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mdca.py
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mdca.py
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from cmath import inf
from matplotlib import projections
import numpy as np
import cvxpy as cp
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import axes3d, Axes3D
from matplotlib.axes import Axes
class MDCA:
def __init__(self,UAVs,v_min,v_max,d_safe):
self.UAVs = UAVs
self.v_min = v_min
self.v_max = v_max
self.d_safe = d_safe
def check_intersection(self, wp1_1, wp1_2, wp2_1, wp2_2):
# L1 = ( 1 - t )*wp1_1 + t*wp1_2
# L2 = ( 1 - s )*wp2_1 + s*wp2_2
x1 = wp1_1[0]
y1 = wp1_1[1]
x2 = wp1_2[0]
y2 = wp1_2[1]
x3 = wp2_1[0]
y3 = wp2_1[1]
x4 = wp2_2[0]
y4 = wp2_2[1]
if (y4 - y3)*(x2 - x1) - (x4 -x3)*(y2 - y1) == 0: # parallel
return np.zeros(1)
else:
t = ( (x4 - x3)*(y1- y3) - (y4 - y3)*(x1 - x3) ) / ( (y4 - y3)*(x2 - x1) - (x4 -x3)*(y2 - y1) )
s = ( (x2 - x1)*(y1- y3) - (y2 - y1)*(x1 - x3) ) / ( (y4 - y3)*(x2 - x1) - (x4 -x3)*(y2 - y1) )
if ( t < 0 or 1 < t ) or ( s < 0 or 1 < s ):
return np.zeros(1)
else:
wp_c = np.zeros((2))
wp_c[0] = x1 + t*(x2 -x1)
wp_c[1] = y1 + t*(y2 -y1)
return wp_c
def check_collision_point(self):
K = len(self.UAVs) # total number of UAVs
collision_points = {} # contains 'i,j, ik,jk'
for i in range(K):
for j in range(K-i-1):
uavi = self.UAVs[i] # ith uav
uavj = self.UAVs[i+j+1] # jth uav
for ik in range(uavi.N-1): # for N_i waypoints of uav_i
wpi_1 = uavi.wp[ik]
wpi_2 = uavi.wp[ik+1]
for jk in range(uavj.N-1): # for N_j waypoints of uav_j
wpj_1 = uavj.wp[jk]
wpj_2 = uavj.wp[jk+1]
wp_c = self.check_intersection(wpi_1,wpi_2,wpj_1,wpj_2)
if len(wp_c) != 1:
d_ci = np.linalg.norm(wpi_1-wp_c)
d_cj = np.linalg.norm(wpj_1-wp_c)
collision_points[(i,i+j+1,ik,jk,d_ci,d_cj)] = wp_c
# indexes of collided uav set : i,j
# indexes of waypoint passing through : ik, jk
return collision_points
def constraints(self,x_c1,x_c2,x_safe):
return np.clip( np.abs(x_c1-x_c2)-x_safe ,0,inf) + x_safe
def run(self, avoidance=True, simul_arr=True):
K = len(self.UAVs) # total number of uavs
t = [] # t = [t^1, t^2, ... , t^K]
d = [] # d = [d^1, d^2, ... , d^K]
N = [] # N = [N^1, N^2, ... , N^K]
t_c = [] # t_c = [t_c_1, t_c_2, ... , t_c_n ]
obj = 0 # objective function
const = [] # constraints
# t_opt = [] # optimal time set : [t_opt^1, t_opt^2, ... , t_opt^K]
# v_opt = [] # optimal velocity set : [v_opt^1, v_opt^2, ... , v_opt^K]
''' Initializing Variables & Objective Function '''
for uav in self.UAVs: # for i'th drone
ti = cp.Variable( uav.N - 1 ) # t^i = [t^i_1, t^i_2, ... , t^i_{N^i-1}]
di = uav.d # d^i = [d^i_1, d^i_2, ... , d^i_{N^i-1}]
t.append(ti) # t = [t^1, t^2, ... , t^K]
d.append(di) # d = [d^1, d^2, ... , d^K]
N.append(uav.N) # N = [N^1, N^2, ... , N^K]
obj += ( ti[-1] ) # cost = Sum of arrival time of UAVs
if simul_arr: # additional cost function : simultaneus arrival cost
for i in range(K):
for j in range(K-i-1):
t_arr_i = t[i]
t_arr_j = t[i+j+1]
obj += 10*cp.norm(t_arr_i[-1] - t_arr_j[-1]) # cost = sum( |t_i - t_j|^2 )
''' Constraints #1 : Velocity constraints
d_k/v_max < t_k < d_k/v_min
'''
for i in range(K):
## Selection Matrix ###
S = np.eye( N[i]-1 )
for j in range(N[i] - 2):
S[j+1,j] = -1
### Velocity Constraints ###
const += [ S@t[i] - d[i]/self.v_min <= 0 ]
const += [ d[i]/self.v_max - S@t[i] <= 0 ]
if avoidance:
''' Constraints #2 : Collision avoidance constraints
| t^i_c - t^j_c | > t_safety
'''
### check collision risk point ###
collision_points = self.check_collision_point() # set of collision points
x = []
### appending collision avoidance constraints ###
for indexes, collision_point in collision_points.items():
