Implement A* search algorithm. Upload your source code and the final grid image

Question

Implement A* search algorithm. Upload your source code and the final grid image with the shorted path in this project report.

The following figure contains a robot, a door, and six chairs, each of them takes one grid. The figure also contains 10 by 10 = 100 grids. The robot need to avoid six chairs and find out a shortest path to the door. For each step of the A* search, the robot can only move to one neighbor grid of 8 neighbors (east, southeast, south, southwest, west, northwest, north, and northeast).

You can reference A* search algorithm: http://theory.stanford.edu/~amitp/GameProgramming/AStarComparison.html

For reference code of programming languages of C++, Java, Javascript, Python, Objective C +, Lua, Ruby, C#, and Processing, you can reference the webpage:

http://theory.stanford.edu/~amitp/GameProgramming/ImplementationNotes.html#code

(Hint: can use a 10 x 10 matrix for modeling the 10 x 10 grids. Each element in the matrix is relevant to a grid in the picture. After the A* search, visualize this matrix to show the shortest path.)

Explanation / Answer

Algorithm is taken from this source and implemented according to the mentioned requirements:

http://code.activestate.com/recipes/577519-a-star-shortest-path-algorithm/

Code:

# A* Shortest Path Algorithm

from heapq import heappush, heappop # for priority queue
import math
import time
import random

class node:
xPos = 0 # x position
yPos = 0 # y position
distance = 0 # total distance already travelled to reach the node
priority = 0 # priority = distance + remaining distance estimate
def __init__(self, xPos, yPos, distance, priority):
self.xPos = xPos
self.yPos = yPos
self.distance = distance
self.priority = priority
def __lt__(self, other): # comparison method for priority queue
return self.priority < other.priority
def updatePriority(self, xDest, yDest):
self.priority = self.distance + self.estimate(xDest, yDest) * 10 # A*
# give higher priority to going straight instead of diagonally
def nextMove(self, dirs, d): # d: direction to move
if dirs == 8 and d % 2 != 0:
self.distance += 14
else:
self.distance += 10
# Estimation function for the remaining distance to the goal.
def estimate(self, xDest, yDest):
xd = xDest - self.xPos
yd = yDest - self.yPos
# Euclidian Distance
d = math.sqrt(xd * xd + yd * yd)
return(d)

# A-star algorithm.
# The path returned will be a string of digits of directions.
def pathFind(the_map, n, m, dirs, dx, dy, xA, yA, xB, yB):
closed_nodes_map = [] # map of closed (tried-out) nodes
open_nodes_map = [] # map of open (not-yet-tried) nodes
dir_map = [] # map of dirs
row = [0] * n
for i in range(m): # create 2d arrays
closed_nodes_map.append(list(row))
open_nodes_map.append(list(row))
dir_map.append(list(row))

pq = [[], []] # priority queues of open (not-yet-tried) nodes
pqi = 0 # priority queue index
# create the start node and push into list of open nodes
n0 = node(xA, yA, 0, 0)
n0.updatePriority(xB, yB)
heappush(pq[pqi], n0)
open_nodes_map[yA][xA] = n0.priority # mark it on the open nodes map

# A* search
while len(pq[pqi]) > 0:
# get the current node w/ the highest priority
# from the list of open nodes
n1 = pq[pqi][0] # top node
n0 = node(n1.xPos, n1.yPos, n1.distance, n1.priority)
x = n0.xPos
y = n0.yPos
heappop(pq[pqi]) # remove the node from the open list
open_nodes_map[y][x] = 0
closed_nodes_map[y][x] = 1 # mark it on the closed nodes map

# quit searching when the goal is reached
# if n0.estimate(xB, yB) == 0:
if x == xB and y == yB:
# generate the path from finish to start
# by following the dirs
path = ''
while not (x == xA and y == yA):
j = dir_map[y][x]
c = str((j + dirs / 2) % dirs)
path = c + path
x += dx[j]
y += dy[j]
return path

# generate moves (child nodes) in all possible dirs
for i in range(dirs):
xdx = x + dx[i]
ydy = y + dy[i]
if not (xdx < 0 or xdx > n-1 or ydy < 0 or ydy > m - 1
or the_map[ydy][xdx] == 1 or closed_nodes_map[ydy][xdx] == 1):
# generate a child node
m0 = node(xdx, ydy, n0.distance, n0.priority)
m0.nextMove(dirs, i)
m0.updatePriority(xB, yB)
# if it is not in the open list then add into that
if open_nodes_map[ydy][xdx] == 0:
open_nodes_map[ydy][xdx] = m0.priority
heappush(pq[pqi], m0)
# mark its parent node direction
dir_map[ydy][xdx] = (i + dirs / 2) % dirs
elif open_nodes_map[ydy][xdx] > m0.priority:
# update the priority
open_nodes_map[ydy][xdx] = m0.priority
# update the parent direction
dir_map[ydy][xdx] = (i + dirs / 2) % dirs
# replace the node
# by emptying one pq to the other one
# except the node to be replaced will be ignored
# and the new node will be pushed in instead
while not (pq[pqi][0].xPos == xdx and pq[pqi][0].yPos == ydy):
heappush(pq[1 - pqi], pq[pqi][0])
heappop(pq[pqi])
heappop(pq[pqi]) # remove the target node
# empty the larger size priority queue to the smaller one
if len(pq[pqi]) > len(pq[1 - pqi]):
pqi = 1 - pqi
while len(pq[pqi]) > 0:
heappush(pq[1-pqi], pq[pqi][0])
heappop(pq[pqi])   
pqi = 1 - pqi
heappush(pq[pqi], m0) # add the better node instead
return ' ' # if no route found

# MAIN
dirs = 8 # number of possible directions to move on the map
if dirs == 4:
dx = [1, 0, -1, 0]
dy = [0, 1, 0, -1]
elif dirs == 8:
dx = [1, 1, 0, -1, -1, -1, 0, 1]
dy = [0, 1, 1, 1, 0, -1, -1, -1]

n = 10 # horizontal size of the map
m = 10 # vertical size of the map
the_map = []
row = [0] * n
for i in range(m): # create empty map
the_map.append(list(row))

#settin up the obstacles
the_map[4][2] = 1
the_map[5][3] = 1
the_map[4][4] = 1
the_map[4][5] = 1
the_map[3][6] = 1
the_map[2][7] = 1

#starting position
xA=0
yA=0
#ending position
xB=9
yB=9

print 'Map size (X,Y): ', n, m
print 'Start: ', xA, yA
print 'Finish: ', xB, yB
t = time.time()
route = pathFind(the_map, n, m, dirs, dx, dy, xA, yA, xB, yB)
print 'Time to generate the route (seconds): ', time.time() - t
print 'Route:'
print route

# mark the route on the map
if len(route) > 0:
x = xA
y = yA
the_map[y][x] = 2
for i in range(len(route)):
j = int(route[i])
x += dx[j]
y += dy[j]
the_map[y][x] = 3
the_map[y][x] = 4

# display the map with the route added
print 'Map:'
for y in range(m):
for x in range(n):
xy = the_map[y][x]
if xy == 0:
print '.', # space
elif xy == 1:
print 'O', # obstacle
elif xy == 2:
print 'S', # start
elif xy == 3:
print 'R', # route
elif xy == 4:
print 'F', # finish
print
  

Output:

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