Perform path calculation on 2D grid with Networkx
It seemed easy to use the Python library Networkx to do a simple path calculation, so I tried using it.
First, consider the following two-dimensional grid environment. The grid size is 20x20.
import networkx as nx
import matplotlib.pyplot as plt
ngrid = 20
gp = nx.grid_graph(dim=[ngrid, ngrid])
nx.draw(gp,
pos=dict((n, n) for n in gp.nodes()),
node_color=[gp.node[n].get('color', 'white') for n in gp.nodes_iter()],
node_size=200)
plt.axis('equal')
plt.show()
I also wanted the grid-like diagonal paths to be OK, so I'll add diagonal edges to each node.
import networkx as nx
import matplotlib.pyplot as plt
def add_cross_edge(gp, shape):
"""
Add diagonal edges to a 2D Grid graph
"""
for node in gp.nodes_iter():
nx_node = (node[0] + 1, node[1] + 1)
if nx_node[0] < shape[0] and nx_node[1] < shape[1]:
gp.add_edge(node, nx_node)
nx_node = (node[0] + 1, node[1] - 1)
if nx_node[0] < shape[0] and nx_node[1] >= 0:
gp.add_edge(node, nx_node)
ngrid = 20
gp = nx.grid_graph(dim=[ngrid, ngrid])
add_cross_edge(gp, [ngrid, ngrid])
nx.draw(gp,
pos=dict((n, n) for n in gp.nodes()),
node_color=[gp.node[n].get('color', 'white') for n in gp.nodes_iter()],
node_size=200)
plt.axis('equal')
plt.show()
Finally, set obstacles and start goals, and you're done building the environment itself. Here, the obstacles are colored black, the start is colored green, and the goal is colored red. Using this environment, we will calculate the path connecting the start and the goal while avoiding obstacles.
import networkx as nx
import matplotlib.pyplot as plt
def add_cross_edge(gp, shape):
"""
Add diagonal edges to a 2D Grid graph
"""
for node in gp.nodes_iter():
nx_node = (node[0] + 1, node[1] + 1)
if nx_node[0] < shape[0] and nx_node[1] < shape[1]:
gp.add_edge(node, nx_node)
nx_node = (node[0] + 1, node[1] - 1)
if nx_node[0] < shape[0] and nx_node[1] >= 0:
gp.add_edge(node, nx_node)
ngrid = 20
gp = nx.grid_graph(dim=[ngrid, ngrid])
add_cross_edge(gp, [ngrid, ngrid])
idcs = np.random.choice(len(gp.nodes()), int(ngrid * ngrid * 0.2), replace=False)
#Set start / goal / obstacle
st, gl, obs = gp.nodes()[idcs[0]], gp.nodes()[idcs[1]], [gp.nodes()[i] for i in idcs[2:]]
gp.node[st]['color'] = 'green'
gp.node[gl]['color'] = 'red'
for o in obs:
gp.node[o]['color'] = 'black'
nx.draw(gp,
pos=dict((n, n) for n in gp.nodes()),
node_color=[gp.node[n].get('color', 'white') for n in gp.nodes_iter()],
node_size=200)
plt.axis('equal')
plt.show()
Then set a Weight between each edge to avoid obstacles. I try to impose a penalty when the node is wearing an obstacle.
import numpy as np
def cost(a, b):
"""
Cost function
"""
x1 = np.array(a, dtype=np.float32)
x2 = np.array(b, dtype=np.float32)
dist = np.linalg.norm(x1 - x2)
if any([(a == o or b == o) for o in obs]):
penalty = 1.0e6
else:
penalty = 0.0
return dist + penalty
for u, v, d in gp.edges_iter(data=True):
d['weight'] = cost(u, v)
There are several path search functions in Networkx, but this time we will use the A * algorithm. The A * algorithm requires something called a heuristic function, which is set as follows.
def dist(a, b):
"""
Heuristic function
"""
x1 = np.array(a, dtype=np.float32)
x2 = np.array(b, dtype=np.float32)
return np.linalg.norm(x1 - x2)
path = nx.astar_path(gp, st, gl, dist)
length = nx.astar_path_length(gp, st, gl, dist)
print(path)
print(length)
Finally, let's draw the path search result. The nodes on the path are shown in blue.
for p in path[1:-1]:
if gp.node[p].get('color', '') == 'black':
print('Invalid path')
continue
gp.node[p]['color'] = 'blue'
nx.draw(gp,
pos=dict((n, n) for n in gp.nodes()),
node_color=[gp.node[n].get('color', 'white') for n in gp.nodes_iter()],
node_size=200)
plt.axis('equal')
plt.show()
The whole code looks like this:
#!/usr/bin/env python
# -*- coding: utf-8 -*-
import numpy as np
import networkx as nx
import matplotlib.pyplot as plt
def add_cross_edge(gp, shape):
"""
Add diagonal edges to a 2D Grid graph
"""
for node in gp.nodes_iter():
nx_node = (node[0] + 1, node[1] + 1)
if nx_node[0] < shape[0] and nx_node[1] < shape[1]:
gp.add_edge(node, nx_node)
nx_node = (node[0] + 1, node[1] - 1)
if nx_node[0] < shape[0] and nx_node[1] >= 0:
gp.add_edge(node, nx_node)
ngrid = 20
gp = nx.grid_graph(dim=[ngrid, ngrid])
add_cross_edge(gp, [ngrid, ngrid])
idcs = np.random.choice(len(gp.nodes()), int(ngrid * ngrid * 0.2), replace=False)
#Set start / goal / obstacle
st, gl, obs = gp.nodes()[idcs[0]], gp.nodes()[idcs[1]], [gp.nodes()[i] for i in idcs[2:]]
gp.node[st]['color'] = 'green'
gp.node[gl]['color'] = 'red'
for o in obs:
gp.node[o]['color'] = 'black'
def dist(a, b):
"""
Heuristic function
"""
x1 = np.array(a, dtype=np.float32)
x2 = np.array(b, dtype=np.float32)
return np.linalg.norm(x1 - x2)
def cost(a, b, k1=1.0, k2=10.0, kind='intsct'):
"""
Cost function
"""
x1 = np.array(a, dtype=np.float32)
x2 = np.array(b, dtype=np.float32)
dist = np.linalg.norm(x1 - x2)
if any([(a == o or b == o) for o in obs]):
penalty = 1.0e6
else:
penalty = 0.0
return dist + penalty
for u, v, d in gp.edges_iter(data=True):
d['weight'] = cost(u, v)
path = nx.astar_path(gp, st, gl, dist)
length = nx.astar_path_length(gp, st, gl, dist)
print(path)
print(length)
for p in path[1:-1]:
if gp.node[p].get('color', '') == 'black':
print('Invalid path')
continue
gp.node[p]['color'] = 'blue'
nx.draw(gp,
pos=dict((n, n) for n in gp.nodes()),
node_color=[gp.node[n].get('color', 'white') for n in gp.nodes_iter()],
node_size=200)
plt.axis('equal')
plt.show()
Networkx is convenient. The environment with obstacles in the 2D grid set this time seems to be usable for reinforcement learning.