# For the point where the i-th uav and j-th uav can collide.
# the i'th uav and j'th uav was coming from
# ik'th waypoint and j'th waypoint respectively
i = indexes[0]
j = indexes[1]
ik = indexes[2]-1 # index of waypoint where i'th uav came from
jk = indexes[3]-1 # index of waypoint where j'th uav came from
# defining d^i_c and d^j_c
if ik < 0: # if i'th uav came from initial waypoint
ti = t[i] # t^i : t set of i'th uav
ti_n1 = 0
ti_n2 = ti[0] # t^i_1 : t_0 of i'th uav
di_n = self.UAVs[i].d[0] # d^i_1 : d_0 of i'th uav
di_c = indexes[4] # d^i_c : d_col of i'th uav
# sum_di_c = self.UAVs[i].d[0] + di_c
sum_di_c = np.sum(self.UAVs[i].d[:1])
# print(f"sum_di_c : {sum_di_c}")
else:
ti = t[i] # t^i : t set of i'th uav
ti_n1 = ti[ik] # t^i_n : t_n of i'th uav
ti_n2 = ti[ik+1] # t^i_n+1 : t_n+1 of i'th uav
di_n = self.UAVs[i].d[ik+1] # d^i_n : d_n of i'th uav
di_c = indexes[4] # d^i_c : d_col of i'th uav
# sum_di_c = np.sum(self.UAVs[i].d[:ik+1]) + di_c
sum_di_c = np.sum(self.UAVs[i].d[:ik+2])
# print(f"sum_di_c : {sum_di_c}")
if jk < 0:
tj = t[j] # t^j : t set of j'th uav
tj_m1 = 0
tj_m2 = tj[0] # t^j_m : t_0 of j'th uav
dj_m = self.UAVs[j].d[0] # d^j_m : d_0 of j'th uav
dj_c = indexes[5] # d^j_c : d_col of j'th uav
# sum_dj_c = self.UAVs[j].d[0] + dj_c
sum_dj_c = np.sum(self.UAVs[j].d[:jk+2])
# print(f"sum_dj_c : {sum_dj_c}")
else:
tj = t[j] # t^j : t set of j'th uav
tj_m1 = tj[jk] # t^j_m : t_m of j'th uav
tj_m2 = tj[jk+1] # t^j_m+1 : t_m+1 of j'th uav
dj_m = self.UAVs[j].d[jk+1] # d^j_m : d_m of j'th uav
dj_c = indexes[5] # d^j_c : d_col of j'th uav
# sum_dj_c = np.sum(self.UAVs[j].d[:jk+1]) + dj_c
sum_dj_c = np.sum(self.UAVs[j].d[:jk+2])
# print(f"sum_dj_c : {sum_dj_c}")
# total distance from start point to collision point
### t_safety definition ###
t_safety = (self.d_safe/di_n)*(ti_n2-ti_n1)
t_safety = (self.d_safe/dj_m)*(tj_m2-tj_m1)
### ti_c, tj_c definition ###
ti_c = (di_c/di_n)*(ti_n2-ti_n1) + ti_n1
tj_c = (dj_c/dj_m)*(tj_m2-tj_m1) + tj_m1
''' Approach #1 '''
# const += [ t_safety - ti_c + tj_c <= 0 ]
# const += [ t_safety + ti_c - tj_c <= 0 ]
''' Approach #2 '''
if sum_di_c >= sum_dj_c:
const += [ t_safety - (ti_c - tj_c) <= 0 ]
else:
const += [ t_safety + (ti_c - tj_c) <= 0 ]
''' Approach #3 '''
# x_n = cp.Variable(1)
# x.append(x_n)
# const += [ cp.abs(ti_c - tj_c) <= (2**0.5)*x_n ]
# const += [ t_safety - x_n <= 0 ]
# const += [ x_n <= 100 ]
''' Solve '''
cp.Problem( cp.Minimize(obj), const ).solve(verbose=False)
for i in range(K):
ti_opt = t[i].value
ti_1 = ti_opt
ti_2 = np.append(np.zeros(1) ,ti_opt[:-1] )
vi_opt = d[i] / ( ti_1 - ti_2)
(self.UAVs[i]).v_set = vi_opt
self.UAVs[i].t = ti_opt
self.UAVs[i].del_t = ti_1 - ti_2
self.UAVs[i].v = vi_opt
''' for printing result data '''
num = 0
collision_points = self.check_collision_point() # set of collision points
print(f"==== Time differences at collision Points ====")
for indexes, collision_point in collision_points.items():
