def _mga_part_plot(self, x):
"""
Plots the trajectory represented by the decision vector x
Example::
prob.plot(x)
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from PyKEP.orbit_plots import plot_planet, plot_lambert, plot_kepler
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
mpl.rcParams["legend.fontsize"] = 10
fig = plt.figure()
ax = fig.gca(projection="3d", aspect="equal")
ax.scatter(0, 0, 0, color="y")
JR = 71492000.0
legs = len(x) / 4
seq = self.get_sequence()
common_mu = seq[0].mu_central_body
start_mjd2000 = self.t0.mjd2000
# 1 - we 'decode' the chromosome recording the various times of flight (days) in the list T
T = x[3::4]
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (legs + 1))
r_P = list([None] * (legs + 1))
v_P = list([None] * (legs + 1))
for i, planet in enumerate(seq):
t_P[i] = epoch(start_mjd2000 + sum(T[:i]))
r_P[i], v_P[i] = planet.eph(t_P[i])
plot_planet(ax, planet, t0=t_P[i], color=(0.8, 0.6, 0.8), legend=True, units=JR)
v_end_l = [a + b for a, b in zip(v_P[0], self.vinf_in)]
# 4 - And we iterate on the legs
for i in xrange(0, legs):
# Fly-by
v_out = fb_prop(v_end_l, v_P[i], x[1 + 4 * i] * seq[i - 1].radius, x[4 * i], seq[i].mu_self)
# s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out, x[4 * i + 2] * T[i] * DAY2SEC, common_mu)
plot_kepler(
ax, r_P[i], v_out, x[4 * i + 2] * T[i] * DAY2SEC, common_mu, N=500, color="b", legend=False, units=JR
)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[4 * i + 2]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt, common_mu, False, False)
plot_lambert(ax, l, sol=0, color="r", legend=False, units=JR, N=500)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
plt.show()
return ax
def _compute_DV_DT_incipit(self,x): """ This method computes, for each leg, all the velocity increments coming from deep space manoeuvres and all the transfer times. Use: DV,DT = prob.compute_DV_DT(x) * x: trajectory encoding """ from PyKEP import epoch, lambert_problem, DAY2SEC, fb_prop, propagate_lagrangian from math import pi, acos,cos,sin,sqrt from scipy.linalg import norm #1 - we 'decode' the chromosome recording the various times of flight (days) in the list T for convenience T = x[3::4] n_legs = len(x)/4 seq = self.get_sequence() common_mu = seq[0].mu_central_body #2 - We compute the epochs and ephemerides of the planetary encounters t_P = list([None] * (n_legs)) r_P = list([None] * (n_legs)) v_P = list([None] * (n_legs)) DV = list([None] * (n_legs)) for i,planet in enumerate(seq): t_P[i] = epoch(x[0]+sum(T[:i+1])) r_P[i],v_P[i] = seq[i].eph(t_P[i]) #3 - We start with the first leg: a lambert arc theta = 2*pi*x[1] phi = acos(2*x[2]-1)-pi/2 r = [cos(phi)*sin(theta), cos(phi)*cos(theta), sin(phi)] #phi close to zero is in the moon orbit plane injection r = [JR*1000*d for d in r] l = lambert_problem(r,r_P[0],T[0]*DAY2SEC,common_mu, False, False) #Lambert arc to reach seq[1] v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] #First DSM occuring at the very beginning (will be cancelled by the optimizer) DV[0] = abs(norm(v_beg_l) - 3400) #4 - And we proceed with each successive leg for i in xrange(1,n_legs): #Fly-by v_out = fb_prop(v_end_l,v_P[i-1],x[1+4*i]*seq[i-1].radius,x[4*i],seq[i-1].mu_self) #s/c propagation before the DSM r,v = propagate_lagrangian(r_P[i-1],v_out,x[4*i+2]*T[i]*DAY2SEC,common_mu) #Lambert arc to reach Earth during (1-nu2)*T2 (second segment) dt = (1-x[4*i+2])*T[i]*DAY2SEC l = lambert_problem(r,r_P[i],dt,common_mu, False, False) v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] #DSM occuring at time nu2*T2 DV[i] = norm([a-b for a,b in zip(v_beg_l,v)]) return (DV,T)
def _get_score_data_part(self,x):
from PyKEP import epoch, lambert_problem, DAY2SEC, fb_prop, propagate_lagrangian
from math import pi, acos,cos,sin,sqrt
from scipy.linalg import norm
from copy import deepcopy
"""
This method returns the data needed to compute the score of a trajectory.
"""
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T for convenience
T = x[3::4]
nlegs = len(x)/4
seq = self.get_sequence()
common_mu = seq[0].mu_central_body
t0 = self.t0.mjd2000
vinf_in = deepcopy(self.vinf_in)
#2 - We compute the epochs and ephemerides of the planetary encounters
ep_list = list([None] * (nlegs+1))
t_P = list([None] * (nlegs+1))
r_P = list([None] * (nlegs+1))
v_P = list([None] * (nlegs+1))
DV = list([None] * nlegs)
for i,planet in enumerate(seq):
ep_list[i] = t0+sum(T[:i])
t_P[i] = epoch(t0+sum(T[:i]))
r_P[i],v_P[i] = seq[i].eph(t_P[i])
#init lists for fly-by parameters
vinf_list = []
rp_list = []
beta_list = []
v_end_l = [a+b for a,b in zip(vinf_in, v_P[0])]
#3 - And we proceed with each successive leg
for i in xrange(nlegs):
#Fly-by
v_out = fb_prop(v_end_l,v_P[i],x[1+4*i]*seq[i].radius,x[4*i],seq[i].mu_self)
vinf_list.append( [a-b for a,b in zip(v_end_l,v_P[i])] )
rp_list.append(x[1+4*i]*seq[i].radius)
beta_list.append(x[4*i])
#s/c propagation before the DSM
r,v = propagate_lagrangian(r_P[i],v_out,x[4*i+2]*T[i]*DAY2SEC,common_mu)
#Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1-x[4*i+2])*T[i]*DAY2SEC
l = lambert_problem(r,r_P[i+1],dt,common_mu, False, False)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
vinf_list.append([a-b for a,b in zip(v_end_l,v_P[-1])])
rp_list.append(None)
beta_list.append(None)
return zip(ep_list, seq, vinf_list, rp_list, beta_list)
def _mga_1dsm_tof_plot(self, x):
"""
Plots the trajectory represented by the decision vector x
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from PyKEP.orbit_plots import plot_planet, plot_lambert, plot_kepler
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.scatter(0, 0, 0, color='y')
seq = self.get_sequence()
# 2 - We plot the first leg
r_P0, v_P0 = seq[0].eph(epoch(x[0]))
plot_planet(ax, seq[0], t0=epoch(x[0]), color=(
0.8, 0.6, 0.8), legend=True, units = AU)
r_P1, v_P1 = seq[1].eph(epoch(x[0] + x[5]))
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
Vinfx = x[3] * cos(phi) * cos(theta)
Vinfy = x[3] * cos(phi) * sin(theta)
Vinfz = x[3] * sin(phi)
v0 = [a + b for a, b in zip(v_P0, [Vinfx, Vinfy, Vinfz])]
r, v = propagate_lagrangian(
r_P0, v0, x[4] * x[5] * DAY2SEC, seq[0].mu_central_body)
plot_kepler(
ax,
r_P0,
v0,
x[4] *
x[5] *
DAY2SEC,
seq[0].mu_central_body,
N=100,
color='b',
legend=False,
units=AU)
# Lambert arc to reach seq[1]
dt = (1 - x[4]) * x[5] * DAY2SEC
l = lambert_problem(r, r_P1, dt, seq[0].mu_central_body)
plot_lambert(ax, l, sol=0, color='r', legend=False, units=AU)
v_end_l = l.get_v2()[0]
vinf_in = [a - b for a, b in zip(v_end_l, v_P1)]
_part_plot(x[6:], AU, ax, seq[1:], x[0] + x[5], vinf_in)
return ax
def plot_kepler(r, v, t, mu, N=60, units=1, color='b', legend=False, ax=None):
"""
ax = plot_kepler(r, v, t, mu, N=60, units=1, color='b', legend=False, ax=None):
- ax: 3D axis object created using fig.gca(projection='3d')
- r: initial position (cartesian coordinates)
- v: initial velocity (cartesian coordinates)
- t: propagation time
- mu: gravitational parameter
- N: number of points to be plotted along one arc
- units: the length unit to be used in the plot
- color: matplotlib color to use to plot the line
- legend when True it plots also the legend
Plots the result of a keplerian propagation
"""
from PyKEP import propagate_lagrangian
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
if ax is None:
fig = plt.figure()
axis = fig.gca(projection='3d')
else:
axis = ax
# We define the integration time ...
dt = t / (N - 1)
# ... and calculate the cartesian components for r
x = [0.0] * N
y = [0.0] * N
z = [0.0] * N
# We calculate the spacecraft position at each dt
for i in range(N):
x[i] = r[0] / units
y[i] = r[1] / units
z[i] = r[2] / units
r, v = propagate_lagrangian(r, v, dt, mu)
# And we plot
if legend:
label = 'ballistic arc'
else:
label = None
axis.plot(x, y, z, c=color, label=label)
if legend:
axis.legend()
if ax is None: # show only if axis is not set
plt.show()
return axis
def planet_planet(start_planet, arrive_planet, tlaunch, tarrive, rev, N):
# Create PyKEP epoch objects and calculate flight time
t1 = epoch(tlaunch)
t2 = epoch(tarrive)
dt = (tarrive - tlaunch) * DAY2SEC
OBJ1 = planet_ss(start_planet)
OBJ2 = planet_ss(arrive_planet) # Calculate location of objects in flight path
r1, v1 = OBJ1.eph(t1)
r2, v2 = OBJ2.eph(t2)
# Find trajectory
l = lambert_problem(r1, r2, dt, MU_SUN)
#extract relevant information from solution
r = l.get_r1()
v = l.get_v1()[0]
mu = l.get_mu()
#define the integration time
dtn = dt / (N - 1)
dtn_days = dtn * SEC2DAY
#alocate the cartesian components for r
t = np.array([0.0] * N)
x = np.array([0.0] * N)
y = np.array([0.0] * N)
z = np.array([0.0] * N)
#calculate the spacecraft position at each dt
for i in range(N):
t[i] = tlaunch + dtn_days * i
x[i] = r[0] / AU
y[i] = r[1] / AU
z[i] = r[2] / AU
r, v = propagate_lagrangian(r, v, dtn, mu)
#traj = [t, x, y, z]
vin = l.get_v1()[rev]
vout = l.get_v2()[rev]
#dV=fb_vel(vin,vout,planet_ss(arrive_planet))
#dV=np.sqrt( np.square(vin[0]/vout[0])+np.square(vin[1]/vout[1])+np.square(vin[2]/vout[2]))
#dV=np.sqrt( np.square(vin[0]-v1[0])+np.square(v1[1]-vin[1])+np.square(v1[2]-vin[2]))
#dV=np.sqrt( np.square(v2[0]-vout[0])+np.square(v2[1]-vout[1])+np.square(v2[2]-vout[2]))
#dV=np.sqrt( np.square(v1[0]/vin[0])+np.square(v1[1]/vin[1])+np.square(v1[2]/vin[2]))
C3_launch = (np.sqrt(np.square(vin[0] - v1[0]) + np.square(vin[1] - v1[1]) + np.square(vin[2] - v1[2]))) ** 2
C3_arrive = (np.sqrt(np.square(vout[0] - v2[0]) + np.square(vout[1] - v2[1]) + np.square(vout[2] - v2[2]))) ** 2
C3 = np.sqrt((C3_arrive ** 2) + (C3_launch ** 2))
return C3
def _part_plot(x, units, axis, seq, start_mjd2000, vinf_in):
"""
Plots the trajectory represented by a decision vector x = [beta,rp,eta,T] * N
associated to a sequence seq, a start_mjd2000 and an incoming vinf_in
"""
from PyKEP.orbit_plots import plot_planet, plot_lambert, plot_kepler
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
legs = len(x) // 4
common_mu = seq[0].mu_central_body
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T
T = x[3::4]
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (legs + 1))
r_P = list([None] * (legs + 1))
v_P = list([None] * (legs + 1))
for i, planet in enumerate(seq):
t_P[i] = epoch(start_mjd2000 + sum(T[:i]))
r_P[i], v_P[i] = planet.eph(t_P[i])
plot_planet(planet, t0=t_P[i], color=(
0.8, 0.6, 0.8), legend=True, units = units, ax=axis)
v_end_l = [a + b for a, b in zip(v_P[0], vinf_in)]
# 4 - And we iterate on the legs
for i in range(0, legs):
# Fly-by
v_out = fb_prop(v_end_l,
v_P[i],
x[1 + 4 * i] * seq[i].radius,
x[4 * i],
seq[i].mu_self)
# s/c propagation before the DSM
r, v = propagate_lagrangian(
r_P[i], v_out, x[4 * i + 2] * T[i] * DAY2SEC, common_mu)
plot_kepler(r_P[i], v_out, x[4 * i + 2] * T[i] * DAY2SEC,
common_mu, N=500, color='b', legend=False, units=units, ax=axis)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[4 * i + 2]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt, common_mu, False, False)
plot_lambert(
l, sol=0, color='r', legend=False, units=units, N=500, ax=axis)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
def positions_lambert(self, l, sol=0, units = 1.0, index = 0):
"""
Plots a particular solution to a Lambert's problem
USAGE: plot_lambert(ax,l, N=60, sol=0, units = 'PyKEP.AU', legend = 'False')
* l: PyKEP.lambert_problem object
* sol: solution to the Lambert's problem we want to plot (must be in 0..Nmax*2)
where Nmax is the maximum number of revolutions for which there exist a solution.
* units: the length unit to be used in the plot
"""
from PyKEP import propagate_lagrangian, AU
if sol > l.get_Nmax()*2:
raise ValueError("sol must be in 0 .. NMax*2 \n * Nmax is the maximum number of revolutions for which there exist a solution to the Lambert's problem \n * You can compute Nmax calling the get_Nmax() method of the lambert_problem object")
#We extract the relevant information from the Lambert's problem
r = l.get_r1()
v = l.get_v1()[sol]
T = l.get_tof()
mu = l.get_mu()
#We define the integration time ...
if T/86400. < 1:
N = int(T) #...compute number of points...
dt = T / (N-1.)
else:
N = int(2*T/86400.) #...compute number of points...
dt = T / (N-1.)
