • WrenchAvailable, JackAvailable, Loose(FlatTire) is False initially

  • Removed(FlatTire) is False initially

  • Mounted(SpareTire) is False initially

Goal State

  • Mounted(SpareTire)

  • ¬On(FlatTire, Axle)

  • ¬In(SpareTire, Trunk)

ADL Description

1. Remove(FlatTire, Axle)

Preconditions:
  On(FlatTire, Axle) ∧ Loose(FlatTire)
 
Effects:
  ¬On(FlatTire, Axle)
  ∧ Removed(FlatTire)

2. Loosen(FlatTire)

Preconditions:
  On(FlatTire, Axle) ∧ WrenchAvailable
 
Effects:
  Loose(FlatTire)

3. GetSpare(SpareTire)

Preconditions:
  In(SpareTire, Trunk)
 
Effects:
  ¬In(SpareTire, Trunk)

4. Mount(SpareTire, Axle)

Preconditions:
  Removed(FlatTire) ∧ ¬On(FlatTire, Axle) ∧ ¬In(SpareTire, Trunk)
 
Effects:
  On(SpareTire, Axle)
  ∧ Mounted(SpareTire)

Solution Steps (Valid Plan)

  1. Loosen(FlatTire) – Loosen the flat tire bolts

  2. Remove(FlatTire, Axle) – Take off the flat tire

  3. GetSpare(SpareTire) – Take the spare tire out of the trunk

  4. Mount(SpareTire, Axle) – Mount the spare tire on the axle

Graph View

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