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a_star.py
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a_star.py
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#!/usr/bin/env python
import math
import numpy as np
import heapq
import collections
import copy
def dist_between(point_a, point_b):
"""
Pothagoreans theorm, the distance between 2 cells.
This represents the cost to move from 1 cell to another.
"""
a = point_b[0] - point_a[0]
b = point_b[1] - point_a[1]
result = math.sqrt(a ** 2.0 + b ** 2.0)
# print result
return result
class AStar(object):
"""
AStar represents an instance of the A* algorithm.
"""
def __init__(self, field, start, goal, heuristic_cost_estimate):
"""
Creates a new AStar instance.
"""
self.start = start
self.goal = goal
self.width = field.width
self.height = field.height
self.field = field
self.heuristic_cost_estimate = heuristic_cost_estimate
self.g_score = np.zeros(self.width * self.height, dtype=float)\
.reshape(self.width, self.height)
self.h_score = np.zeros(self.width * self.height, dtype=float)\
.reshape(self.width, self.height)
self.f_score = np.zeros(self.width * self.height, dtype=float)\
.reshape(self.width, self.height)
# The set of nodes already evaluated.
self.closedset = set()
# The set of tentative nodes to be evaluated, initially containing the
# start node
self.openset = [(self.f_score[start], start)]
heapq.heapify(self.openset)
# The map of navigated nodes.
self.came_from = {start: None}
# The path to the goal
self.path = []
# Cost from start along best known path.
self.g_score[start] = 0
self.h_score[start] = self.heuristic_cost_estimate(field, start, goal)
# Estimated total cost from start to goal through y.
self.f_score[start] = self.g_score[start] + self.h_score[start]
def solve(self):
"""
Solves for the path.
"""
while self.step_solution():
pass
self.draw_path()
return True
def draw_path(self):
"""
Draws the path in the field.
"""
max_cell = self.field.data.max() * -1.0
max_counter = 0
self.field[self.field.data == -1] = max_cell / 2.0
if self.path:
for (x, y) in self.path:
max_counter += 1
self.field[x, y] = -20
def step_solution(self):
"""
A function that returns a path as a list of coordinates.
field = A representation of the playing field or graph.
start = The starting position
goal = The target position
heuristic_cost_estimate = A function to estimate the cost of moving
into a neighboring cell.
neighbors_fn = None | A function to get neighbors of a point.
return = A list of points that make up a path.
"""
# Find the lowest scoring node in the openset
try:
current_node = heapq.heappop(self.openset)
except IndexError:
return False
x = current_node[1]
if x == self.goal:
if x == self.goal and x == self.start:
self.path = []
else:
self.path = reconstruct_path(self.came_from,
self.came_from[self.goal])
self.path.append(self.goal)
self.draw_path()
return False
self.closedset.add(x)
for y in self.field.get_neighbors(*x):
# If the value is in the closedset we don't need to revisit it
if y in self.closedset:
continue
if self.field[y] == -1:
continue
tentative_g_score = self.g_score[x] + dist_between(x, y)
# Strip out the f_scores from the openset and check if it exists
if y not in [v[1] for v in self.openset]:
self.came_from[y] = x
self.g_score[y] = tentative_g_score
self.h_score[y] = self.heuristic_cost_estimate(self.field,
y,
self.goal)
self.f_score[y] = self.g_score[y] + self.h_score[y]
self.field[y] = self.f_score[y]
heapq.heappush(self.openset, (self.f_score[y], y))
elif tentative_g_score < self.g_score[y]:
self.came_from[y] = x
self.g_score[y] = tentative_g_score
self.h_score[y] = self.heuristic_cost_estimate(self.field,
y,
self.goal)
self.f_score[y] = self.g_score[y] + self.h_score[y]
self.field[y] = self.f_score[y]
return True
# 3 distinct heuristics
# I include the field incase future heuristics need to access values from it.
def crow(f, cell0, cell1):
"A hypotense of a triangle."
return dist_between(cell0, cell1)
def manhattan(f, cell0, cell1):
"""
Calculate the manhattan distance.
"""
return (abs(cell1[0] - cell0[0]) + abs(cell1[1] - cell0[1]))
def naive(f, cell0, cell1):
"Simply returns 0"
return 0
def reconstruct_path(came_from, current_node):
"""
Takes a dictionary with the path in it and follows it to the root.
"""
if came_from[current_node]:
p = reconstruct_path(came_from, came_from[current_node])
p.append(current_node)
return p
else:
return [current_node]
if __name__ == '__main__':
from costmap import Costmap2D
from obstacle import Obstacle
from matplotlib.pyplot import plot, show
from matplotlib.pylab import imshow, show, figure
import time
c = Costmap2D(10, 20, resolution=0.5)
c.goal = (0, 0)
c.start = (c.width - 1, c.height - 1)
Obstacle(4, 3, 3, 3).draw(c)
Obstacle(5, 9, 3, 3).draw(c)
Obstacle(4, 16, 3, 3).draw(c)
a_star = AStar(c, c.start, c.goal, naive)
start = time.time()
a_star.solve()
end = time.time()
print 'Naive:', end - start
imshow(a_star.field.data, interpolation='nearest')
show()