timetuple = [i*dt for i in range(N)]
#... and alocate the cartesian components for r
x = [0.0]*N
y = [0.0]*N
z = [0.0]*N
#We calculate the spacecraft position at each dt
for i in range(N):
x[i] = r[0]/units
y[i] = r[1]/units
z[i] = r[2]/units
r,v = propagate_lagrangian(r,v,dt,mu)
self.trajectory_positions.append([index, x, y, z, timetuple])
def _objfun_impl(self,x): #1 - we 'decode' the chromosome recording the various times of flight (days) in the list T for convenience T = x[3::4] #2 - We compute the epochs and ephemerides of the planetary encounters t_P = list([None] * (self.__n_legs)) r_P = list([None] * (self.__n_legs)) v_P = list([None] * (self.__n_legs)) DV = list([None] * (self.__n_legs)) for i,planet in enumerate(self.seq): t_P[i] = epoch(x[0]+sum(T[:i+1])) r_P[i],v_P[i] = self.seq[i].eph(t_P[i]) #3 - We start with the first leg: a lambert arc theta = 2*pi*x[1] phi = acos(2*x[2]-1)-pi/2 r = [cos(phi)*sin(theta), cos(phi)*cos(theta), sin(phi)] #phi close to zero is in the moon orbit plane injection r = [JR*1000*d for d in r] l = lambert_problem(r,r_P[0],T[0]*DAY2SEC,self.common_mu, False, False) #Lambert arc to reach seq[1] v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] #First DSM occuring at the very beginning (will be cancelled by the optimizer) DV[0] = abs(norm(v_beg_l) - 3400) #4 - And we proceed with each successive leg for i in xrange(1,self.__n_legs): #Fly-by v_out = fb_prop(v_end_l,v_P[i-1],x[1+4*i]*self.seq[i-1].radius,x[4*i],self.seq[i-1].mu_self) #s/c propagation before the DSM r,v = propagate_lagrangian(r_P[i-1],v_out,x[4*i+2]*T[i]*DAY2SEC,self.common_mu) #Lambert arc to reach Earth during (1-nu2)*T2 (second segment) dt = (1-x[4*i+2])*T[i]*DAY2SEC l = lambert_problem(r,r_P[i],dt,self.common_mu, False, False) v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] #DSM occuring at time nu2*T2 DV[i] = norm([a-b for a,b in zip(v_beg_l,v)]) return (sum(DV),)
def plot_kepler(ax,r,v,t,mu, N=60, units = 1, color = 'b', legend = False): """ Plots the result of a keplerian propagation USAGE: plot_kepler(ax,r,v,t,mu, N=60, units = 1, color = 'b', legend = False): * ax: 3D axis object created using fig.gca(projection='3d') * r: initial position (cartesian coordinates) * v: initial velocity (cartesian coordinates) * t: propagation time * mu: gravitational parameter * N: number of points to be plotted along one arc * units: the length unit to be used in the plot * color: matplotlib color to use to plot the line * legend when True it plots also the legend """ from PyKEP import propagate_lagrangian #We define the integration time ... dt = t / (N-1) #... and calculate the cartesian components for r x = [0.0]*N y = [0.0]*N z = [0.0]*N #We calculate the spacecraft position at each dt for i in range(N): x[i] = r[0]/units y[i] = r[1]/units z[i] = r[2]/units r,v = propagate_lagrangian(r,v,dt,mu) #And we plot if legend: label = 'ballistic arc' else: label = None ax.plot(x, y, z, c=color, label=label) if legend: ax.legend()
def positions_kepler(self, r,v,t,mu, units = 1, index = 0):
"""
Plots the result of a keplerian propagation
USAGE: plot_kepler(ax,r,v,t,mu, N=60, units = 1, color = 'b', legend = False):
* r: initial position (cartesian coordinates)
* v: initial velocity (cartesian coordinates)
* t: propagation time
* mu: gravitational parameter
* units: the length unit to be used in the plot
"""
from PyKEP import propagate_lagrangian
#We define the integration time ...
if t/86400. < 1:
N = int(t) #...compute number of points...
dt = t / (N-1.)
else:
N = int(2*t/86400.) #...compute number of points...
dt = t / (N-1.)
timetuple = [i*dt for i in range(N)]
#... and calcuate the cartesian components for r
x = [0.0]*N
y = [0.0]*N
z = [0.0]*N
#We calculate the spacecraft position at each dt
for i in range(N):
x[i] = r[0]/units
y[i] = r[1]/units
z[i] = r[2]/units
r,v = propagate_lagrangian(r,v,dt,mu)
self.trajectory_positions.append([index, x, y, z, timetuple])
def pretty(self,x):
"""
Prints human readable information on the trajectory represented by the decision vector x
Example::
prob.pretty(x)
"""
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T for convenience
T = list([0]*(self.__n_legs))
for i in xrange(self.__n_legs):
T[i] = (x[4+4*i]/sum(x[4::4]))*x[3]
#2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n_legs))
r_P = list([None] * (self.__n_legs))
v_P = list([None] * (self.__n_legs))
DV = list([None] * (self.__n_legs))
close_d = list([None] * (self.__n_legs))
for i,planet in enumerate(self.seq):
t_P[i] = epoch(x[0]+sum(T[:i+1]))
r_P[i],v_P[i] = self.seq[i].eph(t_P[i])
#3 - We start with the first leg: a lambert arc
theta = 2*pi*x[1]
phi = acos(2*x[2]-1)-pi/2
r = [cos(phi)*sin(theta), cos(phi)*cos(theta), sin(phi)] #phi close to zero is in the moon orbit plane injection
r = [JR*1000*d for d in r]
l = lambert_problem(r,r_P[0],T[0]*DAY2SEC,self.common_mu, False, False)
#Lambert arc to reach seq[1]
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
close_d[0] = closest_distance(r,v_beg_l, r_P[0], v_end_l, self.common_mu)[0] / JR
#First DSM occuring at the very beginning (will be cancelled by the optimizer)
DV[0] = abs(norm(v_beg_l) - 3400)
print "\nFirst Leg: 1000JR to " + self.seq[0].name
print "\tDeparture: " + str(t_P[0]) + " (" + str(t_P[0].mjd2000) + " mjd2000) "
print "\tDuration: " + str(T[0]) + "days"
print "\tInitial Velocity Increment (m/s): " + str(DV[0])
print "\tArrival relative velocity at " + self.seq[0].name +" (m/s): " + str(norm([a-b for a,b in zip(v_end_l,v_P[0])]))
print "\tClosest approach distance: " + str(close_d[0])
#4 - And we proceed with each successive leg
for i in xrange(1,self.__n_legs):
#Fly-by
v_out = fb_prop(v_end_l,v_P[i-1],x[6+(i-1)*4]*self.seq[i-1].radius,x[5+(i-1)*4],self.seq[i-1].mu_self)
#s/c propagation before the DSM
r,v = propagate_lagrangian(r_P[i-1],v_out,x[7+(i-1)*4]*T[i]*DAY2SEC,self.common_mu)
tmp, ra = closest_distance(r_P[i-1],v_out, r,v, self.common_mu)
#Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1-x[7+(i-1)*4])*T[i]*DAY2SEC
l = lambert_problem(r,r_P[i],dt,self.common_mu, False, False)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
tmp2, ra2 = closest_distance(r,v_beg_l, r_P[i], v_end_l, self.common_mu)
if tmp < tmp2:
close_d[i] = tmp/JR
ra = ra/JR
else:
close_d[i] = tmp2/JR
ra = ra2/JR
#DSM occuring at time nu2*T2
DV[i] = norm([a-b for a,b in zip(v_beg_l,v)])
print "\nleg no. " + str(i+1) + ": " + self.seq[i-1].name + " to " + self.seq[i].name
print "\tDuration (days): " + str(T[i])
print "\tFly-by epoch: " + str(t_P[i]) + " (" + str(t_P[i].mjd2000) + " mjd2000) "
print "\tFly-by altitude (km): " + str((x[6+(i-1)*4]*self.seq[i-1].radius-self.seq[i-1].radius)/1000)
print "\tDSM after (days): " + str(x[7+(i-1)*4]*T[i])
print "\tDSM magnitude (m/s): " + str(DV[i])
print "\tClosest approach distance: " + str(close_d[i])
print "\tApoapsis at closest distance: " + str(ra)
print "\tV in (m/s): " + str(v_end_l)
print "\tV out (m/s): " + str(v_out)
print "\nArrival at " + self.seq[-1].name
vel_inf = [a-b for a,b in zip(v_end_l,v_P[-1])]
print "Arrival epoch: " + str(t_P[-1]) + " (" + str(t_P[-1].mjd2000) + " mjd2000) "
print "Arrival Vinf (m/s): " + vel_inf.__repr__() + " - " + str(norm(vel_inf))
print "Total mission time (days): " + str(sum(T))
print "Total DV (m/s): " + str(sum(DV))
def plot(self,x): """ Plots the trajectory represented by the decision vector x Example:: prob.plot(x) """ import matplotlib as mpl from mpl_toolkits.mplot3d import Axes3D import matplotlib.pyplot as plt from PyKEP.orbit_plots import plot_planet, plot_lambert, plot_kepler mpl.rcParams['legend.fontsize'] = 10 fig = plt.figure() ax = fig.gca(projection='3d') ax.scatter(0,0,0, color='y') #1 - we 'decode' the chromosome recording the various times of flight (days) in the list T for convenience T = list([0]*(self.__n_legs)) for i in xrange(self.__n_legs): T[i] = (x[4+4*i]/sum(x[4::4]))*x[3] #2 - We compute the epochs and ephemerides of the planetary encounters t_P = list([None] * (self.__n_legs)) r_P = list([None] * (self.__n_legs)) v_P = list([None] * (self.__n_legs)) DV = list([None] * (self.__n_legs)) for i,planet in enumerate(self.seq): t_P[i] = epoch(x[0]+sum(T[:i+1])) r_P[i],v_P[i] = self.seq[i].eph(t_P[i]) plot_planet(ax, planet, t0=t_P[i], color=(0.8,0.6,0.8), legend=True, units = JR) #3 - We start with the first leg: a lambert arc theta = 2*pi*x[1] phi = acos(2*x[2]-1)-pi/2 r = [cos(phi)*sin(theta), cos(phi)*cos(theta), sin(phi)] #phi close to zero is in the moon orbit plane injection r = [JR*1000*d for d in r] l = lambert_problem(r,r_P[0],T[0]*DAY2SEC,self.common_mu, False, False) plot_lambert(ax,l, sol = 0, color='k', legend=False, units = JR, N=500) #Lambert arc to reach seq[1] v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] #First DSM occuring at the very beginning (will be cancelled by the optimizer) DV[0] = abs(norm(v_beg_l) - 3400) #4 - And we proceed with each successive leg for i in xrange(1,self.__n_legs): #Fly-by v_out = fb_prop(v_end_l,v_P[i-1],x[6+(i-1)*4]*self.seq[i-1].radius,x[5+(i-1)*4],self.seq[i-1].mu_self) #s/c propagation before the DSM r,v = propagate_lagrangian(r_P[i-1],v_out,x[4*i+3]*T[i]*DAY2SEC,self.common_mu) plot_kepler(ax,r_P[i-1],v_out,x[7+(i-1)*4]*T[i]*DAY2SEC,self.common_mu,N = 500, color='b', legend=False, units = JR) #Lambert arc to reach Earth during (1-nu2)*T2 (second segment) dt = (1-x[7+(i-1)*4])*T[i]*DAY2SEC l = lambert_problem(r,r_P[i],dt,self.common_mu, False, False) plot_lambert(ax,l, sol = 0, color='r', legend=False, units = JR, N=500) v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] #DSM occuring at time nu2*T2 DV[i] = norm([a-b for a,b in zip(v_beg_l,v)]) plt.show()
def _mga_1dsm_tof_plot(self, x):
"""
Plots the trajectory represented by the decision vector x
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from PyKEP.orbit_plots import plot_planet, plot_lambert, plot_kepler
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.scatter(0, 0, 0, color='y')
seq = self.get_sequence()
n = (len(seq) - 1)
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T
T = x[5::4]
#2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (n + 1))
r_P = list([None] * (n + 1))
v_P = list([None] * (n + 1))
DV = list([None] * (n + 1))
for i, planet in enumerate(seq):
t_P[i] = epoch(x[0] + sum(T[0:i]))
r_P[i], v_P[i] = planet.eph(t_P[i])
plot_planet(ax,
planet,
t0=t_P[i],
color=(0.8, 0.6, 0.8),
legend=True,
units=AU)
#3 - We start with the first leg
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
Vinfx = x[3] * cos(phi) * cos(theta)
Vinfy = x[3] * cos(phi) * sin(theta)
Vinfz = x[3] * sin(phi)
v0 = [a + b for a, b in zip(v_P[0], [Vinfx, Vinfy, Vinfz])]
r, v = propagate_lagrangian(r_P[0], v0, x[4] * T[0] * DAY2SEC,
seq[0].mu_central_body)
plot_kepler(ax,
r_P[0],
v0,
x[4] * T[0] * DAY2SEC,
seq[0].mu_central_body,
N=100,
color='b',
legend=False,
units=AU)
#Lambert arc to reach seq[1]
dt = (1 - x[4]) * T[0] * DAY2SEC
l = lambert_problem(r, r_P[1], dt, seq[0].mu_central_body)
plot_lambert(ax, l, sol=0, color='r', legend=False, units=AU)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
#First DSM occuring at time nu1*T1
DV[0] = norm([a - b for a, b in zip(v_beg_l, v)])
#4 - And we proceed with each successive leg
for i in range(1, n):
#Fly-by
v_out = fb_prop(v_end_l, v_P[i], x[7 + (i - 1) * 4] * seq[i].radius,
x[6 + (i - 1) * 4], seq[i].mu_self)
#s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out,
x[8 + (i - 1) * 4] * T[i] * DAY2SEC,
seq[0].mu_central_body)
plot_kepler(ax,
r_P[i],
v_out,
x[8 + (i - 1) * 4] * T[i] * DAY2SEC,
seq[0].mu_central_body,
N=100,
color='b',
legend=False,
units=AU)
#Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[8 + (i - 1) * 4]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt, seq[0].mu_central_body)
plot_lambert(ax, l, sol=0, color='r', legend=False, units=AU)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
#DSM occurring at time nu2*T2
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
return ax
def _leg_get_states(self):
"""
Returns the spacecraft states (t,r,v,m) at the leg grid points
Examples::
times,r,v,m = PyKEP.sims_flanagan.leg.get_states()
"""
from PyKEP import propagate_lagrangian, AU, DAY2SEC, G0, propagate_taylor
import numpy as np
from scipy.linalg import norm
from math import exp
# We compute the number of segments for forward and backward propagation
n_seg = len(self.get_throttles())
fwd_seg = (n_seg + 1) // 2
back_seg = n_seg // 2
# We extract information on the spacecraft
sc = self.get_spacecraft()
isp = sc.isp
max_thrust = sc.thrust
# And on the leg
throttles = self.get_throttles()
mu = self.get_mu()
# time grid
t_grid = [0.0] * (n_seg * 2 + 2)
# Forward propagation
# x,y,z contain the cartesian components of all points (grid+midpints)
x = [0.0] * (fwd_seg * 2 + 1)
y = [0.0] * (fwd_seg * 2 + 1)
z = [0.0] * (fwd_seg * 2 + 1)
vx = [0.0] * (fwd_seg * 2 + 1)
vy = [0.0] * (fwd_seg * 2 + 1)
vz = [0.0] * (fwd_seg * 2 + 1)
mass = [0.0] * (fwd_seg * 2 + 1)
state = self.get_xi()
# Initial conditions
r = state.r
v = state.v
m = state.m
x[0], y[0], z[0] = r
vx[0], vy[0], vz[0] = v
mass[0] = m
# We compute all points by propagation
for i, t in enumerate(throttles[:fwd_seg]):
t_grid[2 * i] = t.start.mjd2000
t_grid[2 * i + 1] = t.start.mjd2000 + \
(t.end.mjd2000 - t.start.mjd2000) / 2.
dt = (t.end.mjd - t.start.mjd) * DAY2SEC
alpha = min(norm(t.value), 1.0)
# Keplerian propagation and dV application
if self.high_fidelity is False:
dV = [max_thrust / m * dt * dumb for dumb in t.value]
r, v = propagate_lagrangian(r, v, dt / 2, mu)
x[2 * i + 1], y[2 * i + 1], z[2 * i + 1] = r
vx[2 * i + 1], vy[2 * i + 1], vz[2 * i + 1] = v
mass[2 * i + 1] = m
# v= v+dV
v = [a + b for a, b in zip(v, dV)]
r, v = propagate_lagrangian(r, v, dt / 2, mu)
m *= exp(-norm(dV) / isp / G0)
x[2 * i + 2], y[2 * i + 2], z[2 * i + 2] = r
vx[2 * i + 2], vy[2 * i + 2], vz[2 * i + 2] = v
mass[2 * i + 2] = m
# Taylor propagation of constant thrust u
else:
u = [max_thrust * dumb for dumb in t.value]
r, v, m = propagate_taylor(
r, v, m, u, dt / 2, mu, isp * G0, -12, -12)
x[2 * i + 1], y[2 * i + 1], z[2 * i + 1] = r
vx[2 * i + 1], vy[2 * i + 1], vz[2 * i + 1] = v
mass[2 * i + 1] = m
r, v, m = propagate_taylor(
r, v, m, u, dt / 2, mu, isp * G0, -12, -12)
x[2 * i + 2], y[2 * i + 2], z[2 * i + 2] = r
vx[2 * i + 2], vy[2 * i + 2], vz[2 * i + 2] = v
mass[2 * i + 2] = m
t_grid[2 * i + 2] = t.end.mjd2000
# Backward propagation
# x,y,z will contain the cartesian components of
x_back = [0.123] * (back_seg * 2 + 1)
y_back = [0.123] * (back_seg * 2 + 1)
z_back = [0.123] * (back_seg * 2 + 1)
vx_back = [0.0] * (back_seg * 2 + 1)
vy_back = [0.0] * (back_seg * 2 + 1)
vz_back = [0.0] * (back_seg * 2 + 1)
mass_back = [0.0] * (back_seg * 2 + 1)
state = self.get_xf()
# Final conditions
r = state.r
v = state.v
m = state.m
x_back[-1], y_back[-1], z_back[-1] = r
vx_back[-1], vy_back[-1], vz_back[-1] = v
mass_back[-1] = m
for i, t in enumerate(throttles[-1:-back_seg - 1:-1]):
t_grid[-2 * i - 2] = t.end.mjd2000 - \
(t.end .mjd2000 - t.start.mjd2000) / 2.
