def plot(self, x, ax=None):
"""
ax = prob.plot(x, ax=None)
- x: encoded trajectory
- ax: matplotlib axis where to plot. If None figure and axis will be created
- [out] ax: matplotlib axis where to plot
Plots the trajectory represented by a decision vector x on the 3d axis ax
Example::
ax = prob.plot(x)
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from PyKEP import epoch, AU
from PyKEP.sims_flanagan import sc_state
from PyKEP.orbit_plots import plot_planet, plot_sf_leg
# Creating the axis if necessary
if ax is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axis = fig.gca(projection='3d')
else:
axis = ax
# Plotting the Sun ........
axis.scatter([0], [0], [0], color='y')
# Plotting the legs .......
# 1 - We decode the chromosome extracting the time of flights
T = list([0] * (self.__n_legs))
for i in range(self.__n_legs):
T[i] = x[1 + i * 8]
# 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))
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 iterate through legs to compute mismatches and throttles constraints
ceq = list()
cineq = list()
m0 = self.__sc.mass
for i in range(self.__n_legs):
# First Leg
v = [a + b for a, b in zip(v_P[i], x[(3 + i * 8):(6 + i * 8)])]
x0 = sc_state(r_P[i], v, m0)
v = [
a + b for a, b in zip(v_P[i + 1], x[(6 + i * 8):(11 + i * 8)])
]
xe = sc_state(r_P[i + 1], v, x[2 + i * 8])
throttles = x[(1 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i])):(
1 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i]) +
3 * self.__n_seg[i])]
self.__leg.set(t_P[i], x0, throttles, t_P[i + 1], xe)
# update mass!
m0 = x[2 + 8 * i]
plot_sf_leg(self.__leg, units=AU, N=10, ax=axis)
# Plotting planets
for i, planet in enumerate(self.seq):
plot_planet(planet,
t_P[i],
units=AU,
legend=True,
color=(0.7, 0.7, 1),
ax=axis)
plt.show()
return axis
def _compute_constraints_impl(self, x):
# 1 - We decode the chromosome extracting the time of flights
T = list([0] * (self.__n_legs))
for i in range(self.__n_legs):
T[i] = x[1 + i * 8]
# 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))
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 iterate through legs to compute mismatches and throttles constraints
ceq = list()
cineq = list()
m0 = self.__sc.mass
for i in range(self.__n_legs):
# First Leg
v = [a + b for a, b in zip(v_P[i], x[(3 + i * 8):(6 + i * 8)])]
x0 = sc_state(r_P[i], v, m0)
v = [a + b for a, b in zip(v_P[i + 1], x[(6 + i * 8):(9 + i * 8)])]
xe = sc_state(r_P[i + 1], v, x[2 + i * 8])
throttles = x[(1 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i])):(
1 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i]) +
3 * self.__n_seg[i])]
self.__leg.set(t_P[i], x0, throttles, t_P[i + 1], xe)
# update mass!
m0 = x[2 + 8 * i]
ceq.extend(self.__leg.mismatch_constraints())
cineq.extend(self.__leg.throttles_constraints())
# Adding the boundary constraints
# departure
v_dep_con = (x[3]**2 + x[4]**2 + x[5]**2 -
self.__vinf_dep**2) / (EARTH_VELOCITY**2)
# arrival
v_arr_con = (x[6 +
(self.__n_legs - 1) * 8]**2 + x[7 +
(self.__n_legs - 1) * 8]
**2 + x[8 + (self.__n_legs - 1) * 8]**2 -
self.__vinf_arr**2) / (EARTH_VELOCITY**2)
cineq.append(v_dep_con * 100)
cineq.append(v_arr_con * 100)
# We add the fly-by constraints
for i in range(self.__n_legs - 1):
DV_eq, alpha_ineq = fb_con(x[6 + i * 8:9 + i * 8],
x[11 + i * 8:14 + i * 8],
self.seq[i + 1])
ceq.append(DV_eq / (EARTH_VELOCITY**2))
cineq.append(alpha_ineq)
# Making the mismatches non dimensional
for i in range(self.__n_legs):
ceq[0 + i * 7] /= AU
ceq[1 + i * 7] /= AU
ceq[2 + i * 7] /= AU
ceq[3 + i * 7] /= EARTH_VELOCITY
ceq[4 + i * 7] /= EARTH_VELOCITY
ceq[5 + i * 7] /= EARTH_VELOCITY
ceq[6 + i * 7] /= self.__sc.mass
# We assemble the constraint vector
retval = list()
retval.extend(ceq)
retval.extend(cineq)
return retval
def plot(self, x, ax=None):
"""
ax = prob.plot(x, ax=None)
- x: encoded trajectory
- ax: matplotlib axis where to plot. If None figure and axis will be created
- [out] ax: matplotlib axis where to plot
Plots the trajectory represented by a decision vector x on the 3d axis ax
Example::
ax = prob.plot(x)
"""
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from PyKEP import epoch, AU
from PyKEP.sims_flanagan import sc_state
from PyKEP.orbit_plots import plot_planet, plot_sf_leg
# Creating the axis if necessary
if ax is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axis = fig.gca(projection='3d')
else:
axis = ax
# Plotting the Sun ........
axis.scatter([0], [0], [0], color='y')
# Plotting the legs .......
# 1 - We decode the chromosome extracting the time of flights
T = list([0] * (self.__n_legs))
for i in range(self.__n_legs):
T[i] = x[1 + i * 8]
# 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))
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 iterate through legs to compute mismatches and throttles constraints
ceq = list()
cineq = list()
m0 = self.__sc.mass
for i in range(self.__n_legs):
# First Leg
v = [a + b for a, b in zip(v_P[i], x[(3 + i * 8):(6 + i * 8)])]
x0 = sc_state(r_P[i], v, m0)
v = [a + b for a, b in zip(v_P[i + 1], x[(6 + i * 8):(11 + i * 8)])]
xe = sc_state(r_P[i + 1], v, x[2 + i * 8])
throttles = x[(1 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i])):(1 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i]) + 3 * self.__n_seg[i])]
self.__leg.set(t_P[i], x0, throttles, t_P[i + 1], xe)
# update mass!
m0 = x[2 + 8 * i]
plot_sf_leg(self.__leg, units=AU, N=10, ax=axis)
# Plotting planets
for i, planet in enumerate(self.seq):
plot_planet(planet, t_P[i], units=AU, legend=True, color=(0.7, 0.7, 1), ax = axis)
plt.show()
return axis
def _compute_constraints_impl(self, x):
# 1 - We decode the chromosome extracting the time of flights
T = list([0] * (self.__n_legs))
for i in range(self.__n_legs):
T[i] = x[1 + i * 8]
# 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))
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 iterate through legs to compute mismatches and throttles constraints
ceq = list()
cineq = list()
m0 = self.__sc.mass
for i in range(self.__n_legs):
# First Leg
v = [a + b for a, b in zip(v_P[i], x[(3 + i * 8):(6 + i * 8)])]
x0 = sc_state(r_P[i], v, m0)
v = [a + b for a, b in zip(v_P[i + 1], x[(6 + i * 8):(9 + i * 8)])]
xe = sc_state(r_P[i + 1], v, x[2 + i * 8])
throttles = x[(1 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i])):(1 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i]) + 3 * self.__n_seg[i])]
self.__leg.set(t_P[i], x0, throttles, t_P[i + 1], xe)
# update mass!
m0 = x[2 + 8 * i]
ceq.extend(self.__leg.mismatch_constraints())
cineq.extend(self.__leg.throttles_constraints())
# Adding the boundary constraints
# departure
v_dep_con = (x[3] ** 2 + x[4] ** 2 + x[5] ** 2 - self.__vinf_dep ** 2) / (EARTH_VELOCITY ** 2)
# arrival
v_arr_con = (x[6 + (self.__n_legs - 1) * 8] ** 2 + x[7 + (self.__n_legs - 1) * 8] ** 2 + x[8 + (self.__n_legs - 1) * 8] ** 2 - self.__vinf_arr ** 2) / (EARTH_VELOCITY ** 2)
cineq.append(v_dep_con * 100)
cineq.append(v_arr_con * 100)
# We add the fly-by constraints
for i in range(self.__n_legs - 1):
DV_eq, alpha_ineq = fb_con(x[6 + i * 8:9 + i * 8], x[11 + i * 8:14 + i * 8], self.seq[i + 1])
ceq.append(DV_eq / (EARTH_VELOCITY ** 2))
cineq.append(alpha_ineq)
# Making the mismatches non dimensional
for i in range(self.__n_legs):
ceq[0 + i * 7] /= AU
ceq[1 + i * 7] /= AU
ceq[2 + i * 7] /= AU
ceq[3 + i * 7] /= EARTH_VELOCITY
ceq[4 + i * 7] /= EARTH_VELOCITY
ceq[5 + i * 7] /= EARTH_VELOCITY
ceq[6 + i * 7] /= self.__sc.mass
# We assemble the constraint vector
retval = list()
retval.extend(ceq)
retval.extend(cineq)
return retval
def point(self, x, filename):
"""
prob.point(decision_vector, filename)
This method will save all the relevant simulation data for the trajectory described by decision_vector
in json form in the file 'filename.json'.
