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A_star.py
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A_star.py
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#!/usr/bin/env python
import numpy as np
import matplotlib.pyplot as plt
import math
import cv2
########################### Authors #####################
# 117054859 Aditya Varadaraj
# 118133959 Saurabh Palande
#########################################################
# Generalized Action Function
def take_action(cur_state,l, i):
status = False
x = cur_state[0] + l*math.cos(math.radians(cur_state[2]+(i*30)))
y = cur_state[1] + l*math.sin(math.radians(cur_state[2]+(i*30)))
if (y <= 250 and y>=0 and x>=0 and x<= 400):
new_node = [x, y, int(cur_state[2]+(i*30))]
n = new_node.copy()
if n[2]<0:
n[2] = (360 + n[2])
elif n[2]>360:
n[2] = (n[2]-360)
else:
n[2] = n[2]
status = True
else:
n = [0,0,0]
return status, n
def euclidean_dist(p1,p2):
point1 = [p1[0],p1[1]]
point2 = [p2[0],p2[1]]
return round(math.dist(point1,point2),2)
# function to check if the goal has reached
def check_goal(g, node):
n = node.copy()
d = euclidean_dist(g,n)
t = abs(g[2] - n[2])
return(d<=1.5 and t<=30)
#function to check if the child node is in obstacle space or not
def check_obstacle(node,c,r):
a = math.sqrt(3)
x = node[0]
y = node[1]
flag1 = False
flag2 = False
flag3 = False
flag4 = False
# Polygon space with clearance + radius
if (x>=36-c-r and x<=115+c+r and y>=100-c-r and y<= 210+c+r ):
if((y - (6/7)*x >= 780/7-c-r) or (y + (16/5)*x <= 2180/5+c+r)):
if((y + (85/69)*x >= 15825/69-c-r) and (y -(25/79)*x <=13320/79+c+r)):
flag1 = True
# Circle with clearance + radius
if((x-300)**2 + (y-185)**2 <= pow((40+c+r), 2)):
flag2 = True
# Hexagon with clearance + radius
if ( x >= 165-c-r and x <= 235+c+r and y>= (100 - 70/a)-c-r and y<= (100 + 70/a)+c+r):
if ((y + (2021/3500)*x >= 61273/350 -c-r) and (y - (2021/3500)*x >= -19567/350 - c-r)):
if ((y + (101/175)*x <= 179087/700 +c+r) and (y - (101/175)*x <= 17487/700 + c+r)):
flag3 = True
# padding of clearance+radius on both x and y
if(((x>=0) and (x<=5)) or ((x>=395) and (x<=400)) and ((y>=0) and (y<=5)) or ((y>=245) and (y<=250))):
flag4 = True
return (flag1 or flag2 or flag3 or flag4)
#function to check if the child node is in visited or not
def check_visited(node, v_array):
n = node.copy()
for i in range(2):
x = n[i]%(math.floor(n[i]))
if(x<0.25):
n[i] = math.floor(n[i])
elif(x > 0.75):
n[i] = math.floor(n[i]) + 1
else:
n[i] = math.floor(n[i])+0.5
n[2] = n[2]/30
return v_array[int(2*n[1]), int(2*n[0]), int(n[2])-1] == 1
# function to find the parent node (used in back-tracking)
def find_parent(c,visited_list):
for i in range(len(visited_list)):
if(visited_list[i][2] == c):
return i
break
def create_obstacles(r,c):
grid_points =[]
obstacles=[]
obstacles_clearance = []
x= 400
y = 250
a = math.sqrt(3)
for i in range(x+1):
for j in range(y+1):
grid_points.append([i,j])
# define the obstacle space
for x,y in grid_points:
# for the polygon
if (x>=36 and x<=115 and y>=100 and y<= 210 ):
if((y - (6/7)*x >= 780/7) or (y + (16/5)*x <= 2180/5 )):
if((y + (85/69)*x >= 15825/69) and (y -(25/79)*x <=13320/79)):
obstacles.append([x,y])
# Polygon space with clearance of c and robot radius of r
if (x>=36-c-r and x<=115+c+r and y>=100-c-r and y<= 210+c+r ):
if((y - (6/7)*x >= 780/7-c-r) or (y + (16/5)*x <= 2180/5+c+r)):
if((y + (85/69)*x >= 15825/69-c-r) and (y -(25/79)*x <=13320/79+c+r)):
obstacles_clearance.append([x,y])
# for the circle
if((x-300)**2 + (y-185)**2 <= 1600):
obstacles.append([x,y])
# Circle with clearance of c and robot radius of r
if((x-300)**2 + (y-185)**2 <= pow((40+c+r), 2)):
obstacles_clearance.append([x,y])
# for the hexagon
if ( x >= 165 and x <= 235 and y>= (100 - 70/a) and y<= (100 + 70/a)):
if ((y + (2021/3500)*x >= 61273/350) and (y - (2021/3500)*x >= -19567/350 )):
if ((y + (101/175)*x <= 179087/700) and (y - (101/175)*x <= 17487/700 )):
obstacles.append([x,y])
# Hexagon with clearance of c and robot radius of r
if ( x >= 165-c-r and x <= 235+c+r and y>= (100 - 70/a)-c-r and y<= (100 + 70/a)+c+r):
if ((y + (2021/3500)*x >= 61273/350 -c-r) and (y - (2021/3500)*x >= -19567/350 - c-r)):
if ((y + (101/175)*x <= 179087/700 +c+r) and (y - (101/175)*x <= 17487/700 + c+r)):
obstacles_clearance.append([x,y])
# padding of 5 on both x and y
if(((x>=0) and (x<=5)) or ((x>=395) and (x<=400))):
obstacles_clearance.append([x,y])
if(((y>=0) and (y<=5)) or ((y>=245) and (y<=250))):
obstacles_clearance.append([x,y])