t_grid[-2 * i - 1] = t.end.mjd2000
dt = (t.end.mjd - t.start.mjd) * DAY2SEC
alpha = min(norm(t.value), 1.0)
if self.high_fidelity is False:
dV = [max_thrust / m * dt * dumb for dumb in t.value]
r, v = propagate_lagrangian(r, v, -dt / 2, mu)
x_back[-2 * i - 2], y_back[-2 * i - 2], z_back[-2 * i - 2] = r
vx_back[-2 * i - 2], vy_back[-2 * i - 2], vz_back[-2 * i - 2] = v
mass_back[-2 * i - 2] = m
# v= v+dV
v = [a - b for a, b in zip(v, dV)]
r, v = propagate_lagrangian(r, v, -dt / 2, mu)
m *= exp(norm(dV) / isp / G0)
x_back[-2 * i - 3], y_back[-2 * i - 3], z_back[-2 * i - 3] = r
vx_back[-2 * i - 3], vy_back[-2 * i - 3], vz_back[-2 * i - 3] = v
mass_back[-2 * i - 3] = m
else:
u = [max_thrust * dumb for dumb in t.value]
r, v, m = propagate_taylor(
r, v, m, u, -dt / 2, mu, isp * G0, -12, -12)
x_back[-2 * i - 2], y_back[-2 * i - 2], z_back[-2 * i - 2] = r
vx_back[-2 * i - 2], vy_back[-2 * i - 2], vz_back[-2 * i - 2] = v
mass_back[-2 * i - 2] = m
r, v, m = propagate_taylor(
r, v, m, u, -dt / 2, mu, isp * G0, -12, -12)
x_back[-2 * i - 3], y_back[-2 * i - 3], z_back[-2 * i - 3] = r
vx_back[-2 * i - 3], vy_back[-2 * i - 3], vz_back[-2 * i - 3] = v
mass_back[-2 * i - 3] = m
t_grid[-2 * i - 3] = t.start.mjd2000
x = x + x_back
y = y + y_back
z = z + z_back
vx = vx + vx_back
vy = vy + vy_back
vz = vz + vz_back
mass = mass + mass_back
return t_grid, list(zip(x, y, z)), list(zip(vx, vy, vz)), mass
def plot_lambert(l, N=60, sol=0, units=1.0, color='b', legend=False, ax=None, alpha=1.):
"""
ax = plot_lambert(l, N=60, sol=0, units='PyKEP.AU', legend='False', ax=None, alpha=1.)
- ax: 3D axis object created using fig.gca(projection='3d')
- l: PyKEP.lambert_problem object
- N: number of points to be plotted along one arc
- sol: solution to the Lambert's problem we want to plot (must be in 0..Nmax*2)
where Nmax is the maximum number of revolutions for which there exist a solution.
- units: the length unit to be used in the plot
- color: matplotlib color to use to plot the line
- legend: when True it plots also the legend with info on the Lambert's solution chosen
Plots a particular solution to a Lambert's problem
Example::
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.gca(projection='3d')
t1 = epoch(0)
t2 = epoch(640)
dt = (t2.mjd2000 - t1.mjd2000) * DAY2SEC
pl = planet_ss('earth')
plot_planet(pl, t0=t1, ax=ax, color='k')
rE,vE = pl.eph(t1)
pl = planet_ss('mars')
plot_planet(pl, t0=t2, ax=ax, color='r')
rM, vM = pl.eph(t2)
l = lambert_problem(rE,rM,dt,MU_SUN)
plot_lambert(l, ax=ax, color='b')
plot_lambert(l, sol=1, ax=ax, color='g')
plot_lambert(l, sol=2, ax=ax, color='g')
plt.show()
"""
from PyKEP import propagate_lagrangian, AU
import numpy as np
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
if ax is None:
fig = plt.figure()
axis = fig.gca(projection='3d')
else:
axis = ax
if sol > l.get_Nmax() * 2:
raise ValueError("sol must be in 0 .. NMax*2 \n * Nmax is the maximum number of revolutions for which there exist a solution to the Lambert's problem \n * You can compute Nmax calling the get_Nmax() method of the lambert_problem object")
# We extract the relevant information from the Lambert's problem
r = l.get_r1()
v = l.get_v1()[sol]
T = l.get_tof()
mu = l.get_mu()
# We define the integration time ...
dt = T / (N - 1)
# ... and alocate the cartesian components for r
x = np.array([0.0] * N)
y = np.array([0.0] * N)
z = np.array([0.0] * N)
# We calculate the spacecraft position at each dt
for i in range(N):
x[i] = r[0] / units
y[i] = r[1] / units
z[i] = r[2] / units
r, v = propagate_lagrangian(r, v, dt, mu)
# And we plot
if legend:
label = 'Lambert solution (' + str((sol + 1) / 2) + ' revs.)'
else:
label = None
axis.plot(x, y, z, c=color, label=label, alpha=alpha)
if legend:
axis.legend()
if ax is None: # show only if axis is not set
plt.show()
return axis
def getTraj_simple(start_planet, arrive_planet, tlaunch, tarrive, N):
'''
Finds a trajectory between two objects orbiting the Sun
USAGE: traj = getTraj(K1, K2, tlaunch, tarrive)
K: array of object parameters.
epoch: epoch of Keplerian orbital elements (JD)
a: semimajor axis (AU)
e: eccentricity (none)
i: inclination (deg)
om: longitude of the ascending node (deg)
w: argument of perihelion (deg)
ma: mean anomaly at epoch (deg)
mass: mass of object (kg)
r: radius of object (m)
sr: safe radius to approach object (m)
K1: [epoch1,a1,e1,i1,om1,w1,ma1,mass1,r1,sr1]
K2: [epoch2,a2,e2,i2,om2,w2,ma2,mass2,r2,sr2]
tlaunch: launch time (JD)
tarrive: arrival time (JD)
N: number of points in calculated trajectory
'''
import numpy as np
from PyKEP import epoch, DAY2SEC, SEC2DAY, AU, DEG2RAD, MU_SUN, planet, lambert_problem, propagate_lagrangian, fb_vel
# Create PyKEP epoch objects and calculate flight time
t1 = epoch(tlaunch)
t2 = epoch(tarrive)
dt = (tarrive - tlaunch) * DAY2SEC
rev=0 #number of revolutions before intercept
OBJ1 = planet.jpl_lp(start_planet)
OBJ2 = planet.jpl_lp(arrive_planet) # Calculate location of objects in flight path
r1, v1 = OBJ1.eph(t1)
r2, v2 = OBJ2.eph(t2)
#Find trajectory
l = lambert_problem(r1, r2, dt, MU_SUN)
#extract relevant information from solution
r = l.get_r1()
v = l.get_v1()[0]
mu = l.get_mu()
#define the integration time
dtn = dt / (N - 1)
dtn_days = dtn * SEC2DAY
#alocate the cartesian components for r
t = np.array([0.0] * N)
x = np.array([0.0] * N)
y = np.array([0.0] * N)
z = np.array([0.0] * N)
#calculate the spacecraft position at each dt
for i in range(N):
t[i] = tlaunch + dtn_days * i
x[i] = r[0] / AU
y[i] = r[1] / AU
z[i] = r[2] / AU
r, v = propagate_lagrangian(r, v, dtn, mu)
#traj = [t, x, y, z]
vin=l.get_v1()[rev]
vout=l.get_v2()[rev]
dV=fb_vel(vin,vout,planet.jpl_lp(arrive_planet))
#dV=np.sqrt( np.square(vout[0])+np.square(vout[1])+np.square(vout[2]))-np.sqrt( np.square(vin[0])+np.square(vin[1])+np.square(vin[2]))
return dV
def traj_planet_asteroid(source, dest, tlaunch, tarrive, rev, N):
t1 = epoch(tlaunch)
t2 = epoch(tarrive)
dt = (tarrive - tlaunch) * DAY2SEC
target = source['orbit']
ep = epoch(jd_to_mjd(tlaunch), epoch.epoch_type.MJD)
a = target["a"] * AU
e = target["e"]
i = target["i"] * DEG2RAD
om = target["om"] * DEG2RAD
w = target["w"] * DEG2RAD
ma = target["ma"] * DEG2RAD
as_mu = 1E17 * 6.67384E-11 # maybe need to calculate actual mass from density and radius
r = (10 / 2) * 1000
sr = r * 1.1
OBJ1 = planet(ep, (a, e, i, om, w, ma), MU_SUN, as_mu, r, sr)
target = dest['orbit']
ep = epoch(jd_to_mjd(tarrive), epoch.epoch_type.MJD)
a = target["a"] * AU
e = target["e"]
i = target["i"] * DEG2RAD
om = target["om"] * DEG2RAD
w = target["w"] * DEG2RAD
ma = target["ma"] * DEG2RAD
as_mu = 1E17 * 6.67384E-11 # maybe need to calculate actual mass from density and radius
r = (10 / 2) * 1000
sr = r * 1.1
OBJ2 = planet(ep, (a, e, i, om, w, ma), MU_SUN, as_mu, r, sr)
# Calculate location of objects in flight path
r1, v1 = OBJ1.eph(t1)
r2, v2 = OBJ2.eph(t2)
#Find trajectory
l = lambert_problem(r1, r2, dt, MU_SUN)
#extract relevant information from solution
r = l.get_r1()
v = l.get_v1()[0]
mu = l.get_mu() #define the integration time
dtn = dt / (N - 1)
dtn_days = dtn * SEC2DAY
#alocate the cartesian components for r
t = np.array([0.0] * N)
x = np.array([0.0] * N)
y = np.array([0.0] * N)
z = np.array([0.0] * N)
#calculate the spacecraft position at each dt
for i in range(N):
t[i] = tlaunch + dtn_days * i
x[i] = r[0] / AU
y[i] = r[1] / AU
z[i] = r[2] / AU
r, v = propagate_lagrangian(r, v, dtn, mu)
traj = [t.tolist(), x.tolist(), y.tolist(), z.tolist()]
return traj
def pretty(self, x):
"""
Prints human readable information on the trajectory represented by the decision vector x
Example::
prob.pretty(x)
"""
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T for convenience
T = x[3::4]
#2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n_legs))
r_P = list([None] * (self.__n_legs))
v_P = list([None] * (self.__n_legs))
DV = list([None] * (self.__n_legs))
close_d = list([None] * (self.__n_legs))
for i, planet in enumerate(self.seq):
t_P[i] = epoch(x[0] + sum(T[:i + 1]))
r_P[i], v_P[i] = self.seq[i].eph(t_P[i])
#3 - We start with the first leg: a lambert arc
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
r = [cos(phi) * sin(theta),
cos(phi) * cos(theta),
sin(phi)] #phi close to zero is in the moon orbit plane injection
r = [JR * 1000 * d for d in r]
l = lambert_problem(r, r_P[0], T[0] * DAY2SEC, self.common_mu, False,
False)
#Lambert arc to reach seq[1]
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
close_d[0] = closest_distance(r, v_beg_l, r_P[0], v_end_l,
self.common_mu)[0] / JR
#First DSM occuring at the very beginning (will be cancelled by the optimizer)
DV[0] = abs(norm(v_beg_l) - 3400)
print "\nFirst Leg: 1000JR to " + self.seq[0].name
print "\tDeparture: " + str(t_P[0]) + " (" + str(
t_P[0].mjd2000) + " mjd2000) "
print "\tDuration: " + str(T[0]) + "days"
print "\tInitial Velocity Increment (m/s): " + str(DV[0])
print "\tArrival relative velocity at " + self.seq[
0].name + " (m/s): " + str(
norm([a - b for a, b in zip(v_end_l, v_P[0])]))
print "\tClosest approach distance: " + str(close_d[0])
#4 - And we proceed with each successive leg
for i in xrange(1, self.__n_legs):
#Fly-by
v_out = fb_prop(v_end_l, v_P[i - 1],
x[1 + 4 * i] * self.seq[i - 1].radius, x[4 * i],
self.seq[i - 1].mu_self)
#s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i - 1], v_out,
x[4 * i + 2] * T[i] * DAY2SEC,
self.common_mu)
tmp, ra = closest_distance(r_P[i - 1], v_out, r, v, self.common_mu)
#Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[4 * i + 2]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i], dt, self.common_mu, False, False)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
tmp2, ra2 = closest_distance(r, v_beg_l, r_P[i], v_end_l,
self.common_mu)
if tmp < tmp2:
close_d[i] = tmp / JR
ra = ra / JR
else:
close_d[i] = tmp2 / JR
ra = ra2 / JR
#DSM occuring at time nu2*T2
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
print "\nleg no. " + str(i + 1) + ": " + self.seq[
i - 1].name + " to " + self.seq[i].name
print "\tDuration (days): " + str(T[i])
print "\tFly-by epoch: " + str(t_P[i]) + " (" + str(
t_P[i].mjd2000) + " mjd2000) "
print "\tFly-by altitude (km): " + str(
(x[4 * i + 1] * self.seq[i - 1].radius -
self.seq[i - 1].radius) / 1000)
print "\tDSM after (days): " + str(x[4 * i + 2] * T[i])
print "\tDSM magnitude (m/s): " + str(DV[i])
print "\tClosest approach distance: " + str(close_d[i])
print "\tApoapsis at closest distance: " + str(ra)
print "\nArrival at " + self.seq[-1].name
vel_inf = [a - b for a, b in zip(v_end_l, v_P[-1])]
print "Arrival epoch: " + str(t_P[-1]) + " (" + str(
t_P[-1].mjd2000) + " mjd2000) "
print "Arrival Vinf (m/s): " + vel_inf.__repr__() + " - " + str(
norm(vel_inf))
print "Total mission time (days): " + str(sum(T))
def traj_planet_asteroid(source, dest, tlaunch, tarrive, rev, N):
t1 = epoch(tlaunch)
t2 = epoch(tarrive)
dt = (tarrive - tlaunch) * DAY2SEC
target = source['orbit']
ep = epoch(jd_to_mjd(tlaunch), epoch.epoch_type.MJD)
a = target["a"] * AU
e = target["e"]
i = target["i"] * DEG2RAD
om = target["om"] * DEG2RAD
w = target["w"] * DEG2RAD
ma = target["ma"] * DEG2RAD
as_mu = 1E17 * 6.67384E-11 # maybe need to calculate actual mass from density and radius
r = (10 / 2) * 1000
sr = r * 1.1
OBJ1 = planet(ep, (a, e, i, om, w, ma), MU_SUN, as_mu, r, sr)
target = dest['orbit']
ep = epoch(jd_to_mjd(tarrive), epoch.epoch_type.MJD)
a = target["a"] * AU
e = target["e"]
i = target["i"] * DEG2RAD
om = target["om"] * DEG2RAD
w = target["w"] * DEG2RAD
ma = target["ma"] * DEG2RAD
as_mu = 1E17 * 6.67384E-11 # maybe need to calculate actual mass from density and radius
r = (10 / 2) * 1000
sr = r * 1.1
OBJ2 = planet(ep, (a, e, i, om, w, ma), MU_SUN, as_mu, r, sr)
# Calculate location of objects in flight path
r1, v1 = OBJ1.eph(t1)
r2, v2 = OBJ2.eph(t2)
#Find trajectory
l = lambert_problem(r1, r2, dt, MU_SUN)
#extract relevant information from solution
r = l.get_r1()
v = l.get_v1()[0]
mu = l.get_mu() #define the integration time
dtn = dt / (N - 1)
dtn_days = dtn * SEC2DAY
#alocate the cartesian components for r
t = np.array([0.0] * N)
x = np.array([0.0] * N)
y = np.array([0.0] * N)
z = np.array([0.0] * N)
#calculate the spacecraft position at each dt
for i in range(N):
t[i] = tlaunch + dtn_days * i
x[i] = r[0] / AU
y[i] = r[1] / AU
z[i] = r[2] / AU
r, v = propagate_lagrangian(r, v, dtn, mu)
traj = [t.tolist(), x.tolist(), y.tolist(), z.tolist()]
return traj
def plot(self, x):
"""
Plots the trajectory represented by the decision vector x
Example::
prob.plot(x)
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from PyKEP.orbit_plots import plot_planet, plot_lambert, plot_kepler
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.scatter(0, 0, 0, color='y')