The data generated can then be used by the postprocessing toolbox (from this fork of PyKEP : PyKEP/postProcessingToolbox/), without having to
re-create a prob abject. Indeed, if the problem definition is changed, the decision_vector will not mean anything:
it only encode a trajectory for a very specific problem. When tens or hundreds of trajectories are generated, and
then compared, keeping only the decision vector is not a good idea, if the parameters of the problems have been tweaked
to realize those tens or hundreds of different simulations.
The data stored in the file can be imported using import.json from the json package. The description of the stored data
has still to be described in detail
// TODO : description of the content of the .json file
Those files are to be given as parameters for the postprocessing toolbox.
"""
from PyKEP import epoch, AU
from PyKEP.sims_flanagan import sc_state
from PyKEP.orbit_plots import plot_planet, plot_sf_leg
from PyKEP.orbit_plots import point_sf_leg, point_kepler, point_taylor, point_planet
from scipy.linalg import norm
from math import sqrt
import csv
import pprint
from PyKEP.trajopt.motor import getObjectMotor
from PyKEP.trajopt.spacecraft import getObjectSpacecraft
XYZ = []
xx = []
yy = []
zz = []
tt = []
mm = []
x_bounds = []
y_bounds = []
z_bounds = []
seq1 = self.seq1
seq2 = self.seq2
data = {}
# Plotting the legs .......
# 1 - We decode the chromosome extracting the time of flights
T = list([0] * (self.__n_legs))
for i in range(self.__n_legs):
T[i] = x[3 + i * 8]
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n_legs + 2))
r_P = list([None] * (self.__n_legs + 2))
v_P = list([None] * (self.__n_legs + 2))
for i, planet in enumerate(self.seq1):
t_P[i] = epoch(x[0] + sum(T[0:i]))
r_P[i], v_P[i] = self.seq1[i].eph(t_P[i])
for i, planet in enumerate(self.seq2):
t_P[i + len(seq1)] = epoch(x[0] + sum(T[0:i + len(seq1) - 1]) +
x[1])
r_P[i + len(seq1)], v_P[i + len(seq1)] = self.seq2[i].eph(
t_P[i + len(seq1)])
# 3 - We iterate through legs to compute mismatches and throttles constraints
ceq = list()
cineq = list()
m0 = x[2]
data['legs'] = []
massesAlongTheWay = [m0]
self.__leg.set_spacecraft(self.__spacecrafts[0])
sc = self.__spacecrafts[0]
for i in range(len(self.seq1) - 1):
# First Leg
v = [a + b for a, b in zip(v_P[i], x[(5 + i * 8):(8 + i * 8)])]
x0 = sc_state(r_P[i], v, m0)
v = [
a + b for a, b in zip(v_P[i + 1], x[(8 + i * 8):(11 + i * 8)])
]
xe = sc_state(r_P[i + 1], v, x[4 + i * 8])
throttles = x[(3 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i])):(
3 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i]) +
3 * self.__n_seg[i])]
self.__leg.set(t_P[i], x0, throttles, t_P[i + 1], xe)
# update mass!
minit = m0
m0 = x[4 + 8 * i]
massesAlongTheWay = massesAlongTheWay + [m0]
xi, yi, zi, mi, ti, Txi, Tyi, Tzi, Tmaxi, x_boundsi, y_boundsi, z_boundsi = point_sf_leg(
self.__leg, units=AU, N=10)
xx = xx + xi
yy = yy + yi
zz = zz + zi
ti = [e + t_P[i].jd for e in ti]
#for k in range(len(Txi)):
# print norm([Tyi[k],Txi[k],Tzi[k]])
data['legs'] = data['legs'] + [{
'x': [e for e in xi],
'y': [e for e in yi],
'z': [e for e in zi],
'm': [e for e in mi],
't': [e for e in ti],
'P_tot': [sc.get_totalPower(norm(e)) for e in zip(xi, yi, zi)],
'P_engine': [
sc.DutyCycle *
sc.get_powerThrust(norm(e[0:3]) * e[3] / sc.DutyCycle)
for e in zip(Txi, Tyi, Tzi, Tmaxi)
],
'Tx': [e for e in Txi],
'Ty': [e for e in Tyi],
'Tz': [e for e in Tzi],
'Tmax': [e for e in Tmaxi],
'mi':
minit,
'mf':
m0,
'planet1': {
'name': seq1[i].name,
'date': t_P[i].jd
},
'planet2': {
'name': seq1[i + 1].name,
'date': t_P[i + 1].jd
}
}]
XYZ = XYZ + [xi] + [yi] + [zi]
x_bounds = x_bounds + x_boundsi
y_bounds = y_bounds + y_boundsi
z_bounds = z_bounds + z_boundsi
#outbound
m0 = m0 - self.__dm # mass lost around ceres
massesAlongTheWay = massesAlongTheWay + [m0]
self.__leg.set_spacecraft(self.__spacecrafts[1])
sc = self.__spacecrafts[1]
for i in range(
len(self.seq1) - 1,
len(self.seq1) + len(self.seq2) - 2):
# First Leg
v = [a + b for a, b in zip(v_P[i + 1], x[(5 + i * 8):(8 + i * 8)])]
x0 = sc_state(r_P[i + 1], v, m0)
v = [
a + b for a, b in zip(v_P[i + 2], x[(8 + i * 8):(11 + i * 8)])
]
xe = sc_state(r_P[i + 2], v, x[4 + i * 8])
throttles = x[(3 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i])):(
3 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i]) +
3 * self.__n_seg[i])]
self.__leg.set(t_P[i + 1], x0, throttles, t_P[i + 2], xe)
