Airport Pickup

Problem Description

A planning problem than that involves moving objects around a weighted graph.

Imagine a city composed of locations and possible driveways between these locations. Two of this locations are Airports and some are Gas Stations. A set of passengers are waiting in Airport #1 and Airport #2. Passengers from Airport #1 need to reach Airport #2 and vice-versa.

A set of vehicles are located around the city. Each of these vehicles can pick and transport one passenger at a time.

Driving a vehicle between two city locations costs the vehicle certain amount of gasoline. Initially all vehicles have certain amount of gasoline already in them. If a Vehicle runs out of gasoline, it cannot be driven anymore. Vehicles can re-fill gasoline at a Gas Station.

Find a plan to drive the vehicles and move all the passengers to their respective destinations.

A problem instance consists of a description of a city's (a weighted undirected graph), information about which locations in the city are Airports and Gas Stations, and statements about the location and status of vehicles and passengers.

Predicates

• Input: location/1, driveway/3, airport/1, gasstation/1, passenger/1, init_at/2, vehicle/2, init_at/2, init_gas/2

• Output: drive/3,  pick/2,  drop/2 and refuel/2

Input format

1. Atoms to describe the city:

   1. location(L) listing the names of locations.

   2. driveway(L1, L2, D) where L1 and L2 are locations, indicating that it is possible to drive from L1 to L2 ( and from L2 to L1 ) and that the gasoline cost from L1 to L2 is D. 0 < D <= 100.

   3. airport(L) indicating that location L is an airport. (there will be exactly 2 locations listed as airports)

   4. gasstation(L) indicating that location L is a gas station.

   B. Atoms to describe the passengers:

   1. passenger(P) listing the names of passengers

   2. init_at(P,L) stating that passenger P is initially at location L, where L is an airport.

   C. Atoms to describe the vehicles:

   1. vehicle(V, M) stating that V is a vehicle and its maximum gasoline capacity is M, 100 < M <= 500.

   2. init_at(V, L) stating that vehicle V is initially at location L.

   3. init_gas(V, G) indicating that initially, vehicle V has G units of gasoline. 0<= G <= M. where M is the maximum gasoline capacity of the vehicle.

Output format

The output format is a sequence of instructions to drive the cars and move the passengers. This sequence is formed with the atoms drive(V,L,S), pick(V,P), drop(V,P) and refuel(V,S) where:

1. drive(V,L,S) indicates vehicle V drives to location L at step S of the instruction sequence. This action is possible only if V is in a location adjacent to L at step S.

   B. pick(V,P,S) indicates vehicle V picks passenger P at step S. This action is possible only if V and P are at the same location at step S.

   C. drop(V,P,S) indicates vehicle V drops passenger P at step S. This action is possible only if V is carrying P at step S.

   D. refuel(V,S) indicated vehicle V fills up its gas tank at step S of the sequence.

This action is only possible if V is at a gas station.

Sample #1 input

location(1). location(2). location(3). location(4).
airport(1). airport(4).
gasstation(3).
driveway(1,2,10).
driveway(2,3,20).
driveway(3,4,15). 

passenger(a).
init_at(a,1).

vehicle(taxi_1, 100).
init_at(taxi_1, 2).  init_gas(taxi_1, 50).

Sample #1 output

drive(taxi_1, 1, 0).   
pick(taxi_1, a, 1). 
drive(taxi_1, 2, 2).   
drive(taxi_1, 3, 3).   
refuel(taxi_1, 4)      
drive(taxi_1, 4, 5).   
drop(taxi_1, a, 6). 

Sample #2 input

location(1). location(2). location(3). location(4).
airport(1). airport(4).
gasstation(3).
driveway(1,2,10).
driveway(2,3,20).
driveway(3,4,15). 

passenger(a).  init_at(a,1).
passenger(b).  init_at(b,4).

vehicle(taxi_1, 100). init_at(taxi_1, 1).  init_gas(taxi_1, 50).
vehicle(taxi_2, 80).  init_at(taxi_2, 4).  init_gas(taxi_1, 80). 

Sample #2 output

pick(taxi_1, a, 0).    pick(taxi_2, b, 0) 
drive(taxi_1, 2, 1).   drive(taxi_2, 3, 1).   
drive(taxi_1, 3, 2).   drive(taxi_2, 2, 2).         
drive(taxi_1, 4, 3).   drive(taxi_2, 1, 3).   
drop(taxi_1, a, 4).    drop(taxi_2, b, 4). 

Author(s)

Author: A. Ricardo Morales
Affiliation: Texas Tech University, United States