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T
T = x[3::4]
#2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n_legs))
r_P = list([None] * (self.__n_legs))
v_P = list([None] * (self.__n_legs))
DV = list([None] * (self.__n_legs))
for i, planet in enumerate(self.seq):
t_P[i] = epoch(x[0] + sum(T[:i + 1]))
r_P[i], v_P[i] = self.seq[i].eph(t_P[i])
plot_planet(ax,
planet,
t0=t_P[i],
color=(0.8, 0.6, 0.8),
legend=True,
units=JR)
#3 - We start with the first leg: a lambert arc
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
r = [cos(phi) * sin(theta),
cos(phi) * cos(theta),
sin(phi)] #phi close to zero is in the moon orbit plane injection
r = [JR * 1000 * d for d in r]
l = lambert_problem(r, r_P[0], T[0] * DAY2SEC, self.common_mu, False,
False)
plot_lambert(ax, l, sol=0, color='k', legend=False, units=JR, N=500)
#Lambert arc to reach seq[1]
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
#First DSM occuring at the very beginning (will be cancelled by the optimizer)
DV[0] = abs(norm(v_beg_l) - 3400)
#4 - And we proceed with each successive leg
for i in xrange(1, self.__n_legs):
#Fly-by
v_out = fb_prop(v_end_l, v_P[i - 1],
x[1 + 4 * i] * self.seq[i - 1].radius, x[4 * i],
self.seq[i - 1].mu_self)
#s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i - 1], v_out,
x[4 * i + 2] * T[i] * DAY2SEC,
self.common_mu)
plot_kepler(ax,
r_P[i - 1],
v_out,
x[4 * i + 2] * T[i] * DAY2SEC,
self.common_mu,
N=500,
color='b',
legend=False,
units=JR)
#Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[4 * i + 2]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i], dt, self.common_mu, False, False)
plot_lambert(ax,
l,
sol=0,
color='r',
legend=False,
units=JR,
N=500)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
#DSM occuring at time nu2*T2
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
plt.show()
return ax
def plot(self, x):
"""
Plots the trajectory represented by the decision vector x
Example::
prob.plot(x)
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from PyKEP.orbit_plots import plot_planet, plot_lambert, plot_kepler
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.scatter(0, 0, 0, color='y')
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T
T = list([0] * (self.__n_legs))
#a[-i] = x[-1-(i-1)*4]
for i in xrange(self.__n_legs - 1):
j = i + 1
T[-j] = (x[5] - sum(T[-(j - 1):])) * x[-1 - (j - 1) * 4]
T[0] = x[5] - sum(T)
#2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n_legs + 1))
r_P = list([None] * (self.__n_legs + 1))
v_P = list([None] * (self.__n_legs + 1))
DV = list([None] * (self.__n_legs + 1))
for i, planet in enumerate(self.seq):
t_P[i] = epoch(x[0] + sum(T[0:i]))
r_P[i], v_P[i] = planet.eph(t_P[i])
plot_planet(ax,
planet,
t0=t_P[i],
color=(0.8, 0.6, 0.8),
legend=True,
units=AU)
#3 - We start with the first leg
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
Vinfx = x[3] * cos(phi) * cos(theta)
Vinfy = x[3] * cos(phi) * sin(theta)
Vinfz = x[3] * sin(phi)
v0 = [a + b for a, b in zip(v_P[0], [Vinfx, Vinfy, Vinfz])]
r, v = propagate_lagrangian(r_P[0], v0, x[4] * T[0] * DAY2SEC,
self.common_mu)
plot_kepler(ax,
r_P[0],
v0,
x[4] * T[0] * DAY2SEC,
self.common_mu,
N=100,
color='b',
legend=False,
units=AU)
#Lambert arc to reach seq[1]
dt = (1 - x[4]) * T[0] * DAY2SEC
l = lambert_problem(r, r_P[1], dt, self.common_mu, False, False)
plot_lambert(ax, l, sol=0, color='r', legend=False, units=AU)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
#First DSM occuring at time nu1*T1
DV[0] = norm([a - b for a, b in zip(v_beg_l, v)])
#4 - And we proceed with each successive leg
for i in range(1, self.__n_legs):
#Fly-by
v_out = fb_prop(v_end_l, v_P[i],
x[7 + (i - 1) * 4] * self.seq[i].radius,
x[6 + (i - 1) * 4], self.seq[i].mu_self)
#s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out,
x[8 + (i - 1) * 4] * T[i] * DAY2SEC,
self.common_mu)
plot_kepler(ax,
r_P[i],
v_out,
x[8 + (i - 1) * 4] * T[i] * DAY2SEC,
self.common_mu,
N=100,
color='b',
legend=False,
units=AU)
#Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[8 + (i - 1) * 4]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt, self.common_mu, False,
False)
plot_lambert(ax,
l,
sol=0,
color='r',
legend=False,
units=AU,
N=1000)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
#DSM occuring at time nu2*T2
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
plt.show()
def _mga_part_plot(self, x):
"""
Plots the trajectory represented by the decision vector x
Example::
prob.plot(x)
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from PyKEP.orbit_plots import plot_planet, plot_lambert, plot_kepler
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d', aspect='equal')
ax.scatter(0, 0, 0, color='y')
JR = 71492000.0
legs = len(x) / 4
seq = self.get_sequence()
common_mu = seq[0].mu_central_body
start_mjd2000 = self.t0.mjd2000
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T
T = x[3::4]
#2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (legs + 1))
r_P = list([None] * (legs + 1))
v_P = list([None] * (legs + 1))
for i, planet in enumerate(seq):
t_P[i] = epoch(start_mjd2000 + sum(T[:i]))
r_P[i], v_P[i] = planet.eph(t_P[i])
plot_planet(ax,
planet,
t0=t_P[i],
color=(0.8, 0.6, 0.8),
legend=True,
units=JR)
v_end_l = [a + b for a, b in zip(v_P[0], self.vinf_in)]
#4 - And we iterate on the legs
for i in xrange(0, legs):
#Fly-by
v_out = fb_prop(v_end_l, v_P[i], x[1 + 4 * i] * seq[i - 1].radius,
x[4 * i], seq[i].mu_self)
#s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out,
x[4 * i + 2] * T[i] * DAY2SEC, common_mu)
plot_kepler(ax,
r_P[i],
v_out,
x[4 * i + 2] * T[i] * DAY2SEC,
common_mu,
N=500,
color='b',
legend=False,
units=JR)
#Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[4 * i + 2]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt, common_mu, False, False)
plot_lambert(ax, l, sol=0, color='r', legend=False, units=JR, N=500)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
plt.show()
return ax
def _mga_incipit_plot(self, x, plot_leg_0=False):
"""
Plots the trajectory represented by the decision vector x
Example::
prob.plot(x)
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from PyKEP.orbit_plots import plot_planet, plot_lambert, plot_kepler
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d', aspect='equal')
ax.scatter(0, 0, 0, color='y')
JR = 71492000.0
legs = len(x) / 4
seq = self.get_sequence()
common_mu = seq[0].mu_central_body
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T
T = x[3::4]
#2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * legs)
r_P = list([None] * legs)
v_P = list([None] * legs)
DV = list([None] * legs)
for i, planet in enumerate(seq):
t_P[i] = epoch(x[0] + sum(T[:i + 1]))
r_P[i], v_P[i] = planet.eph(t_P[i])
plot_planet(ax,
planet,
t0=t_P[i],
color=(0.8, 0.6, 0.8),
legend=True,
units=JR)
#3 - We start with the first leg: a lambert arc
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
r = [cos(phi) * sin(theta),
cos(phi) * cos(theta),
sin(phi)] #phi close to zero is in the moon orbit plane injection
r = [JR * 1000 * d for d in r]
l = lambert_problem(r, r_P[0], T[0] * DAY2SEC, common_mu, False, False)
if (plot_leg_0):
plot_lambert(ax, l, sol=0, color='k', legend=False, units=JR, N=500)
#Lambert arc to reach seq[1]
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
#4 - And we proceed with each successive leg
for i in xrange(1, legs):
#Fly-by
v_out = fb_prop(v_end_l, v_P[i - 1], x[1 + 4 * i] * seq[i - 1].radius,
x[4 * i], seq[i - 1].mu_self)
#s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i - 1], v_out,
x[4 * i + 2] * T[i] * DAY2SEC, common_mu)
plot_kepler(ax,
r_P[i - 1],
v_out,
x[4 * i + 2] * T[i] * DAY2SEC,
common_mu,
N=500,
color='b',
legend=False,
units=JR)
#Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[4 * i + 2]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i], dt, common_mu, False, False)
plot_lambert(ax, l, sol=0, color='r', legend=False, units=JR, N=500)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
plt.show()
return ax
def stats(self,x):
import matplotlib as mpl
import matplotlib.pyplot as plt
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T for convenience
T = list([0]*(self.__n_legs))
for i in xrange(self.__n_legs):
T[i] = (x[4+4*i]/sum(x[4::4]))*x[3]
#2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n_legs))
r_P = list([None] * (self.__n_legs))
v_P = list([None] * (self.__n_legs))
DV = list([None] * (self.__n_legs))
close_d = list([None] * (self.__n_legs))
for i,planet in enumerate(self.seq):
t_P[i] = epoch(x[0]+sum(T[:i+1]))
r_P[i],v_P[i] = self.seq[i].eph(t_P[i])
#3 - We start with the first leg: a lambert arc
theta = 2*pi*x[1]
phi = acos(2*x[2]-1)-pi/2
r = [cos(phi)*sin(theta), cos(phi)*cos(theta), sin(phi)] #phi close to zero is in the moon orbit plane injection
r = [JR*1000*d for d in r]
l = lambert_problem(r,r_P[0],T[0]*DAY2SEC,self.common_mu, False, False)
#Lambert arc to reach seq[1]
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
close_d[0] = closest_distance(r,v_beg_l, r_P[0], v_end_l, self.common_mu)[0] / JR
#First DSM occuring at the very beginning (will be cancelled by the optimizer)
DV[0] = abs(norm(v_beg_l) - 3400)
#4 - And we proceed with each successive leg
for i in xrange(1,self.__n_legs):
#Fly-by
v_out = fb_prop(v_end_l,v_P[i-1],x[6+(i-1)*4]*self.seq[i-1].radius,x[5+(i-1)*4],self.seq[i-1].mu_self)
#s/c propagation before the DSM
r,v = propagate_lagrangian(r_P[i-1],v_out,x[7+(i-1)*4]*T[i]*DAY2SEC,self.common_mu)
tmp, ra = closest_distance(r_P[i-1],v_out, r,v, self.common_mu)
#Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1-x[7+(i-1)*4])*T[i]*DAY2SEC
l = lambert_problem(r,r_P[i],dt,self.common_mu, False, False)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
tmp2, ra2 = closest_distance(r,v_beg_l, r_P[i], v_end_l, self.common_mu)
if tmp < tmp2:
close_d[i] = tmp/JR
ra = ra/JR
else:
close_d[i] = tmp2/JR
ra = ra2/JR
#DSM occuring at time nu2*T2
DV[i] = norm([a-b for a,b in zip(v_beg_l,v)])
#print "Total mission time (days): " + str(sum(T))
#print "Total DV (m/s): " + str(sum(DV))
symbol_dict = {
'io' : 'yo',
'europa' : 'bo',
'ganymede' : 'ro',
'callisto' : 'ko' }
#for i in xrange(0,self.__n_legs):
# plt.plot(sum(DV), sum(T), symbol_dict[self.seq[0].name])
#n = 0
ratio = list([0]*(self.__n_legs))
coeff = 0.3
for i in xrange(0,self.__n_legs):
ratio[i] = (DV[i]/(T[i]*DAY2SEC))
if close_d[0] >= 2:
if close_d[1] >= 2:
if close_d[2] >= 2:
if close_d[3] >= 2:
if ratio[1] <= coeff*(0.1/2000):
if ratio[2] <= coeff*(0.1/2000):
if ratio[3] <= coeff*(0.1/2000):
if ratio[0] <= coeff*(0.1/2000):
plt.plot(sum(DV), sum(T), symbol_dict[self.seq[0].name])
#for i in xrange(0,self.__n_legs):
# if close_d[i] > 2:
# plt.plot(sum(DV), sum(T), symbol_dict[self.seq[0].name])
# else:
# print "\n the closest distance is less than 2*Rj "
#print "\n number of sequences that do not crash " + str(n)
plt.show()
def _mga_1dsm_tof_plot_old(self, x):
"""
Plots the trajectory represented by the decision vector x
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from PyKEP.orbit_plots import plot_planet, plot_lambert, plot_kepler
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.scatter(0, 0, 0, color='y')
seq = self.get_sequence()
n = (len(seq) - 1)
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T
T = x[5::4]
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (n + 1))
r_P = list([None] * (n + 1))
v_P = list([None] * (n + 1))
DV = list([None] * (n + 1))
for i, planet in enumerate(seq):
t_P[i] = epoch(x[0] + sum(T[0:i]))
r_P[i], v_P[i] = planet.eph(t_P[i])
plot_planet(ax, planet, t0=t_P[i], color=(
0.8, 0.6, 0.8), legend=True, units = AU)
# 3 - We start with the first leg
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
Vinfx = x[3] * cos(phi) * cos(theta)
Vinfy = x[3] * cos(phi) * sin(theta)
Vinfz = x[3] * sin(phi)
v0 = [a + b for a, b in zip(v_P[0], [Vinfx, Vinfy, Vinfz])]
r, v = propagate_lagrangian(
r_P[0], v0, x[4] * T[0] * DAY2SEC, seq[0].mu_central_body)
plot_kepler(
ax,
r_P[0],
v0,
x[4] *
T[0] *
DAY2SEC,
seq[0].mu_central_body,
N=100,
color='b',
legend=False,
units=AU)
# Lambert arc to reach seq[1]
dt = (1 - x[4]) * T[0] * DAY2SEC
l = lambert_problem(r, r_P[1], dt, seq[0].mu_central_body)
plot_lambert(ax, l, sol=0, color='r', legend=False, units=AU)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# First DSM occuring at time nu1*T1
DV[0] = norm([a - b for a, b in zip(v_beg_l, v)])
# 4 - And we proceed with each successive leg
for i in range(1, n):
# Fly-by
v_out = fb_prop(v_end_l,
v_P[i],
x[7 + (i - 1) * 4] * seq[i].radius,
x[6 + (i - 1) * 4],
seq[i].mu_self)
# s/c propagation before the DSM
r, v = propagate_lagrangian(
r_P[i], v_out, x[8 + (i - 1) * 4] * T[i] * DAY2SEC, seq[0].