# update mass!
minit = m0
m0 = x[4 + 8 * i]
massesAlongTheWay = massesAlongTheWay + [m0]
xi, yi, zi, mi, ti, Txi, Tyi, Tzi, Tmaxi, x_boundsi, y_boundsi, z_boundsi = point_sf_leg(
self.__leg, units=AU, N=10)
xx = xx + xi
yy = yy + yi
zz = zz + zi
ti = [e + t_P[i + 1].jd for e in ti]
#for k in range(len(Txi)):
# print norm([Tyi[k],Txi[k],Tzi[k]])
data['legs'] = data['legs'] + [{
'x': [e for e in xi],
'y': [e for e in yi],
'z': [e for e in zi],
'm': [e for e in mi],
't': [e for e in ti],
'P_tot': [sc.get_totalPower(norm(e)) for e in zip(xi, yi, zi)],
'P_engine': [
sc.DutyCycle *
sc.get_powerThrust(norm(e[0:3]) * e[3] / sc.DutyCycle)
for e in zip(Txi, Tyi, Tzi, Tmaxi)
],
'Tx': [e for e in Txi],
'Ty': [e for e in Tyi],
'Tz': [e for e in Tzi],
'Tmax': [e for e in Tmaxi],
'mi':
minit,
'mf':
m0,
'planet1': {
'name': seq2[i - len(seq1) - 2].name,
'date': t_P[i + 1].jd
},
'planet2': {
'name': seq2[i + 1 - len(seq1) - 2].name,
'date': t_P[i + 2].jd
}
}]
XYZ = XYZ + [xi] + [yi] + [zi]
x_bounds = x_bounds + x_boundsi
y_bounds = y_bounds + y_boundsi
z_bounds = z_bounds + z_boundsi
XYZplanet = []
data['planetOrbits'] = []
data['planetPosition'] = []
listAlreadySaved = []
for i, planet in enumerate(self.seq1):
xp, yp, zp = point_planet(planet, t_P[i], units=AU)
#Save orbit if it has not been done already
if (seq1[i].name not in listAlreadySaved):
listAlreadySaved.append(seq1[i].name)
data['planetOrbits'].append({
'name': seq1[i].name,
'x': [e for e in xp],
'y': [e for e in yp],
'z': [e for e in zp]
})
data['planetPosition'].append({
'name': seq1[i].name,
'x': xp[0],
'y': yp[0],
'z': zp[0],
'dateS': pprint.pformat(t_P[i])[0:20],
'date': t_P[i].jd,
'scmass': massesAlongTheWay[i]
})
for i, planet in enumerate(self.seq2):
xp, yp, zp = point_planet(planet, t_P[i + len(seq1)], units=AU)
#Save orbit if it has not been done already
if (seq2[i].name not in listAlreadySaved):
listAlreadySaved.append(seq2[i].name)
data['planetOrbits'].append({
'name': seq2[i].name,
'x': [e for e in xp],
'y': [e for e in yp],
'z': [e for e in zp]
})
data['planetPosition'].append({
'name':
seq2[i].name,
'x':
xp[0],
'y':
yp[0],
'z':
zp[0],
'dateS':
pprint.pformat(t_P[i + len(seq1)])[0:20],
'date':
t_P[i + len(seq1)].jd,
'scmass':
massesAlongTheWay[i + 3]
})
#Calculate vinf velocities
v_dep_1 = sqrt(x[5]**2 + x[6]**2 + x[7]**2)
v_arr_1 = sqrt(x[8 + (len(seq1) - 2) * 8]**2 +
x[9 + (len(seq1) - 2) * 8]**2 +
x[10 + (len(seq1) - 2) * 8]**2)
v_dep_2 = sqrt(x[5 + (len(seq1) - 1) * 8]**2 +
x[6 + (len(seq1) - 1) * 8]**2 +
x[7 + (len(seq1) - 1) * 8]**2)
v_arr_2 = sqrt(x[8 + (len(seq1) - 1 + len(seq2) - 2) * 8]**2 +
x[9 + (len(seq1) - 1 + len(seq2) - 2)]**2 +
x[10 * (len(seq1) - 1 + len(seq2) - 2)]**2)
#Logging all trajectory parameters
data['traj'] = {}
data['traj']['high_fidelity'] = self.__leg.high_fidelity