o = np.array(obstacles)
oc = np.array(obstacles_clearance)
plt.xlim(0, 400)
plt.ylim(0, 250)
plt.scatter(oc[:,0], oc[:,1], c = 'g', s= 1, label = 'clearance and robot radius')
plt.scatter(o[:,0], o[:,1], c = 'r', s =1, label = 'obstacles')
plt.title('Obstacle space')
plt.savefig('Obstacle_space.png')
return obstacles, obstacles_clearance
def modify_visited_array(array, node):
a = array.copy()
n = node.copy()
for i in range(2):
x = node[i]%(math.floor(n[i]))
if(x<0.25):
n[i] = math.floor(n[i])
elif(x > 0.75):
n[i] = math.floor(n[i]) + 1
else:
n[i] = math.floor(n[i])+0.5
n[2] = n[2]/30
a[int(2*n[1]),int(2*n[0]), int(n[2])-1] =1
return a
def A_star(open_queue, start, goal, obstacles_clearance, l, k, o, b, c, r):
print('*******Started A* Algorithm*******')
visited_array = np.zeros((501,801,12))
visited_list = []
node_index = 1 # initial node index
parent_node = 1 #initial parent index
ctc = 0
ctg = euclidean_dist(start, goal)
tc = ctc + ctg
open_queue.update({tuple(start):[tc, ctc, node_index ,parent_node]})# adding start to the open list
while True:
n_k = min(open_queue.items(), key=lambda x: x[1][0])[0]
n_v = open_queue[n_k]
del open_queue[n_k]
cur_node = n_k
visited_list.append([n_v[0], n_v[1], n_v[2], n_v[3], n_k])
visited_array = modify_visited_array(visited_array, list(cur_node))
if(check_goal(goal, list(cur_node))):
print('*******Goal reached*******')
print('The total cost to reach the goal is', n_v[0])
break
else:
for i in range(-k,k+1):
status, node_state = take_action(list(cur_node), l, i)
if status:
if((not check_obstacle(node_state, c, r)) and (not check_visited(node_state, visited_array))):
cv2.line(b, (int(2*n_k[0]), int(500 - 2*n_k[1])), (int(2*node_state[0]), int(500-2*node_state[1])),(0,255,255), 1 )
ctc = n_v[1] + 1
ctg = euclidean_dist(goal, node_state)
tc = ctc + ctg
if (tuple(node_state) in open_queue.keys()):
val = open_queue[tuple(node_state)][0]
if(val > tc):
open_queue[tuple(node_state)] = [tc,ctc, open_queue[tuple(node_state)][2], n_v[2]]
else:
node_index +=1
open_queue[tuple(node_state)] = [tc,ctc, node_index, n_v[2]]
o.write(b)
return visited_list, o, b, n_v[0]
def main():
node_queue = {} #open list
correct = False
while(not correct):
print('Enter the start and goal location coordinates(x,y,theta)')
s_x = int(input('Enter the x coordinate of start location '))
s_y = int(input('Enter the y coordinate of start location '))
theta_s = int(input('Enter the start angle'))
g_x = int(input('Enter the x coordinate of goal location '))
g_y = int(input('Enter the y coordinate of goal location '))
theta_g = int(input('Enter the goal angle'))
l = int(input('Enter the step size (between 1 and 10)'))
k = int(input('Enter the number of steps of 30 in each direction'))
r = int(input('Enter the robot radius'))
cl = int(input('Enter the clearance'))
start = [int(s_x), int(s_y), theta_s]
goal = [int(g_x), int(g_y), theta_g]
obstacles, obstacles_clearance = create_obstacles(r,cl)
background = np.zeros((501,801,3),np.uint8)
background.fill(255)
frameSize = (800, 500)
fourcc = cv2.VideoWriter_fourcc('m', 'p', '4', 'v')
out = cv2.VideoWriter('Astar_visualisation.mp4',fourcc, 25, frameSize)
#for every point that belongs within the obstacle
for c in obstacles:
x = c[0]*2
y = c[1]*2
background[(500-y,x)]=[0,0,255] #assigning a red colour for the obstacles
out.write(background)
if (check_obstacle(start,cl,r) or check_obstacle(goal,cl,r)):
print('Enter the value again')
continue
else:
correct = True
visited_list, out, background, tc = A_star(node_queue , start, goal, obstacles_clearance, l, k, out, background, cl, r)
path_list = []
path_list.append(goal)
goal_parent = visited_list[-1][3]
child = goal_parent
rechd_start = False
while True:
index = find_parent(child, visited_list)
path_list.append(visited_list[index][-1])
if(visited_list[index][2] == 1):
break
child = visited_list[index][3]
print('Path generated using back-tracking')
for i in range(len(path_list)-1):
x1 = path_list[i][0]*2
y1 = 500 - path_list[i][1]*2
x2 = path_list[i+1][0]*2
y2 = 500 - path_list[i+1][1]*2
cv2.line(background, (int(x1), int(y1)), (int(x2), int(y2)) , (0,0,0), 1 )
for i in range(int(10*tc)):
out.write(background)
out.release()
path = np.array(path_list)
print('Visualisation video created')
v = []
o = np.array(obstacles)
plt.xlim(0, 400)
plt.ylim(0, 250)
plt.scatter(o[:,0], o[:,1], c = 'r', s = 0.5)
plt.plot(path[:,0], path[:,1], c = 'k')
plt.savefig('Final_output.png')
if __name__ == '__main__':
main()