mu_central_body)
plot_kepler(ax,
r_P[i],
v_out,
x[8 + (i - 1) * 4] * T[i] * DAY2SEC,
seq[0].mu_central_body,
N=100,
color='b',
legend=False,
units=AU)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[8 + (i - 1) * 4]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt, seq[0].mu_central_body)
plot_lambert(ax, l, sol=0, color='r', legend=False, units=AU)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# DSM occurring at time nu2*T2
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
return ax
def _objfun_impl(self,x): #1 - we 'decode' the chromosome recording the various times of flight (days) in the list T for convenience T = list([0]*(self.__n_legs)) #sum_alpha = 0 #for i in range(self.__n_legs-1): # sum_alpha = sum_alpha+x[4+4*i] #for i in xrange(self.__n_legs-1): # T[i] = (x[4+4*i]/sum_alpha)*x[3] for i in xrange(0,self.__n_legs): T[i] = (x[4+4*i]/sum(x[4::4]))*x[3] #print "\tDuration: " + str(T) + "days" #return(T,) #2 - We compute the epochs and ephemerides of the planetary encounters t_P = list([None] * (self.__n_legs)) r_P = list([None] * (self.__n_legs)) v_P = list([None] * (self.__n_legs)) DV = list([None] * (self.__n_legs)) for i,planet in enumerate(self.seq): t_P[i] = epoch(x[0]+sum(T[:i+1])) r_P[i],v_P[i] = self.seq[i].eph(t_P[i]) #3 - We start with the first leg: a lambert arc theta = 2*pi*x[1] phi = acos(2*x[2]-1)-pi/2 r = [cos(phi)*sin(theta), cos(phi)*cos(theta), sin(phi)] #phi close to zero is in the moon orbit plane injection r = [JR*1000*d for d in r] l = lambert_problem(r,r_P[0],T[0]*DAY2SEC,self.common_mu, False, False) #Lambert arc to reach seq[1] v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] #First DSM occuring at the very beginning (will be cancelled by the optimizer) DV[0] = abs(norm(v_beg_l) - 3400) #4 - And we proceed with each successive leg for i in xrange(1,self.__n_legs): #Fly-by v_out = fb_prop(v_end_l,v_P[i-1],x[6+(i-1)*4]*self.seq[i-1].radius,x[5+(i-1)*4],self.seq[i-1].mu_self) #s/c propagation before the DSM r,v = propagate_lagrangian(r_P[i-1],v_out,x[7+(i-1)*4]*T[i]*DAY2SEC,self.common_mu) #Lambert arc to reach Earth during (1-nu2)*T2 (second segment) dt = (1-x[7+(i-1)*4])*T[i]*DAY2SEC l = lambert_problem(r,r_P[i],dt,self.common_mu, False, False) v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] tmp2, ra2 = closest_distance(r,v_beg_l, r_P[i], v_end_l, self.common_mu) if tmp < tmp2: close_d[i] = tmp/JR ra = ra/JR else: close_d[i] = tmp2/JR ra = ra2/JR #DSM occuring at time nu2*T2 DV[i] = norm([a-b for a,b in zip(v_beg_l,v)]) coeff = 0.3 for i in xrange(0,self.__n_legs): ratio[i] = (DV[i]/(T[i]*DAY2SEC)) DV_2rj[i] = DV[i] + max((2.0-close_d[i]),0.0)*1000 + max((ratio[i]-coeff*(0.1/2000)),0.0)*100 T_2rj[i] = T[i] + max((2.0-close_d[i]),0.0)*1000 + max((ratio[i]-coeff*(0.1/2000)),0.0)*100 #if self.f_dimension == 1: # return (sum(DV) #else: # return (sum(DV), sum(T)) if self.f_dimension == 1: return (sum(DV_2rj)) else: return (sum(DV_2rj), sum(T_2rj))
def _get_penalty_data(self,x): """ getTrajectory takes a genome x, and returns a Trajectory variable that is a list of all r, v, and time of flights Trajectory = [[r0, v0_out, r1, v1_in, tof, rp, ra, Trev, vinf], [r1, v1_out, r2, v2_in, tof, rp, ra, Trev, vinf], [...]] tof in days """ from PyKEP import epoch, lambert_problem, propagate_lagrangian, fb_prop, DAY2SEC; from math import pi, acos, cos, sin; import numpy as np; from _mass_penalty import get_rp_ra_Trev Trajectory = []; #1 - we 'decode' the chromosome recording the various times of flight (days) in the list T for convenience T = x[3::4] # reconstruct properties that are known in _mga_incipit: self.seq = self.get_sequence(); self.__n_legs = len(self.seq); self.common_mu = self.seq[0].mu_central_body #2 - We compute the epochs and ephemerides of the planetary encounters t_P = list([None] * (self.__n_legs)) r_P = list([None] * (self.__n_legs)) v_P = list([None] * (self.__n_legs)) DV = list([None] * (self.__n_legs)) for i,planet in enumerate(self.seq): t_P[i] = epoch(x[0]+sum(T[:i+1])) r_P[i],v_P[i] = self.seq[i].eph(t_P[i]) #3 - We start with the first leg: a lambert arc theta = 2*pi*x[1] phi = acos(2*x[2]-1)-pi/2 r = [cos(phi)*sin(theta), cos(phi)*cos(theta), sin(phi)] #phi close to zero is in the moon orbit plane injection r = [JR*1000*d for d in r] l = lambert_problem(r,r_P[0],T[0]*DAY2SEC,self.common_mu, False, False) #Lambert arc to reach seq[1] v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] Tr = [tuple(r), v_beg_l, r_P[0], v_end_l, T[0]*DAY2SEC]; rPvec = np.asarray(r_P[0]); vPvec = np.asarray(v_end_l); Tr = Tr + get_rp_ra_Trev(rPvec, vPvec); vinf = vPvec - np.asarray(v_P[0]); Tr = Tr + [vinf]; Trajectory.append(Tr); #First DSM occuring at the very beginning (will be cancelled by the optimizer) DV[0] = abs(np.linalg.norm(v_beg_l) - 3400) #4 - And we proceed with each successive leg for i in xrange(1,self.__n_legs): #Fly-by v_out = fb_prop(v_end_l,v_P[i-1],x[1+4*i]*self.seq[i-1].radius,x[4*i],self.seq[i-1].mu_self) #s/c propagation before the DSM r,v = propagate_lagrangian(r_P[i-1],v_out,x[4*i+2]*T[i]*DAY2SEC,self.common_mu) # append r, v, etc. to the Trajectory: Tr = [r_P[i-1], v_out, r, v, x[4*i+2]*T[i]*DAY2SEC]; rPvec = np.asarray(r); vPvec = np.asarray(v); Tr = Tr + get_rp_ra_Trev(rPvec, vPvec); vinf = []; Tr = Tr + [vinf]; Trajectory.append(Tr); #Lambert arc to reach Earth during (1-nu2)*T2 (second segment) dt = (1-x[4*i+2])*T[i]*DAY2SEC l = lambert_problem(r,r_P[i],dt,self.common_mu, False, False) v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] # append r, v, etc. to the Trajectory: Tr = [r, v_beg_l, r_P[i], v_end_l, (1-x[4*i+2])*T[i]*DAY2SEC]; rPvec = np.asarray(r_P[i]); vPvec = np.asarray(v_end_l); Tr = Tr + get_rp_ra_Trev(rPvec, vPvec); vinf = vPvec - np.asarray(v_P[i]); Tr = Tr + [vinf]; Trajectory.append(Tr); #DSM occuring at time nu2*T2 DV[i] = np.linalg.norm([a-b for a,b in zip(v_beg_l,v)]) return Trajectory;
def plot_sf_leg(leg, N=5, units=1, color='b', legend=False, plot_line=True, plot_segments=True, ax=None):
"""
ax = plot_sf_leg(leg, N=5, units=1, color='b', legend=False, no_trajectory=False, ax=None):
- ax: 3D axis object created using fig.gca(projection='3d')
- leg: a PyKEP.sims_flanagan.leg
- N: number of points to be plotted along one arc
- units: the length unit to be used in the plot
- color: matplotlib color to use to plot the trajectory and the grid points
- legend when True it plots also the legend
- plot_line: when True plots also the trajectory (between mid-points and grid points)
Plots a Sims-Flanagan leg
Example::
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.gca(projection='3d')
t1 = epoch(0)
pl = planet_ss('earth')
rE,vE = pl.eph(t1)
plot_planet(pl,t0=t1, units=AU, ax=ax)
t2 = epoch(440)
pl = planet_ss('mars')
rM, vM = pl.eph(t2)
plot_planet(pl,t0=t2, units=AU, ax=ax)
sc = sims_flanagan.spacecraft(4500,0.5,2500)
x0 = sims_flanagan.sc_state(rE,vE,sc.mass)
xe = sims_flanagan.sc_state(rM,vM,sc.mass)
l = sims_flanagan.leg(t1,x0,[1,0,0]*5,t2,xe,sc,MU_SUN)
plot_sf_leg(l, units=AU, ax=ax)
"""
from PyKEP import propagate_lagrangian, AU, DAY2SEC, G0, propagate_taylor
import numpy as np
from scipy.linalg import norm
from math import exp
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
if ax is None:
fig = plt.figure()
axis = fig.gca(projection='3d')
else:
axis = ax
# We compute the number of segments for forward and backward propagation
n_seg = len(leg.get_throttles())
fwd_seg = (n_seg + 1) // 2
back_seg = n_seg // 2
# We extract information on the spacecraft
sc = leg.get_spacecraft()
isp = sc.isp
max_thrust = sc.thrust
# And on the leg
throttles = leg.get_throttles()
mu = leg.get_mu()
# Forward propagation
# x,y,z contain the cartesian components of all points (grid+midpints)
x = [0.0] * (fwd_seg * 2 + 1)
y = [0.0] * (fwd_seg * 2 + 1)
z = [0.0] * (fwd_seg * 2 + 1)
state = leg.get_xi()
# Initial conditions
r = state.r
v = state.v
m = state.m
x[0] = r[0] / units
y[0] = r[1] / units
z[0] = r[2] / units
# We compute all points by propagation
for i, t in enumerate(throttles[:fwd_seg]):
dt = (t.end.mjd - t.start.mjd) * DAY2SEC
alpha = min(norm(t.value), 1.0)
# Keplerian propagation and dV application
if leg.high_fidelity is False:
dV = [max_thrust / m * dt * dumb for dumb in t.value]
if plot_line:
plot_kepler(r, v, dt / 2, mu, N=N, units=units, color=(alpha, 0, 1 - alpha), ax=axis)
r, v = propagate_lagrangian(r, v, dt / 2, mu)
x[2 * i + 1] = r[0] / units
y[2 * i + 1] = r[1] / units
z[2 * i + 1] = r[2] / units
# v= v+dV
v = [a + b for a, b in zip(v, dV)]
if plot_line:
plot_kepler(r, v, dt / 2, mu, N=N, units=units, color=(alpha, 0, 1 - alpha), ax=axis)
r, v = propagate_lagrangian(r, v, dt / 2, mu)
x[2 * i + 2] = r[0] / units
y[2 * i + 2] = r[1] / units
z[2 * i + 2] = r[2] / units
m *= exp(-norm(dV) / isp / G0)
# Taylor propagation of constant thrust u
else:
u = [max_thrust * dumb for dumb in t.value]
if plot_line:
plot_taylor(r, v, m, u, dt / 2, mu, isp * G0, N=N, units=units, color=(alpha, 0, 1 - alpha), ax=axis)
r, v, m = propagate_taylor(r, v, m, u, dt / 2, mu, isp * G0, -12, -12)
x[2 * i + 1] = r[0] / units
y[2 * i + 1] = r[1] / units
z[2 * i + 1] = r[2] / units
if plot_line:
plot_taylor(r, v, m, u, dt / 2, mu, isp * G0, N=N, units=units, color=(alpha, 0, 1 - alpha), ax=axis)
r, v, m = propagate_taylor(r, v, m, u, dt / 2, mu, isp * G0, -12, -12)
x[2 * i + 2] = r[0] / units
y[2 * i + 2] = r[1] / units
z[2 * i + 2] = r[2] / units
x_grid = x[::2]
y_grid = y[::2]
z_grid = z[::2]
x_midpoint = x[1::2]
y_midpoint = y[1::2]
z_midpoint = z[1::2]
if plot_segments:
axis.scatter(x_grid[:-1], y_grid[:-1], z_grid[:-1], label='nodes', marker='o')
axis.scatter(x_midpoint, y_midpoint, z_midpoint, label='mid-points', marker='x')
axis.scatter(x_grid[-1], y_grid[-1], z_grid[-1], marker='^', c='y', label='mismatch point')
# Backward propagation
# x,y,z will contain the cartesian components of
x = [0.0] * (back_seg * 2 + 1)
y = [0.0] * (back_seg * 2 + 1)
z = [0.0] * (back_seg * 2 + 1)
state = leg.get_xf()
# Final conditions
r = state.r
v = state.v
m = state.m
x[-1] = r[0] / units
y[-1] = r[1] / units
z[-1] = r[2] / units
for i, t in enumerate(throttles[-1:-back_seg - 1:-1]):
dt = (t.end.mjd - t.start.mjd) * DAY2SEC
alpha = min(norm(t.value), 1.0)
if leg.high_fidelity is False:
dV = [max_thrust / m * dt * dumb for dumb in t.value]
if plot_line:
plot_kepler(r, v, -dt / 2, mu, N=N, units=units, color=(alpha, 0, 1 - alpha), ax=axis)
r, v = propagate_lagrangian(r, v, -dt / 2, mu)
x[-2 * i - 2] = r[0] / units
y[-2 * i - 2] = r[1] / units
z[-2 * i - 2] = r[2] / units
# v= v+dV
v = [a - b for a, b in zip(v, dV)]
if plot_line:
plot_kepler(r, v, -dt / 2, mu, N=N, units=units, color=(alpha, 0, 1 - alpha), ax=axis)
r, v = propagate_lagrangian(r, v, -dt / 2, mu)
x[-2 * i - 3] = r[0] / units
y[-2 * i - 3] = r[1] / units
z[-2 * i - 3] = r[2] / units
m *= exp(norm(dV) / isp / G0)
else:
u = [max_thrust * dumb for dumb in t.value]
if plot_line:
plot_taylor(r, v, m, u, -dt / 2, mu, isp * G0, N=N, units=units, color=(alpha, 0, 1 - alpha), ax=axis)
r, v, m = propagate_taylor(r, v, m, u, -dt / 2, mu, isp * G0, -12, -12)
x[-2 * i - 2] = r[0] / units
y[-2 * i - 2] = r[1] / units
z[-2 * i - 2] = r[2] / units
if plot_line:
plot_taylor(r, v, m, u, -dt / 2, mu, isp * G0, N=N, units=units, color=(alpha, 0, 1 - alpha), ax=axis)
r, v, m = propagate_taylor(r, v, m, u, -dt / 2, mu, isp * G0, -12, -12)
x[-2 * i - 3] = r[0] / units
y[-2 * i - 3] = r[1] / units
z[-2 * i - 3] = r[2] / units
x_grid = x[::2]
y_grid = y[::2]
z_grid = z[::2]
x_midpoint = x[1::2]
y_midpoint = y[1::2]
z_midpoint = z[1::2]
if plot_segments:
axis.scatter(x_grid[1:], y_grid[1:], z_grid[1:], marker='o')
axis.scatter(x_midpoint, y_midpoint, z_midpoint, marker='x')
axis.scatter(x_grid[0], y_grid[0], z_grid[0], marker='^', c='y')
if legend:
axis.legend()
if ax is None: # show only if axis is not set
plt.show()
return axis
def pretty(self, x):
"""
Prints human readable information on the trajectory represented by the decision vector x
Example::
prob.pretty(x)
"""
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T
T = list([0] * (self.__n_legs))
#a[-i] = x[-1-(i-1)*4]
for i in xrange(self.__n_legs - 1):
j = i + 1
