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planning_utils.py
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from enum import Enum
from queue import PriorityQueue
import numpy as np
import math
from scipy.spatial import Voronoi, voronoi_plot_2d
from bresenham import bresenham
import matplotlib.pyplot as plt
def create_grid(data, drone_altitude, safety_distance):
"""
Returns a grid representation of a 2D configuration space
based on given obstacle data, drone altitude and safety distance
arguments.
"""
# minimum and maximum north coordinates
north_min = np.floor(np.min(data[:, 0] - data[:, 3]))
north_max = np.ceil(np.max(data[:, 0] + data[:, 3]))
# minimum and maximum east coordinates
east_min = np.floor(np.min(data[:, 1] - data[:, 4]))
east_max = np.ceil(np.max(data[:, 1] + data[:, 4]))
# given the minimum and maximum coordinates we can
# calculate the size of the grid.
north_size = int(np.ceil(north_max - north_min))
east_size = int(np.ceil(east_max - east_min))
# Initialize an empty grid
grid = np.zeros((north_size, east_size))
# Populate the grid with obstacles
for i in range(data.shape[0]):
north, east, alt, d_north, d_east, d_alt = data[i, :]
if alt + d_alt + safety_distance > drone_altitude:
obstacle = [
int(np.clip(north - d_north - safety_distance - north_min, 0, north_size-1)),
int(np.clip(north + d_north + safety_distance - north_min, 0, north_size-1)),
int(np.clip(east - d_east - safety_distance - east_min, 0, east_size-1)),
int(np.clip(east + d_east + safety_distance - east_min, 0, east_size-1)),
]
grid[obstacle[0]:obstacle[1]+1, obstacle[2]:obstacle[3]+1] = 1
return grid, int(north_min), int(east_min)
# Assume all actions cost the same.
class Action(Enum):
"""
An action is represented by a 3 element tuple.
The first 2 values are the delta of the action relative
to the current grid position. The third and final value
is the cost of performing the action.
"""
WEST = (0, -1, 1)
EAST = (0, 1, 1)
NORTH = (-1, 0, 1)
SOUTH = (1, 0, 1)
NORTH_WEST = (-1, -1, math.sqrt(2))
NORTH_EAST = (-1, 1, math.sqrt(2))
SOUTH_WEST = (1, -1, math.sqrt(2))
SOUTH_EAST = (1, 1, math.sqrt(2))
@property
def cost(self):
return self.value[2]
@property
def delta(self):
return (self.value[0], self.value[1])
def valid_actions(grid, current_node):
"""
Returns a list of valid actions given a grid and current node.
"""
valid_actions = list(Action)
n, m = grid.shape[0] - 1, grid.shape[1] - 1
x, y = current_node
# check if the node is off the grid or
# it's an obstacle
if x - 1 < 0 or grid[x - 1, y] == 1:
valid_actions.remove(Action.NORTH)
if x + 1 > n or grid[x + 1, y] == 1:
valid_actions.remove(Action.SOUTH)
if y - 1 < 0 or grid[x, y - 1] == 1:
valid_actions.remove(Action.WEST)
if y + 1 > m or grid[x, y + 1] == 1:
valid_actions.remove(Action.EAST)
if x - 1 < 0 or grid[x - 1, y - 1] == 1:
valid_actions.remove(Action.NORTH_WEST)
if x + 1 > n or grid[x - 1, y + 1] == 1:
valid_actions.remove(Action.NORTH_EAST)
if y - 1 < 0 or grid[x + 1, y - 1] == 1:
valid_actions.remove(Action.SOUTH_WEST)
if y + 1 > m or grid[x + 1, y + 1] == 1:
valid_actions.remove(Action.SOUTH_EAST)
return valid_actions
def point(p):
return np.array([p[0], p[1], 0.0])
def collinearity_float(p1, p2, p3, epsilon=1e-3):
collinear = False
mat = np.vstack((point(p1), point(p2), point(p3)))
det = np.linalg.det(mat)
if det < epsilon:
collinear = True
return collinear
def create_grid_and_edges(data, drone_altitude, safety_distance):
"""
Returns a grid representation of a 2D configuration space
along with Voronoi graph edges given obstacle data and the
drone's altitude.