# For the point where the i-th uav and j-th uav can collide.
# the i'th uav and j'th uav was coming from
# ik'th waypoint and j'th waypoint respectively
i = indexes[0]
j = indexes[1]
ik = indexes[2]-1 # index of waypoint where i'th uav came from
jk = indexes[3]-1 # index of waypoint where j'th uav came from
# defining d^i_c and d^j_c
if ik < 0: # if i'th uav came from initial waypoint
ti = self.UAVs[i].t # t^i : t set of i'th uav
ti_n1 = 0
ti_n2 = ti[0] # t^i_1 : t_0 of i'th uav
di_n = self.UAVs[i].d[0] # d^i_1 : d_0 of i'th uav
di_c = indexes[4] # d^i_c : d_col of i'th uav
sum_di_c = self.UAVs[i].d[0] + di_c
else:
ti = self.UAVs[i].t # t^i : t set of i'th uav
ti_n1 = ti[ik] # t^i_n : t_n of i'th uav
ti_n2 = ti[ik+1] # t^i_n+1 : t_n+1 of i'th uav
di_n = self.UAVs[i].d[ik+1] # d^i_n : d_n of i'th uav
di_c = indexes[4] # d^i_c : d_col of i'th uav
sum_di_c = np.sum(self.UAVs[i].d[:ik+1]) + di_c
if jk < 0:
tj = self.UAVs[j].t # t^j : t set of j'th uav
tj_m1 = 0
tj_m2 = tj[0] # t^j_m : t_0 of j'th uav
dj_m = self.UAVs[j].d[0] # d^j_m : d_0 of j'th uav
dj_c = indexes[5] # d^j_c : d_col of j'th uav
sum_dj_c = self.UAVs[j].d[0] + dj_c
else:
tj = self.UAVs[j].t # t^j : t set of j'th uav
tj_m1 = tj[jk] # t^j_m : t_m of j'th uav
tj_m2 = tj[jk+1] # t^j_m+1 : t_m+1 of j'th uav
dj_m = self.UAVs[j].d[jk+1] # d^j_m : d_m of j'th uav
dj_c = indexes[5] # d^j_c : d_col of j'th uav
sum_dj_c = np.sum(self.UAVs[j].d[:jk+1]) + dj_c
# total distance from start point to collision point
### t_safety definition ###
t_safety = (self.d_safe/di_n)*(ti_n2-ti_n1)
t_safety = (self.d_safe/dj_m)*(tj_m2-tj_m1)
### ti_c, tj_c definition ###
ti_c = (di_c/di_n)*(ti_n2-ti_n1) + ti_n1
tj_c = (dj_c/dj_m)*(tj_m2-tj_m1) + tj_m1
print(f"==== Collision Point of ( {i+1}th UAV, {j+1}th UAV ) ====")
print("Collision point arrival time difference | ti_c - tj_c | \n: ",abs(ti_c - tj_c))
print("t_safety calculated \n: ",t_safety)
num += 1
print(f"==== Arrival time differences ====")
for i in range(K):
for j in range(K-i-1):
print(f" {i+1}th UAV, {i+j+2}th UAV : ",abs(self.UAVs[i].t[-1]-self.UAVs[i+j+1].t[-1]))