T[-j] = (x[5] - sum(T[-(j - 1):])) * x[-1 - (j - 1) * 4]
T[0] = x[5] - sum(T)
#2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n_legs + 1))
r_P = list([None] * (self.__n_legs + 1))
v_P = list([None] * (self.__n_legs + 1))
DV = list([None] * (self.__n_legs + 1))
for i, planet in enumerate(self.seq):
t_P[i] = epoch(x[0] + sum(T[0:i]))
r_P[i], v_P[i] = self.seq[i].eph(t_P[i])
#3 - We start with the first leg
print "First Leg: " + self.seq[0].name + " to " + self.seq[1].name
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
Vinfx = x[3] * cos(phi) * cos(theta)
Vinfy = x[3] * cos(phi) * sin(theta)
Vinfz = x[3] * sin(phi)
print "Departure: " + str(t_P[0]) + " (" + str(
t_P[0].mjd2000) + " mjd2000) "
print "Duration: " + str(T[0]) + "days"
print "VINF: " + str(x[3] / 1000) + " km/sec"
v0 = [a + b for a, b in zip(v_P[0], [Vinfx, Vinfy, Vinfz])]
r, v = propagate_lagrangian(r_P[0], v0, x[4] * T[0] * DAY2SEC,
self.common_mu)
print "DSM after " + str(x[4] * T[0]) + " days"
#Lambert arc to reach seq[1]
dt = (1 - x[4]) * T[0] * DAY2SEC
l = lambert_problem(r, r_P[1], dt, self.common_mu, False, False)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
#First DSM occuring at time nu1*T1
DV[0] = norm([a - b for a, b in zip(v_beg_l, v)])
print "DSM magnitude: " + str(DV[0]) + "m/s"
#4 - And we proceed with each successive leg
for i in range(1, self.__n_legs):
print "\nleg no. " + str(
i + 1) + ": " + self.seq[i].name + " to " + self.seq[i +
1].name
print "Duration: " + str(T[i]) + "days"
#Fly-by
v_out = fb_prop(v_end_l, v_P[i],
x[7 + (i - 1) * 4] * self.seq[i].radius,
x[6 + (i - 1) * 4], self.seq[i].mu_self)
print "Fly-by epoch: " + str(t_P[i]) + " (" + str(
t_P[i].mjd2000) + " mjd2000) "
print "Fly-by radius: " + str(x[7 +
(i - 1) * 4]) + " planetary radii"
#s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out,
x[8 + (i - 1) * 4] * T[i] * DAY2SEC,
self.common_mu)
print "DSM after " + str(x[8 + (i - 1) * 4] * T[i]) + " days"
#Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[8 + (i - 1) * 4]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt, self.common_mu, False,
False)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
#DSM occuring at time nu2*T2
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
print "DSM magnitude: " + str(DV[i]) + "m/s"
#Last Delta-v
print "\nArrival at " + self.seq[-1].name
DV[-1] = norm([a - b for a, b in zip(v_end_l, v_P[-1])])
print "Arrival epoch: " + str(t_P[-1]) + " (" + str(
t_P[-1].mjd2000) + " mjd2000) "
print "Arrival Vinf: " + str(DV[-1]) + "m/s"
print "Total mission time: " + str(sum(T) / 365.25) + " years"
def lambertization(prob, x): """ Does all the lambert arc construction to get you DV and stuff """ # get sequence try: seq = prob.seq except AttributeError: seq = prob.get_sequence() # get common mu try: common_mu = prob.common_mu except AttributeError: common_mu = seq[0].mu_central_body # number of legs n_legs = len(seq) # time of flights (days) T = x[3::4] # Epochs and Ephemerides of the planetary encounters t_P = list([None] * (n_legs)) r_P = list([None] * (n_legs)) v_P = list([None] * (n_legs)) DV = list([None] * (n_legs)) close_d = list([None] * (n_legs)) for i,planet in enumerate(seq): t_P[i] = epoch(x[0]+sum(T[:i+1])) r_P[i],v_P[i] = seq[i].eph(t_P[i]) # Lambert arc to 1st leg theta = 2*pi*x[1] phi = acos(2*x[2]-1)-pi/2 r = [cos(phi)*sin(theta), cos(phi)*cos(theta), sin(phi)] #phi close to zero is in the moon orbit plane injection r = [JR*1000*d for d in r] l = lambert_problem(r,r_P[0],T[0]*DAY2SEC,common_mu, False, False) v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] close_d[0] = closest_distance(r,v_beg_l, r_P[0], v_end_l, common_mu)[0] / JR # save the initial conditions on 1000JR initial = ( [epoch(x[0]), t_P[0]], [r,r_P[0]], [v_beg_l, v_end_l] ) # First DSM occuring at the very beginning (will be cancelled by the optimizer) DV[0] = abs(norm(v_beg_l) - 3400) # creating new lists v_sc = [] # Proceed with succeeding legs for i in xrange(1, n_legs): # Fly-by v_out = fb_prop(v_end_l,v_P[i-1],x[1+4*i]*seq[i-1].radius,x[4*i],seq[i-1].mu_self) # s/c propagation before the DSM r,v = propagate_lagrangian(r_P[i-1],v_out,x[4*i+2]*T[i]*DAY2SEC,common_mu) tmp, ra = closest_distance(r_P[i-1],v_out, r,v, common_mu) # Lambert arc to reach Earth during (1-nu2)*T2 (second segment) dt = (1-x[4*i+2])*T[i]*DAY2SEC l = lambert_problem(r,r_P[i],dt,common_mu, False, False) v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] tmp2, ra2 = closest_distance(r,v_beg_l, r_P[i], v_end_l, common_mu) if tmp < tmp2: close_d[i] = tmp/JR ra = ra/JR else: close_d[i] = tmp2/JR ra = ra2/JR # DSM occuring at time nu2*T2 DV[i] = norm([a-b for a,b in zip(v_beg_l,v)]) v_sc.append( (v_out, v_end_l) ) # v_inf_out, v_inf_in return seq, common_mu, n_legs, initial, T, t_P, r_P, v_sc, DV, close_d
def stats(self, x):
import matplotlib as mpl
import matplotlib.pyplot as plt
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T for convenience
T = list([0] * (self.__n_legs))
for i in xrange(self.__n_legs):
T[i] = (x[4 + 4 * i] / sum(x[4::4])) * x[3]
#2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n_legs))
r_P = list([None] * (self.__n_legs))
v_P = list([None] * (self.__n_legs))
DV = list([None] * (self.__n_legs))
close_d = list([None] * (self.__n_legs))
for i, planet in enumerate(self.seq):
t_P[i] = epoch(x[0] + sum(T[:i + 1]))
r_P[i], v_P[i] = self.seq[i].eph(t_P[i])
#3 - We start with the first leg: a lambert arc
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
r = [cos(phi) * sin(theta),
cos(phi) * cos(theta),
sin(phi)] #phi close to zero is in the moon orbit plane injection
r = [JR * 1000 * d for d in r]
l = lambert_problem(r, r_P[0], T[0] * DAY2SEC, self.common_mu, False,
False)
#Lambert arc to reach seq[1]
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
close_d[0] = closest_distance(r, v_beg_l, r_P[0], v_end_l,
self.common_mu)[0] / JR
#First DSM occuring at the very beginning (will be cancelled by the optimizer)
DV[0] = abs(norm(v_beg_l) - 3400)
#4 - And we proceed with each successive leg
for i in xrange(1, self.__n_legs):
#Fly-by
v_out = fb_prop(v_end_l, v_P[i - 1],
x[6 + (i - 1) * 4] * self.seq[i - 1].radius,
x[5 + (i - 1) * 4], self.seq[i - 1].mu_self)
#s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i - 1], v_out,
x[7 + (i - 1) * 4] * T[i] * DAY2SEC,
self.common_mu)
tmp, ra = closest_distance(r_P[i - 1], v_out, r, v, self.common_mu)
#Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[7 + (i - 1) * 4]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i], dt, self.common_mu, False, False)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
tmp2, ra2 = closest_distance(r, v_beg_l, r_P[i], v_end_l,
self.common_mu)
if tmp < tmp2:
close_d[i] = tmp / JR
ra = ra / JR
else:
close_d[i] = tmp2 / JR
ra = ra2 / JR
#DSM occuring at time nu2*T2
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
#print "Total mission time (days): " + str(sum(T))
#print "Total DV (m/s): " + str(sum(DV))
symbol_dict = {
'io': 'yo',
'europa': 'bo',
'ganymede': 'ro',
'callisto': 'ko'
}
#for i in xrange(0,self.__n_legs):
# plt.plot(sum(DV), sum(T), symbol_dict[self.seq[0].name])
#n = 0
ratio = list([0] * (self.__n_legs))
coeff = 0.3
for i in xrange(0, self.__n_legs):
ratio[i] = (DV[i] / (T[i] * DAY2SEC))
if close_d[0] >= 2:
if close_d[1] >= 2:
if close_d[2] >= 2:
if close_d[3] >= 2:
if ratio[1] <= coeff * (0.1 / 2000):
if ratio[2] <= coeff * (0.1 / 2000):
if ratio[3] <= coeff * (0.1 / 2000):
if ratio[0] <= coeff * (0.1 / 2000):
plt.plot(sum(DV), sum(T),
symbol_dict[self.seq[0].name])
#for i in xrange(0,self.__n_legs):
# if close_d[i] > 2:
# plt.plot(sum(DV), sum(T), symbol_dict[self.seq[0].name])
# else:
# print "\n the closest distance is less than 2*Rj "
#print "\n number of sequences that do not crash " + str(n)
plt.show()
def _get_states(self): """ Returns the spacecraft states (t,r,v,m) at the leg grid points Examples:: times,r,v,m = PyKEP.sims_flanagan.leg.get_states() """ from PyKEP import propagate_lagrangian, AU, DAY2SEC, G0, propagate_taylor import numpy as np from scipy.linalg import norm from math import exp #We compute the number of segments for forward and backward propagation n_seg = len(self.get_throttles()) fwd_seg = (n_seg+1)/2 back_seg = n_seg/2 #We extract information on the spacecraft sc = self.get_spacecraft() isp = sc.isp max_thrust = sc.thrust #And on the leg throttles = self.get_throttles() mu = self.get_mu() #time grid t_grid = [0.0]*(n_seg*2+2) #Forward propagation #x,y,z contain the cartesian components of all points (grid+midpints) x = [0.0]*(fwd_seg*2+1) y = [0.0]*(fwd_seg*2+1) z = [0.0]*(fwd_seg*2+1) vx = [0.0]*(fwd_seg*2+1) vy = [0.0]*(fwd_seg*2+1) vz = [0.0]*(fwd_seg*2+1) mass = [0.0]*(fwd_seg*2+1) state = self.get_xi() #Initial conditions r = state.r; v = state.v; m = state.m x[0],y[0],z[0] = r vx[0],vy[0],vz[0] = v mass[0] = m #We compute all points by propagation for i,t in enumerate(throttles[:fwd_seg]): t_grid[2*i] = t.start.mjd2000 t_grid[2*i+1] = t.start.mjd2000 + (t.end.mjd2000 - t.start.mjd2000)/2. dt = (t.end.mjd - t.start.mjd)*DAY2SEC alpha = min(norm(t.value),1.0) #Keplerian propagation and dV application if self.high_fidelity == False: dV = [max_thrust / m * dt * dumb for dumb in t.value] r,v = propagate_lagrangian(r,v,dt/2,mu) x[2*i+1],y[2*i+1],z[2*i+1] = r vx[2*i+1],vy[2*i+1],vz[2*i+1] = v mass[2*i+1] = m #v= v+dV v = [a+b for a,b in zip(v,dV)] r,v = propagate_lagrangian(r,v,dt/2,mu) m *= exp( -norm(dV)/isp/G0 ) x[2*i+2],y[2*i+2],z[2*i+2] = r vx[2*i+2],vy[2*i+2],vz[2*i+2] = v mass[2*i+2] = m #Taylor propagation of constant thrust u else: u = [max_thrust * dumb for dumb in t.value] r,v,m = propagate_taylor(r,v,m,u,dt/2,mu,isp*G0,-10,-10) x[2*i+1],y[2*i+1],z[2*i+1] = r vx[2*i+1],vy[2*i+1],vz[2*i+1] = v mass[2*i+1] = m r,v,m = propagate_taylor(r,v,m,u,dt/2,mu,isp*G0,-10,-10) x[2*i+2],y[2*i+2],z[2*i+2] = r vx[2*i+2],vy[2*i+2],vz[2*i+2] = v mass[2*i+2] = m t_grid[2*i+2] = t.end.mjd2000 #Backward propagation #x,y,z will contain the cartesian components of x_back = [0.123]*(back_seg*2+1) y_back = [0.123]*(back_seg*2+1) z_back = [0.123]*(back_seg*2+1) vx_back = [0.0]*(back_seg*2+1) vy_back = [0.0]*(back_seg*2+1) vz_back = [0.0]*(back_seg*2+1) mass_back = [0.0]*(back_seg*2+1) state = self.get_xf() #Final conditions r = state.r; v = state.v; m = state.m x_back[-1],y_back[-1],z_back[-1] = r vx_back[-1],vy_back[-1],vz_back[-1] = v mass_back[-1] = m for i,t in enumerate(throttles[-1:-back_seg-1:-1]): t_grid[-2*i-2] = t.end.mjd2000 -(t.end.mjd2000 - t.start.mjd2000)/2. t_grid[-2*i-1] = t.end.mjd2000 dt = (t.end.mjd - t.start.mjd)*DAY2SEC alpha = min(norm(t.value),1.0) if self.high_fidelity == False: dV = [max_thrust / m * dt * dumb for dumb in t.value] r,v = propagate_lagrangian(r,v,-dt/2,mu) x_back[-2*i-2],y_back[-2*i-2],z_back[-2*i-2] = r vx_back[-2*i-2],vy_back[-2*i-2],vz_back[-2*i-2] = v mass_back[-2*i-2] = m #v= v+dV v = [a-b for a,b in zip(v,dV)] r,v = propagate_lagrangian(r,v,-dt/2,mu) m *= exp( norm(dV)/isp/G0 ) x_back[-2*i-3],y_back[-2*i-3],z_back[-2*i-3] = r vx_back[-2*i-3],vy_back[-2*i-3],vz_back[-2*i-3] = v mass_back[-2*i-3] = m else: u = [max_thrust * dumb for dumb in t.value] r,v,m = propagate_taylor(r,v,m,u,-dt/2,mu,isp*G0,-10,-10) x_back[-2*i-2],y_back[-2*i-2],z_back[-2*i-2] = r vx_back[-2*i-2],vy_back[-2*i-2],vz_back[-2*i-2] = v mass_back[-2*i-2] = m r,v,m = propagate_taylor(r,v,m,u,-dt/2,mu,isp*G0,-10,-10) x_back[-2*i-3],y_back[-2*i-3],z_back[-2*i-3] = r vx_back[-2*i-3],vy_back[-2*i-3],vz_back[-2*i-3] = v mass_back[-2*i-3] = m t_grid[-2*i-3] = t.start.mjd2000 x = x+x_back y = y+y_back z = z+z_back vx = vx+vx_back vy = vy+vy_back vz = vz+vz_back mass = mass+mass_back return t_grid, zip(x,y,z), zip(vx,vy,vz), mass
def _objfun_impl(self, x):
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T
T = list([0] * (self.__n_legs))
for i in xrange(self.__n_legs - 1):
j = i + 1
T[-j] = (x[5] - sum(T[-(j - 1):])) * x[-1 - (j - 1) * 4]
T[0] = x[5] - sum(T)
#2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n_legs + 1))
r_P = list([None] * (self.__n_legs + 1))
v_P = list([None] * (self.__n_legs + 1))
DV = list([0.0] * (self.__n_legs + 1))
for i, planet in enumerate(self.seq):
t_P[i] = epoch(x[0] + sum(T[0:i]))