"""
# minimum and maximum north coordinates
north_min = np.floor(np.min(data[:, 0] - data[:, 3]))
north_max = np.ceil(np.max(data[:, 0] + data[:, 3]))
# minimum and maximum east coordinates
east_min = np.floor(np.min(data[:, 1] - data[:, 4]))
east_max = np.ceil(np.max(data[:, 1] + data[:, 4]))
# given the minimum and maximum coordinates we can
# calculate the size of the grid.
north_size = int(np.ceil(north_max - north_min))
east_size = int(np.ceil(east_max - east_min))
# Initialize an empty grid
grid = np.zeros((north_size, east_size))
# Initialize an empty list for Voronoi points
points = []
# Populate the grid with obstacles
for i in range(data.shape[0]):
north, east, alt, d_north, d_east, d_alt = data[i, :]
if alt + d_alt + safety_distance > drone_altitude:
obstacle = [
int(np.clip(north - d_north - safety_distance - north_min, 0, north_size-1)),
int(np.clip(north + d_north + safety_distance - north_min, 0, north_size-1)),
int(np.clip(east - d_east - safety_distance - east_min, 0, east_size-1)),
int(np.clip(east + d_east + safety_distance - east_min, 0, east_size-1)),
]
grid[obstacle[0]:obstacle[1]+1, obstacle[2]:obstacle[3]+1] = 1
# add center of obstacles to points list
points.append([north - north_min, east - east_min])
graph = Voronoi(points)
edges = []
for v in graph.ridge_vertices:
p1 = graph.vertices[v[0]]
p2 = graph.vertices[v[1]]
cells = list(bresenham(int(p1[0]), int(p1[1]), int(p2[0]), int(p2[1])))
hit = False
for c in cells:
# First check if we're off the map
if np.amin(c) < 0 or c[0] >= grid.shape[0] or c[1] >= grid.shape[1]:
hit = True
break
# Next check if we're in collision
if grid[c[0], c[1]] == 1:
hit = True
break
# If the edge does not hit on obstacle
# add it to the list
if not hit:
# array to tuple for future graph creation step)
p1 = (int(p1[0]), int(p1[1]))
p2 = (int(p2[0]), int(p2[1]))
edges.append((p1, p2))
nodes = graph.ridge_vertices
return grid, nodes, edges, int(north_min), int(east_min)
def closest_point(nodes, point):
current_point = (point[0], point[1])
closest_point = None
min_dist = np.inf
for p in nodes:
d = np.linalg.norm(np.array(p) - np.array(current_point))
if d < min_dist:
closest_point = p
min_dist = d
return closest_point
def a_star_graph(nodes, h, start, goal):
path = []
path_cost = 0
queue = PriorityQueue()
queue.put((0, start))
visited = set(start)
branch = {}
found = False
print('calculating the path')
while not queue.empty():
item = queue.get()
current_node = item[1]
if current_node == start:
current_cost = 0.0
else:
current_cost = branch[current_node][0]
if current_node == goal:
print('Found a path.')
found = True
break
else:
possible_nodes = []
for node in nodes:
if node[0] == current_node:
possible_nodes.append(node[1])
elif node[1] == current_node:
possible_nodes.append(node[0])
for node in possible_nodes:
# get the tuple representation
next_node = node
branch_cost = current_cost + np.linalg.norm(np.array(next_node) - np.array(current_node))
queue_cost = branch_cost + h(next_node, goal)
if next_node not in visited:
visited.add(next_node)
branch[next_node] = (branch_cost, current_node)
queue.put((queue_cost, next_node))
if found:
# retrace steps
n = goal
path_cost = branch[n][0]
path.append(goal)
while branch[n][1] != start:
path.append(branch[n][1])
n = branch[n][1]
path.append(branch[n][1])
else:
print('**********************')
print('Failed to find a path!')
print('**********************')
return path[::-1], path_cost
def a_star(grid, h, start, goal):
path = []
path_cost = 0
queue = PriorityQueue()
queue.put((0, start))
visited = set(start)
branch = {}
found = False
print('calculating the path')
while not queue.empty():
item = queue.get()
current_node = item[1]
if current_node == start:
current_cost = 0.0
else:
current_cost = branch[current_node][0]
if current_node == goal:
print('Found a path.')
found = True
break
else:
for action in valid_actions(grid, current_node):
# get the tuple representation
da = action.delta
next_node = (current_node[0] + da[0], current_node[1] + da[1])
branch_cost = current_cost + action.cost
queue_cost = branch_cost + h(next_node, goal)
if next_node not in visited:
visited.add(next_node)
branch[next_node] = (branch_cost, current_node, action)
queue.put((queue_cost, next_node))
if found:
# retrace steps
n = goal
path_cost = branch[n][0]
path.append(goal)
while branch[n][1] != start:
path.append(branch[n][1])
n = branch[n][1]
path.append(branch[n][1])
else:
print('**********************')
print('Failed to find a path!')
print('**********************')
return path[::-1], path_cost
def heuristic(position, goal_position):
return np.linalg.norm(np.array(position) - np.array(goal_position))
def visualization(grid, edges):
plt.imshow(grid, origin='lower', cmap='Greys')
# Stepping through each edge
for e in edges:
p1 = e[0]
p2 = e[1]
plt.plot([p1[1], p2[1]], [p1[0], p2[0]], 'b-')
plt.xlabel('EAST')
plt.ylabel('NORTH')
plt.savefig('./graph.png')
print('visualization done')
#plt.show()