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Task 2 (4 constraints with 2 variables)
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Task 2 (4 constraints with 2 variables)
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"""
A* grid planning
author: Atsushi Sakai(@Atsushi_twi)
Nikos Kanargias ([email protected])
See Wikipedia article (https://en.wikipedia.org/wiki/A*_search_algorithm)
This is the simple code for path planning class
"""
import math # mathmatics calculation
import matplotlib.pyplot as plt # draw results
show_animation = True
class AStarPlanner:
def __init__(self, ox, oy, resolution, rr, fc_x, fc_y, tc_x, tc_y):
"""
Initialize grid map for a star planning
ox: x position list of Obstacles [m]
oy: y position list of Obstacles [m]
resolution: grid resolution [m]
rr: robot radius[m]
"""
self.resolution = resolution # get resolution of the grid
self.rr = rr # robot radis
self.min_x, self.min_y = 0, 0
self.max_x, self.max_y = 0, 0
self.obstacle_map = None
self.x_width, self.y_width = 0, 0
self.motion = self.get_motion_model() # motion model for grid search expansion
self.calc_obstacle_map(ox, oy)
self.fc_x = fc_x
self.fc_y = fc_y
self.tc_x = tc_x
self.tc_y = tc_y
############you could modify the setup here for different aircraft models (based on the lecture slide) ##########################
self.C_F = 20
self.Delta_F = 5
self.C_T = 20
self.Delta_T = 5
self.C_C = 10
self.Delta_F_A = 5 # additional fuel
self.Delta_T_A = 5 # additional time
self.costPerGrid = self.C_F * self.Delta_F + self.C_T * self.Delta_T + self.C_C
print("PolyU-A380 cost part1-> ", self.C_F * (self.Delta_F + self.Delta_F_A) )
print("PolyU-A380 cost part2-> ", self.C_T * (self.Delta_T + self.Delta_T_A) )
print("PolyU-A380 cost part3-> ", self.C_C )
class Node: # definition of a sinle node
def __init__(self, x, y, cost, parent_index):
self.x = x # index of grid
self.y = y # index of grid
self.cost = cost
self.parent_index = parent_index
def __str__(self):
return str(self.x) + "," + str(self.y) + "," + str(
self.cost) + "," + str(self.parent_index)
def planning(self, sx, sy, gx, gy):
"""
A star path search
input:
s_x: start x position [m]
s_y: start y position [m]
gx: goal x position [m]
gy: goal y position [m]
output:
rx: x position list of the final path
ry: y position list of the final path
"""
start_node = self.Node(self.calc_xy_index(sx, self.min_x), # calculate the index based on given position
self.calc_xy_index(sy, self.min_y), 0.0, -1) # set cost zero, set parent index -1
goal_node = self.Node(self.calc_xy_index(gx, self.min_x), # calculate the index based on given position
self.calc_xy_index(gy, self.min_y), 0.0, -1)
open_set, closed_set = dict(), dict() # open_set: node not been tranversed yet. closed_set: node have been tranversed already
open_set[self.calc_grid_index(start_node)] = start_node # node index is the grid index
while 1:
if len(open_set) == 0:
print("Open set is empty..")
break
c_id = min(
open_set,
key=lambda o: open_set[o].cost + self.calc_heuristic(self, goal_node,
open_set[
o])) # g(n) and h(n): calculate the distance between the goal node and openset
current = open_set[c_id]
# show graph
if show_animation: # pragma: no cover
plt.plot(self.calc_grid_position(current.x, self.min_x),
self.calc_grid_position(current.y, self.min_y), "xc")
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect('key_release_event',
lambda event: [exit(
0) if event.key == 'escape' else None])
if len(closed_set.keys()) % 10 == 0:
plt.pause(0.001)
# reaching goal
if current.x == goal_node.x and current.y == goal_node.y:
print("Find goal with cost of -> ",current.cost )
goal_node.parent_index = current.parent_index
goal_node.cost = current.cost
break
# Remove the item from the open set
del open_set[c_id]
# Add it to the closed set
closed_set[c_id] = current
# print(len(closed_set))
# expand_grid search grid based on motion model
for i, _ in enumerate(self.motion): # tranverse the motion matrix
node = self.Node(current.x + self.motion[i][0],
current.y + self.motion[i][1],
current.cost + self.motion[i][2] * self.costPerGrid, c_id)
## add more cost in time-consuming area
if self.calc_grid_position(node.x, self.min_x) in self.tc_x:
if self.calc_grid_position(node.y, self.min_y) in self.tc_y:
# print("time consuming area!!")
node.cost = node.cost + self.Delta_T_A * self.motion[i][2]
# add more cost in fuel-consuming area
if self.calc_grid_position(node.x, self.min_x) in self.fc_x:
if self.calc_grid_position(node.y, self.min_y) in self.fc_y:
# print("fuel consuming area!!")
node.cost = node.cost + self.Delta_F_A * self.motion[i][2]
# print()
n_id = self.calc_grid_index(node)
# If the node is not safe, do nothing
if not self.verify_node(node):
continue
if n_id in closed_set:
continue
if n_id not in open_set:
open_set[n_id] = node # discovered a new node
else:
if open_set[n_id].cost > node.cost:
# This path is the best until now. record it
open_set[n_id] = node
rx, ry = self.calc_final_path(goal_node, closed_set)
# print(len(closed_set))
# print(len(open_set))
return rx, ry
def calc_final_path(self, goal_node, closed_set):
# generate final course
rx, ry = [self.calc_grid_position(goal_node.x, self.min_x)], [
self.calc_grid_position(goal_node.y, self.min_y)] # save the goal node as the first point
parent_index = goal_node.parent_index
while parent_index != -1:
n = closed_set[parent_index]
rx.append(self.calc_grid_position(n.x, self.min_x))
ry.append(self.calc_grid_position(n.y, self.min_y))
parent_index = n.parent_index
return rx, ry
@staticmethod
def calc_heuristic(self, n1, n2):
w = 1.0 # weight of heuristic
d = w * math.hypot(n1.x - n2.x, n1.y - n2.y)
d = d * self.costPerGrid
return d
def calc_heuristic_maldis(n1, n2):
w = 1.0 # weight of heuristic
dx = w * math.abs(n1.x - n2.x)
dy = w *math.abs(n1.y - n2.y)
return dx + dy
def calc_grid_position(self, index, min_position):
"""
calc grid position
:param index:
:param min_position:
:return:
"""
pos = index * self.resolution + min_position
return pos
def calc_xy_index(self, position, min_pos):
return round((position - min_pos) / self.resolution)
def calc_grid_index(self, node):
return (node.y - self.min_y) * self.x_width + (node.x - self.min_x)
def verify_node(self, node):
px = self.calc_grid_position(node.x, self.min_x)
py = self.calc_grid_position(node.y, self.min_y)
if px < self.min_x:
return False
elif py < self.min_y:
return False
elif px >= self.max_x:
return False
elif py >= self.max_y:
return False
# collision check
if self.obstacle_map[node.x][node.y]:
return False
return True
def calc_obstacle_map(self, ox, oy):
self.min_x = round(min(ox))
self.min_y = round(min(oy))
self.max_x = round(max(ox))
self.max_y = round(max(oy))
print("min_x:", self.min_x)
print("min_y:", self.min_y)
print("max_x:", self.max_x)
print("max_y:", self.max_y)
self.x_width = round((self.max_x - self.min_x) / self.resolution)
self.y_width = round((self.max_y - self.min_y) / self.resolution)
print("x_width:", self.x_width)
print("y_width:", self.y_width)
# obstacle map generation
self.obstacle_map = [[False for _ in range(self.y_width)]
for _ in range(self.x_width)] # allocate memory
for ix in range(self.x_width):
x = self.calc_grid_position(ix, self.min_x) # grid position calculation (x,y)
for iy in range(self.y_width):
y = self.calc_grid_position(iy, self.min_y)
for iox, ioy in zip(ox, oy): # Python’s zip() function creates an iterator that will aggregate elements from two or more iterables.
d = math.hypot(iox - x, ioy - y) # The math. hypot() method finds the Euclidean norm
if d <= self.rr:
self.obstacle_map[ix][iy] = True # the griid is is occupied by the obstacle
break
@staticmethod
def get_motion_model(): # the cost of the surrounding 8 points
# dx, dy, cost
motion = [[1, 0, 1],
[0, 1, 1],
[-1, 0, 1],
[0, -1, 1],
[-1, -1, math.sqrt(2)],
[-1, 1, math.sqrt(2)],
[1, -1, math.sqrt(2)],
[1, 1, math.sqrt(2)]]
return motion
def main():
print(__file__ + " start the A star algorithm demo !!") # print simple notes
# start and goal position
sx = 0.0 # [m]
sy = 0.0 # [m]
gx = 50.0 # [m]
gy = 50.0 # [m]
grid_size = 1 # [m]
robot_radius = 1.0 # [m]
# set obstacle positions for group 8
# ox, oy = [], []
# for i in range(-10, 60): # draw the button border
# ox.append(i)
# oy.append(-10.0)
# for i in range(-10, 60):
# ox.append(60.0)
# oy.append(i)
# for i in range(-10, 61): # range
# ox.append(i)
# oy.append(60.0)
# for i in range(-10, 61):
# ox.append(-10.0)
# oy.append(i)
# for i in range(-10, 40):
# ox.append(20.0)
# oy.append(i)
# for i in range(0, 40):
# ox.append(40.0)
# oy.append(60.0 - i)
# set obstacle positions for group 9
ox, oy = [], []
for i in range(-10, 60): # draw the button border
ox.append(i)
oy.append(-10.0)
for i in range(-10, 60): # draw the right border
ox.append(60.0)
oy.append(i)
for i in range(-10, 60): # draw the top border
ox.append(i)
oy.append(60.0)
for i in range(-10, 60): # draw the left border
ox.append(-10.0)
oy.append(i)
for i in range(10, 60): # draw the free border
ox.append(i)
oy.append(40)
for i in range(-10, 20):
ox.append(i)
oy.append(-1 * i+20)
# for i in range(40, 45): # draw the button border
# ox.append(i)
# oy.append(30.0)
# set fuel consuming area
fc_x, fc_y = [], []
for i in range(20, 30):
for j in range(0, 25):
fc_x.append(i)
fc_y.append(j)
# set time consuming area
tc_x, tc_y = [], []
for i in range(10, 30):
for j in range(40, 55):
tc_x.append(i)
tc_y.append(j)
if show_animation: # pragma: no cover
plt.plot(ox, oy, ".k") # plot the obstacle
plt.plot(sx, sy, "og") # plot the start position
plt.plot(gx, gy, "xb") # plot the end position
plt.plot(fc_x, fc_y, "oy") # plot the fuel consuming area
plt.plot(tc_x, tc_y, "or") # plot the time consuming area
plt.grid(True) # plot the grid to the plot panel
plt.axis("equal") # set the same resolution for x and y axis
a_star = AStarPlanner(ox, oy, grid_size, robot_radius, fc_x, fc_y, tc_x, tc_y)
rx, ry = a_star.planning(sx, sy, gx, gy)
if show_animation: # pragma: no cover
plt.plot(rx, ry, "-r") # show the route
plt.pause(0.001) # pause 0.001 seconds
plt.show() # show the plot
if __name__ == '__main__':
main()