r_P[i], v_P[i] = self.seq[i].eph(t_P[i])
#3 - We start with the first leg
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
Vinfx = x[3] * cos(phi) * cos(theta)
Vinfy = x[3] * cos(phi) * sin(theta)
Vinfz = x[3] * sin(phi)
v0 = [a + b for a, b in zip(v_P[0], [Vinfx, Vinfy, Vinfz])]
r, v = propagate_lagrangian(r_P[0], v0, x[4] * T[0] * DAY2SEC,
self.common_mu)
#Lambert arc to reach seq[1]
dt = (1 - x[4]) * T[0] * DAY2SEC
l = lambert_problem(r, r_P[1], dt, self.common_mu, False, False)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
#First DSM occuring at time nu1*T1
DV[0] = norm([a - b for a, b in zip(v_beg_l, v)])
#4 - And we proceed with each successive leg
for i in range(1, self.__n_legs):
#Fly-by
v_out = fb_prop(v_end_l, v_P[i],
x[7 + (i - 1) * 4] * self.seq[i].radius,
x[6 + (i - 1) * 4], self.seq[i].mu_self)
#s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out,
x[8 + (i - 1) * 4] * T[i] * DAY2SEC,
self.common_mu)
#Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[8 + (i - 1) * 4]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt, self.common_mu, False,
False)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
#DSM occuring at time nu2*T2
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
#Last Delta-v
if self.__add_vinf_arr:
DV[-1] = norm([a - b for a, b in zip(v_end_l, v_P[-1])])
if self.__add_vinf_dep:
DV[0] += x[3]
if self.f_dimension == 1:
return (sum(DV), )
else:
return (sum(DV), sum(T))
def planet_asteroid(start_planet, target_name, tlaunch, tarrive, rev, N):
# Create PyKEP epoch objects and calculate flight time
t1 = epoch(tlaunch)
t2 = epoch(tarrive)
dt = (tarrive - tlaunch) * DAY2SEC
import py.AsteroidDB as asteroidDB
neo_db = asteroidDB.neo
target = (item for item in neo_db if item["name"] == target_name).next()
ep = epoch(target["epoch_mjd"], epoch.epoch_type.MJD)
a = target["a"] * AU
e = target["e"]
i = target["i"] * DEG2RAD
om = target["om"] * DEG2RAD
w = target["w"] * DEG2RAD
ma = target["ma"] * DEG2RAD
as_mu = 1E17 * 6.67384E-11 # maybe need to calculate actual mass from density and radius
r = (target["diameter"] / 2) * 1000
sr = r * 1.1
OBJ2 = planet(ep, (a, e, i, om, w, ma), MU_SUN, as_mu, r, sr)
OBJ1 = planet_ss(start_planet) # Calculate location of objects in flight path
r1, v1 = OBJ1.eph(t1)
r2, v2 = OBJ2.eph(t2)
# Find trajectory
l = lambert_problem(r1, r2, dt, MU_SUN)
#extract relevant information from solution
r = l.get_r1()
v = l.get_v1()[rev]
mu = l.get_mu()
#define the integration time
dtn = dt / (N - 1)
dtn_days = dtn * SEC2DAY
#alocate the cartesian components for r
t = np.array([0.0] * N)
x = np.array([0.0] * N)
y = np.array([0.0] * N)
z = np.array([0.0] * N)
#calculate the spacecraft position at each dt
for i in range(N):
t[i] = tlaunch + dtn_days * i
x[i] = r[0] / AU
y[i] = r[1] / AU
z[i] = r[2] / AU
r, v = propagate_lagrangian(r, v, dtn, mu)
#traj = [t, x, y, z]
vin = l.get_v1()[rev]
vout = l.get_v2()[rev]
#dV=fb_vel(vin,vout,planet_ss(arrive_planet))
#dV=np.sqrt( np.square(vin[0]/vout[0])+np.square(vin[1]/vout[1])+np.square(vin[2]/vout[2]))
#dV=np.sqrt( np.square(vin[0]-v1[0])+np.square(v1[1]-vin[1])+np.square(v1[2]-vin[2]))
#dV=np.sqrt( np.square(v2[0]-vout[0])+np.square(v2[1]-vout[1])+np.square(v2[2]-vout[2]))
#dV=np.sqrt( np.square(v1[0]/vin[0])+np.square(v1[1]/vin[1])+np.square(v1[2]/vin[2]))
C3_launch = (np.sqrt(np.square(vin[0] - v1[0]) + np.square(vin[1] - v1[1]) + np.square(vin[2] - v1[2]))) ** 2
C3_arrive = (np.sqrt(np.square(vout[0] - v2[0]) + np.square(vout[1] - v2[1]) + np.square(vout[2] - v2[2]))) ** 2
C3 = np.sqrt((C3_arrive ** 2) + (C3_launch ** 2))
return C3
def _objfun_impl(self, x):
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T for convenience
T = list([0] * (self.__n_legs))
#sum_alpha = 0
#for i in range(self.__n_legs-1):
# sum_alpha = sum_alpha+x[4+4*i]
#for i in xrange(self.__n_legs-1):
# T[i] = (x[4+4*i]/sum_alpha)*x[3]
for i in xrange(0, self.__n_legs):
T[i] = (x[4 + 4 * i] / sum(x[4::4])) * x[3]
#print "\tDuration: " + str(T) + "days"
#return(T,)
#2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n_legs))
r_P = list([None] * (self.__n_legs))
v_P = list([None] * (self.__n_legs))
DV = list([None] * (self.__n_legs))
for i, planet in enumerate(self.seq):
t_P[i] = epoch(x[0] + sum(T[:i + 1]))
r_P[i], v_P[i] = self.seq[i].eph(t_P[i])
#3 - We start with the first leg: a lambert arc
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
r = [cos(phi) * sin(theta),
cos(phi) * cos(theta),
sin(phi)] #phi close to zero is in the moon orbit plane injection
r = [JR * 1000 * d for d in r]
l = lambert_problem(r, r_P[0], T[0] * DAY2SEC, self.common_mu, False,
False)
#Lambert arc to reach seq[1]
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
#First DSM occuring at the very beginning (will be cancelled by the optimizer)
DV[0] = abs(norm(v_beg_l) - 3400)
#4 - And we proceed with each successive leg
for i in xrange(1, self.__n_legs):
#Fly-by
v_out = fb_prop(v_end_l, v_P[i - 1],
x[6 + (i - 1) * 4] * self.seq[i - 1].radius,
x[5 + (i - 1) * 4], self.seq[i - 1].mu_self)
#s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i - 1], v_out,
x[7 + (i - 1) * 4] * T[i] * DAY2SEC,
self.common_mu)
#Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[7 + (i - 1) * 4]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i], dt, self.common_mu, False, False)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
tmp2, ra2 = closest_distance(r, v_beg_l, r_P[i], v_end_l,
self.common_mu)
if tmp < tmp2:
close_d[i] = tmp / JR
ra = ra / JR
else:
close_d[i] = tmp2 / JR
ra = ra2 / JR
#DSM occuring at time nu2*T2
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
coeff = 0.3
for i in xrange(0, self.__n_legs):
ratio[i] = (DV[i] / (T[i] * DAY2SEC))
DV_2rj[i] = DV[i] + max((2.0 - close_d[i]), 0.0) * 1000 + max(
(ratio[i] - coeff * (0.1 / 2000)), 0.0) * 100
T_2rj[i] = T[i] + max((2.0 - close_d[i]), 0.0) * 1000 + max(
(ratio[i] - coeff * (0.1 / 2000)), 0.0) * 100
#if self.f_dimension == 1:
# return (sum(DV)
#else:
# return (sum(DV), sum(T))
if self.f_dimension == 1:
return (sum(DV_2rj))
else:
return (sum(DV_2rj), sum(T_2rj))
def _mga_incipit_plot_old(self, x, plot_leg_0=False):
"""
Plots the trajectory represented by the decision vector x
Example::
prob.plot(x)
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from PyKEP.orbit_plots import plot_planet, plot_lambert, plot_kepler
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d', aspect='equal')
ax.scatter(0, 0, 0, color='y')
JR = 71492000.0
legs = len(x) / 4
seq = self.get_sequence()
common_mu = seq[0].mu_central_body
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T
T = x[3::4]
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * legs)
r_P = list([None] * legs)
v_P = list([None] * legs)
DV = list([None] * legs)
for i, planet in enumerate(seq):
t_P[i] = epoch(x[0] + sum(T[:i + 1]))
r_P[i], v_P[i] = planet.eph(t_P[i])
plot_planet(ax, planet, t0=t_P[i], color=(
0.8, 0.6, 0.8), legend=True, units = JR)
# 3 - We start with the first leg: a lambert arc
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
# phi close to zero is in the moon orbit plane injection
r = [cos(phi) * sin(theta), cos(phi) * cos(theta), sin(phi)]
r = [JR * 1000 * d for d in r]
l = lambert_problem(r, r_P[0], T[0] * DAY2SEC, common_mu, False, False)
if (plot_leg_0):
plot_lambert(ax, l, sol=0, color='k', legend=False, units=JR, N=500)
# Lambert arc to reach seq[1]
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# 4 - And we proceed with each successive leg
for i in range(1, legs):
# Fly-by
v_out = fb_prop(v_end_l,
v_P[i - 1],
x[1 + 4 * i] * seq[i - 1].radius,
x[4 * i],
seq[i - 1].mu_self)
# s/c propagation before the DSM
r, v = propagate_lagrangian(
r_P[i - 1], v_out, x[4 * i + 2] * T[i] * DAY2SEC, common_mu)
plot_kepler(ax,
r_P[i - 1],
v_out,
x[4 * i + 2] * T[i] * DAY2SEC,
common_mu,
N=500,
color='b',
legend=False,
units=JR)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[4 * i + 2]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i], dt, common_mu, False, False)
plot_lambert(ax, l, sol=0, color='r', legend=False, units=JR, N=500)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
plt.show()
return ax
def _get_penalty_data_part(self,x):
from PyKEP import epoch, lambert_problem, DAY2SEC, fb_prop, propagate_lagrangian
from math import pi, acos,cos,sin,sqrt
from scipy.linalg import norm
from copy import deepcopy
from _mass_penalty import get_rp_ra_Trev
import numpy as np
"""
This method returns the data needed to compute the score of a trajectory.
"""
Trajectory = [];
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T for convenience
T = x[3::4]
nlegs = len(x)/4
seq = self.get_sequence()
common_mu = seq[0].mu_central_body
t0 = self.t0.mjd2000
vinf_in = deepcopy(self.vinf_in)
#2 - We compute the epochs and ephemerides of the planetary encounters
ep_list = list([None] * (nlegs+1))
t_P = list([None] * (nlegs+1))
r_P = list([None] * (nlegs+1))
v_P = list([None] * (nlegs+1))
DV = list([None] * nlegs)
for i,planet in enumerate(seq):
ep_list[i] = t0+sum(T[:i])
t_P[i] = epoch(t0+sum(T[:i]))
r_P[i],v_P[i] = seq[i].eph(t_P[i])
v_end_l = [a+b for a,b in zip(vinf_in, v_P[0])]
#3 - And we proceed with each successive leg
for i in xrange(nlegs):
#Fly-by
v_out = fb_prop(v_end_l,v_P[i],x[1+4*i]*seq[i].radius,x[4*i],seq[i].mu_self)
#s/c propagation before the DSM
r,v = propagate_lagrangian(r_P[i],v_out,x[4*i+2]*T[i]*DAY2SEC,common_mu)
# append r, v, etc. to the Trajectory:
Tr = [r_P[i-1], v_out, r, v, x[4*i+2]*T[i]*DAY2SEC];
rPvec = np.asarray(r);
vPvec = np.asarray(v);
Tr = Tr + get_rp_ra_Trev(rPvec, vPvec);
vinf = [];
Tr = Tr + [vinf];
Trajectory.append(Tr);
#Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1-x[4*i+2])*T[i]*DAY2SEC
l = lambert_problem(r,r_P[i+1],dt,common_mu, False, False)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# append r, v, etc. to the Trajectory:
Tr = [r, v_beg_l, r_P[i], v_end_l, (1-x[4*i+2])*T[i]*DAY2SEC];
rPvec = np.asarray(r_P[i]);
vPvec = np.asarray(v_end_l);
Tr = Tr + get_rp_ra_Trev(rPvec, vPvec);
vinf = vPvec - np.asarray(v_P[i]);
Tr = Tr + [vinf];
Trajectory.append(Tr);
return Trajectory;
def AIO(self,x, doplot = True, doprint = True, rtrn_desc = True, dists_class = None):
P = doprint
plots_datas = list([None] * (self.__n))
PLDists = list([None] * (self.__n-1))
FBDates = list([None] * (self.__n-1))
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T
T = list([0]*(self.__n))
#a[-i] = x[-1-(i-1)*4]
for i in xrange(self.__n-1):
j = i+1;
T[-j] = (x[5] - sum(T[-(j-1):])) * x[-1-(j-1)*4]
T[0] = x[5] - sum(T)
#2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n+1))
r_P = list([None] * (self.__n+1))
v_P = list([None] * (self.__n+1))
DV = list([None] * (self.__n+1))
for i,planet in enumerate(self.seq):
t_P[i] = epoch(x[0] + sum(T[0:i]))
r_P[i],v_P[i] = self.seq[i].eph(t_P[i])
#3 - We start with the first leg
if P: print "First Leg: " + self.seq[0].name + " to " + self.seq[1].name
theta = 2*pi*x[1]
phi = acos(2*x[2]-1)-pi/2
Vinfx = x[3]*cos(phi)*cos(theta)
Vinfy = x[3]*cos(phi)*sin(theta)
Vinfz = x[3]*sin(phi)
if P:
print("Departure: " + str(t_P[0]) + " (" + str(t_P[0].mjd2000) + " mjd2000) \n"
"Duration: " + str(T[0]) + " days\n"
"VINF: " + str(x[3] / 1000) + " km/sec\n"
"C3: " + str((x[3] / 1000)**2) + " km^2/s^2")
v0 = [a+b for a,b in zip(v_P[0], [Vinfx,Vinfy,Vinfz])]
r,v = propagate_lagrangian(r_P[0], v0, x[4]*T[0]*DAY2SEC, MU_SUN)
if P: print "DSM after " + str(x[4]*T[0]) + " days"
#Lambert arc to reach seq[1]
dt = (1-x[4])*T[0]*DAY2SEC
l = lambert_problem(r, r_P[1], dt, MU_SUN)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# Append data needed for potential plot generation
plots_datas[0] = [v0, x[4]*T[0]*DAY2SEC, l]
#First DSM occuring at time nu1*T1
DV[0] = norm([a-b for a,b in zip(v_beg_l,v)])
if P: print "DSM magnitude: " + str(DV[0]) + "m/s"
#4 - And we proceed with each successive leg
for i in range(1,self.__n):
if P:
print("\nleg no. " + str(i+1) + ": " + self.seq[i].name + " to " + self.seq[i+1].name + "\n"
"Duration: " + str(T[i]) + "days")
#Fly-by
v_out = fb_prop(v_end_l, v_P[i], x[7+(i-1)*4]*self.seq[i].radius, x[6+(i-1)*4], self.seq[i].mu_self)
PLDists[i-1] = (x[7+(i-1)*4] -1)*self.seq[i].radius/1000.
FBDates[i-1] = t_P[i]
if P:
print("Fly-by epoch: " + str(t_P[i]) + " (" + str(t_P[i].mjd2000) + " mjd2000) \n"
"Fly-by radius: " + str(x[7+(i-1)*4]) + " planetary radii\n"
"Fly-by distance: " + str( (x[7+(i-1)*4] -1)*self.seq[i].radius/1000.) + " km")
#s/c propagation before the DSM
r,v = propagate_lagrangian(r_P[i], v_out, x[8+(i-1)*4]*T[i]*DAY2SEC, MU_SUN)
if P: print "DSM after " + str(x[8+(i-1)*4]*T[i]) + " days"
#Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1-x[8+(i-1)*4])*T[i]*DAY2SEC
l = lambert_problem(r, r_P[i+1], dt, MU_SUN)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# Append data needed for potential plot generation
plots_datas[i] = [v_out, x[8+(i-1)*4]*T[i]*DAY2SEC, l]
#DSM occuring at time nu2*T2
DV[i] = norm([a-b for a,b in zip(v_beg_l,v)])
if P: print "DSM magnitude: " + str(DV[i]) + "m/s"
#Last Delta-v
if P: print "\nArrival at " + self.seq[-1].name
DV[-1] = norm([a-b for a,b in zip(v_end_l,v_P[-1])])
if P:
print("Arrival Vinf: " + str(DV[-1]) + "m/s \n"
"Total mission time: " + str(sum(T)/365.25) + " years (" + str(sum(T)) + " days) \n"
"DSMs mag: " + str(sum(DV[:-1])) + "m/s \n"
"Entry Vel: " + str(sqrt(2*(0.5*(DV[-1])**2 + 61933310.95))) + "m/s \n"
"Entry epoch: " + str(epoch(t_P[0].mjd2000 + sum(T))) )
if doplot:
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from PyKEP.orbit_plots import plot_planet, plot_lambert, plot_kepler
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure(figsize=(8, 8), dpi=80)
ax = fig.gca(projection='3d')
ax.scatter(0,0,0, color='y')
for i,planet in enumerate(self.seq):
plot_planet(ax, planet, t0=t_P[i], color=(0.8,0.6,0.8), legend=True, units = AU)
for i, tpl in enumerate(plots_datas):
plot_kepler(ax, r_P[i], tpl[0], tpl[1], MU_SUN ,N = 100, color='b', legend=False, units = AU)
plot_lambert(ax, tpl[2], sol = 0, color='r', legend=False, units = AU)
fig.tight_layout()
plt.show()
if dists_class is not None:
for i, tpl in enumerate(plots_datas):
dists_class.positions_kepler(r_P[i], tpl[0], tpl[1], MU_SUN ,index = 2*i)
dists_class.positions_lambert(tpl[2], sol = 0, index = 2*(i+.5))
dists_class.set_launch_epoch(t_P[0].mjd2000)
return dists_class
if rtrn_desc:
import numpy as np
from math import atan2
desc = dict()
for i in range(len(x)):
desc[i] = x[i]
theta = 2*pi*x[1]
phi = acos(2*x[2]-1)-pi/2
axtl = 23.43929*DEG2RAD # Earth axial tlit
mactran = np.matrix([ [1, 0, 0],
[0, cos(axtl), -sin(axtl)],
[0, sin(axtl), cos(axtl)] ]) # Macierz przejscia z helio do ECI
macdegs = np.matrix([ [cos(phi)*cos(theta)],
[cos(phi)*sin(theta)],
[sin(phi)] ])
aaa = mactran.dot(macdegs)
theta_earth = atan2(aaa[1,0], aaa[0,0]) # Rektascensja asym
phi_earth = asin(aaa[2,0]) # Deklinacja asym
desc['RA'] = 360+RAD2DEG*theta_earth
desc['DEC'] = phi_earth*RAD2DEG
desc['Ldate'] = str(t_P[0])
desc['C3'] = (x[3] / 1000)**2
desc['dVmag'] = sum(DV[:-1])
desc['VinfRE'] = DV[-1]
desc['VRE'] = (DV[-1]**2 + 2*61933310.95)**.5
desc['REDate'] = str(epoch(t_P[0].mjd2000 + sum(T)))
for i in range(1,self.__n):
desc[self.seq[i].name[0].capitalize()+'Dist'] = PLDists[i-1]
desc[self.seq[i].name[0].capitalize()+'FBDate'] = str(FBDates[i-1])
return desc
def _get_lt_problem(self,x,n_seg=[10,10], high_fidelity=True): """ This method returns the equivalent low-thrust problem of an incipit """ from PyKEP import epoch, lambert_problem, DAY2SEC, fb_prop, propagate_lagrangian from PyGMO import population from math import pi, acos,cos,sin,sqrt, exp from scipy.linalg import norm retval = [] #1 - we 'decode' the chromosome recording the various times of flight (days) in the list T for convenience T = x[3::4] n_legs = len(x)/4 seq = self.get_sequence() common_mu = seq[0].mu_central_body #2 - We compute the epochs and ephemerides of the planetary encounters t_P = list([None] * (n_legs)) r_P = list([None] * (n_legs)) v_P = list([None] * (n_legs)) DV = list([None] * (n_legs)) for i,planet in enumerate(seq): t_P[i] = epoch(x[0]+sum(T[:i+1])) r_P[i],v_P[i] = seq[i].eph(t_P[i]) #3 - We start with the first leg: a lambert arc theta = 2*pi*x[1] phi = acos(2*x[2]-1)-pi/2 r = [cos(phi)*sin(theta), cos(phi)*cos(theta), sin(phi)] #phi close to zero is in the moon orbit plane injection r = [JR*1000*d for d in r] l = lambert_problem(r,r_P[0],T[0]*DAY2SEC,common_mu, False, False) #Lambert arc to reach seq[1] v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] #We start appending in the lt chromosome (see mga_incipit_lt) retval.append(theta) retval.append(phi) #First DSM occuring at the very beginning (will be cancelled by the optimizer) DV[0] = abs(norm(v_beg_l) - 3400) #Start of the first lt leg encoding retval.append(T[0]) retval.append(exp(-DV[0]/9.80665/2000)*2000) #Tsiolkowsky retval.extend(v_beg_l) retval.extend([a-b for a,b in zip(v_end_l,v_P[0])]) #4 - And we proceed with each successive leg for i in xrange(1,n_legs): #Fly-by v_out = fb_prop(v_end_l,v_P[i-1],x[1+4*i]*seq[i-1].radius,x[4*i],seq[i-1].mu_self) #s/c propagation before the DSM r,v = propagate_lagrangian(r_P[i-1],v_out,x[4*i+2]*T[i]*DAY2SEC,common_mu) #Lambert arc to reach Earth during (1-nu2)*T2 (second segment) dt = (1-x[4*i+2])*T[i]*DAY2SEC l = lambert_problem(r,r_P[i],dt,common_mu, False, False) v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] #DSM occuring at time nu2*T2 DV[i] = norm([a-b for a,b in zip(v_beg_l,v)]) #lt encoding of all legs retval.append(T[i]) retval.append(exp(-sum(DV[:i+1])/9.80665/2000)*2000) #Tsiolkowsky retval.extend([a-b for a,b in zip(v_out,v_P[i-1])]) if i != n_legs-1: retval.extend([a-b for a,b in zip(v_end_l,v_P[i])]) retval = retval + [0]*sum(n_seg)*3 prob = mga_incipit_lt(high_fidelity=high_fidelity,seq=seq, n_seg = n_seg,tf = epoch(x[0]+sum(T)), vf = [a-b for a,b in zip(v_end_l,v_P[i])]) # solves the problem of chemical trajectories wanting higher launch dv ub = list(prob.ub) lb = list(prob.lb) ub[4:7] = [5000,5000,5000] lb[4:7] = [-5000,-5000,-5000] prob.set_bounds(lb, ub) pop = population(prob) pop.push_back(retval) return (prob,pop)
def _objfun_impl(self,x):
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T
T = list([0]*(self.__n))
#a[-i] = x[-1-(i-1)*4]
for i in xrange(self.__n-1):
j = i+1;
T[-j] = (x[5] - sum(T[-(j-1):])) * x[-1-(j-1)*4]
T[0] = x[5] - sum(T)
#2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n+1))
r_P = list([None] * (self.__n+1))
v_P = list([None] * (self.__n+1))
DV = list([None] * (self.__n+1))
for i,planet in enumerate(self.seq):
t_P[i] = epoch(x[0] + sum(T[0:i]))
r_P[i],v_P[i] = self.seq[i].eph(t_P[i])
#3 - We start with the first leg
theta = 2*pi*x[1]
phi = acos(2*x[2]-1)-pi/2
Vinfx = x[3]*cos(phi)*cos(theta)
Vinfy = x[3]*cos(phi)*sin(theta)
Vinfz = x[3]*sin(phi)
v0 = [a+b for a,b in zip(v_P[0], [Vinfx,Vinfy,Vinfz])]
r,v = propagate_lagrangian(r_P[0], v0, x[4]*T[0]*DAY2SEC, MU_SUN)
#Lambert arc to reach seq[1]
dt = (1-x[4])*T[0]*DAY2SEC
l = lambert_problem(r,r_P[1],dt,MU_SUN)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
#First DSM occuring at time nu1*T1
DV[0] = norm([a-b for a,b in zip(v_beg_l, v)])
#4 - And we proceed with each successive leg
for i in range(1,self.__n):
#Fly-by
v_out = fb_prop(v_end_l, v_P[i] ,x[7+(i-1)*4]*self.seq[i].radius, x[6+(i-1)*4], self.seq[i].mu_self)
#s/c propagation before the DSM
r,v = propagate_lagrangian(r_P[i], v_out, x[8+(i-1)*4]*T[i]*DAY2SEC, MU_SUN)
#Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1-x[8+(i-1)*4])*T[i]*DAY2SEC
l = lambert_problem(r, r_P[i+1], dt, MU_SUN)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
#DSM occuring at time nu2*T2
DV[i] = norm([a-b for a,b in zip(v_beg_l, v)])
#Last Delta-v
DV[-1] = norm([a-b for a,b in zip(v_end_l,v_P[-1])])
#moje
Eh56500 = 61933310.95
#Eh100000 = 61517435.56
entry_Vel = (DV[-1]**2 + 2*Eh56500)**0.5
entry_Vel2 = entry_Vel
#axtl = 23.43929*DEG2RAD
#DEC = abs(asin( sin(axtl)*cos(phi)*sin(theta) + cos(axtl)*sin(phi) ))*RAD2DEG # deklinacja asymptoty ucieczkowej
sum_dv = sum(DV[:-1])
eff_C3 = (x[3])**2
if entry_Vel < self.entry_vel_barrier:
entry_Vel2 = 0.0
del DV[-1]
#~ if eff_C3 < self.C3_barrier:
#~ #eff_C3 = 0
#~ pass
if sum_dv < self.dsm_dv_barrier:
sum_dv = 0+entry_Vel2
else:
sum_dv = sum(DV)
if self.f_dimension == 1:
return (sum_dv,)
else:
return (sum_dv, eff_C3, entry_Vel2) #,
def ic_from_mga_1dsm(self, x):
"""
x_lt = prob.ic_from_mga_1dsm(x_mga)
- x_mga: compatible trajectory as encoded by an mga_1dsm problem
Returns an initial guess for the low-thrust trajectory, converting the mga_1dsm solution x_dsm. The user
is responsible that x_mga makes sense (i.e. it is a viable mga_1dsm representation). The conversion is done by importing in the
low-thrust encoding a) the launch date b) all the legs durations, c) the in and out relative velocities at each planet.
All throttles are put to zero.
Example::
x_lt= prob.ic_from_mga_1dsm(x_mga)
"""
from math import pi, cos, sin, acos
from scipy.linalg import norm
from PyKEP import propagate_lagrangian, lambert_problem, DAY2SEC, fb_prop
retval = list([0.0] * self.dimension)
# 1 - we 'decode' the chromosome recording the various times of flight (days) in the list T
T = list([0] * (self.__n_legs))
for i in range(len(T)):
T[i] = log(x[2 + 4 * i])
total = sum(T)
T = [x[1] * time / total for time in T]
retval[0] = x[0]
for i in range(self.__n_legs):
retval[1 + 8 * i] = T[i]
retval[2 + 8 * i] = self.__sc.mass
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n_legs + 1))
r_P = list([None] * (self.__n_legs + 1))
v_P = list([None] * (self.__n_legs + 1))
DV = list([None] * (self.__n_legs + 1))
for i, planet in enumerate(self.seq):
t_P[i] = epoch(x[0] + sum(T[0:i]))
r_P[i], v_P[i] = self.seq[i].eph(t_P[i])
# 3 - We start with the first leg
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
Vinfx = x[3] * cos(phi) * cos(theta)
Vinfy = x[3] * cos(phi) * sin(theta)
Vinfz = x[3] * sin(phi)
retval[3:6] = [Vinfx, Vinfy, Vinfz]
v0 = [a + b for a, b in zip(v_P[0], [Vinfx, Vinfy, Vinfz])]
r, v = propagate_lagrangian(r_P[0], v0, x[4] * T[0] * DAY2SEC, MU_SUN)
# Lambert arc to reach seq[1]
dt = (1 - x[4]) * T[0] * DAY2SEC
l = lambert_problem(r, r_P[1], dt, MU_SUN)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
retval[6:9] = [a - b for a, b in zip(v_end_l, v_P[1])]
# 4 - And we proceed with each successive leg
for i in range(1, self.__n_legs):
# Fly-by
v_out = fb_prop(v_end_l, v_P[i], x[7 + (i - 1) * 4] * self.seq[i].radius, x[6 + (i - 1) * 4], self.seq[i].mu_self)
retval[3 + i * 8:6 + i * 8] = [a - b for a, b in zip(v_out, v_P[i])]
# s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out, x[8 + (i - 1) * 4] * T[i] * DAY2SEC, MU_SUN)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[8 + (i - 1) * 4]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt, MU_SUN)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# DSM occuring at time nu2*T2
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
retval[6 + i * 8:9 + i * 8] = [a - b for a, b in zip(v_end_l, v_P[i + 1])]
return retval
def _get_score_data_incipit(self,x):
from PyKEP import epoch, lambert_problem, DAY2SEC, fb_prop, propagate_lagrangian
from math import pi, acos,cos,sin,sqrt
from scipy.linalg import norm
"""
This method returns the data needed to compute the score of a trajectory.
"""
#1 - we 'decode' the chromosome recording the various times of flight (days) in the list T for convenience
T = x[3::4]
nlegs = len(x)/4
seq = self.get_sequence()
common_mu = seq[0].mu_central_body
#2 - We compute the epochs and ephemerides of the planetary encounters
ep_list = list([None] * nlegs)
t_P = list([None] * nlegs)
r_P = list([None] * nlegs)
v_P = list([None] * nlegs)
DV = list([None] * nlegs)
for i,planet in enumerate(seq):
ep_list[i] = x[0]+sum(T[:i+1])
t_P[i] = epoch(x[0]+sum(T[:i+1]))
r_P[i],v_P[i] = seq[i].eph(t_P[i])
#3 - We start with the first leg: a lambert arc
theta = 2*pi*x[1]
phi = acos(2*x[2]-1)-pi/2
r = [cos(phi)*sin(theta), cos(phi)*cos(theta), sin(phi)] #phi close to zero is in the moon orbit plane injection
r = [JR*1000*d for d in r]
l = lambert_problem(r,r_P[0],T[0]*DAY2SEC,common_mu, False, False)
#Lambert arc to reach seq[1]
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
#init lists for fly-by parameters
vinf_list = []
rp_list = []
beta_list = []
#First DSM occuring at the very beginning (will be cancelled by the optimizer)
DV[0] = abs(norm(v_beg_l) - 3400)
#4 - And we proceed with each successive leg
for i in xrange(1,nlegs):
#Fly-by
v_out = fb_prop(v_end_l,v_P[i-1],x[1+4*i]*seq[i-1].radius,x[4*i],seq[i-1].mu_self)
vinf_list.append( [a-b for a,b in zip(v_end_l,v_P[i-1])] )
rp_list.append(x[1+4*i]*seq[i-1].radius)
beta_list.append(x[4*i])
#s/c propagation before the DSM
r,v = propagate_lagrangian(r_P[i-1],v_out,x[4*i+2]*T[i]*DAY2SEC,common_mu)
#Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1-x[4*i+2])*T[i]*DAY2SEC
l = lambert_problem(r,r_P[i],dt,common_mu, False, False)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
vinf_list.append([a-b for a,b in zip(v_end_l,v_P[-1])])
rp_list.append(None)
beta_list.append(None)
return zip(ep_list, seq, vinf_list, rp_list, beta_list)
def _part_plot(x, units, axis, seq, start_mjd2000, vinf_in):
"""
Plots the trajectory represented by a decision vector x = [beta,rp,eta,T] * N
associated to a sequence seq, a start_mjd2000 and an incoming vinf_in
"""
from PyKEP.orbit_plots import plot_planet, plot_lambert, plot_kepler
from PyKEP import epoch, propagate_lagrangian, lambert_problem, fb_prop, AU, MU_SUN, DAY2SEC
from math import pi, acos, cos, sin
from scipy.linalg import norm
legs = len(x) / 4
common_mu = seq[0].mu_central_body
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T
T = x[3::4]
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (legs + 1))
r_P = list([None] * (legs + 1))
v_P = list([None] * (legs + 1))
for i, planet in enumerate(seq):
t_P[i] = epoch(start_mjd2000 + sum(T[:i]))
r_P[i], v_P[i] = planet.eph(t_P[i])
plot_planet(planet,
t0=t_P[i],
color=(0.8, 0.6, 0.8),
legend=True,
units=units,
ax=axis)
v_end_l = [a + b for a, b in zip(v_P[0], vinf_in)]
# 4 - And we iterate on the legs
for i in range(0, legs):
# Fly-by
v_out = fb_prop(v_end_l, v_P[i], x[1 + 4 * i] * seq[i].radius,
x[4 * i], seq[i].mu_self)
# s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out,
x[4 * i + 2] * T[i] * DAY2SEC, common_mu)
plot_kepler(r_P[i],
v_out,
x[4 * i + 2] * T[i] * DAY2SEC,
common_mu,
N=500,
color='b',
legend=False,
units=units,
ax=axis)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[4 * i + 2]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt, common_mu, False, False)
plot_lambert(l,
sol=0,
color='r',
legend=False,
units=units,
N=500,
ax=axis)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]