data['traj']['solar_powered'] = self.__leg.solar_powered
data['traj']['outbound'] = [[seq1[i].name, t_P[i].jd]
for i in range(len(seq1))]
data['traj']['inbound'] = [[seq2[i].name, t_P[i + len(seq1)].jd]
for i in range(len(seq2))]
data['traj']['vinf'] = {
'v_dep1': v_dep_1,
'v_dep2': v_dep_2,
'v_arr1': v_arr_1,
'v_arr2': v_arr_2
}
data['traj']['spacecrafts'] = [
getObjectSpacecraft(self.__spacecrafts[0]),
getObjectSpacecraft(self.__spacecrafts[1])
]
data['traj']['duty_cycle'] = [
self.__spacecrafts[0].DutyCycle,
self.__spacecrafts[1].DutyCycle,
]
data['traj']['dm'] = self.__dm
data['traj']['mi'] = x[2]
data['traj']['mf'] = self.__mf
data['traj']['decision_vector'] = x
data['traj']['dt'] = x[1]
data['traj']['t_launch'] = t_P[0].jd
data['traj']['t_launchS'] = pprint.pformat(t_P[0])[0:20]
data['traj']['t_return'] = t_P[-1].jd
data['traj']['t_returnS'] = pprint.pformat(t_P[-1])[0:20]
data['traj']['duration'] = t_P[-1].jd - t_P[0].jd
import json
with open(filename, 'w') as outfile:
json.dump(data, outfile)
# File structure:
# Number of legs, length points, number of planets to plot, length points
# Legs trajectories
# Planets trajectories
# Planets names
#with open('test1.csv', 'w') as csvfile:
# writer = csv.writer(csvfile)
# #writer.writerow([self.__n_legs, len(XYZ[0]), len(list_planet),len(XYZplanet[0])])
# for i in range(len(XYZ)):
# writer.writerow(XYZ[i])
# for i in range(len(XYZplanet)):
# writer.writerow(XYZplanet[i])
# #writer.writerow(list_planet)
return xx, yy, zz, x_bounds, y_bounds, z_bounds, data
def _compute_constraints_impl(self, x):
seq1 = self.seq1
seq2 = self.seq2
# 1 - We decode the chromosome extracting the time of flights
T = list([0] * (self.__n_legs))
for i in range(self.__n_legs):
T[i] = x[3 + i * 8]
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n_legs + 2))
r_P = list([None] * (self.__n_legs + 2))
v_P = list([None] * (self.__n_legs + 2))
for i, planet in enumerate(self.seq1):
t_P[i] = epoch(x[0] + sum(T[0:i]))
r_P[i], v_P[i] = self.seq1[i].eph(t_P[i])
for i, planet in enumerate(self.seq2):
t_P[i + len(seq1)] = epoch(x[0] + sum(T[0:i + len(seq1) - 1]) +
x[1])
r_P[i + len(seq1)], v_P[i + len(seq1)] = self.seq2[i].eph(
t_P[i + len(seq1)])
# 3 - We iterate through legs to compute mismatches and throttles constraints
ceq = list()
cineq = list()
m0 = x[2]
#inbound
self.__leg.set_spacecraft(self.__spacecrafts[0])
for i in range(len(self.seq1) - 1):
# First Leg
v = [a + b for a, b in zip(v_P[i], x[(5 + i * 8):(8 + i * 8)])]
x0 = sc_state(r_P[i], v, m0)
v = [
a + b for a, b in zip(v_P[i + 1], x[(8 + i * 8):(11 + i * 8)])
]
xe = sc_state(r_P[i + 1], v, x[4 + i * 8])
throttles = x[(3 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i])):(
3 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i]) +
3 * self.__n_seg[i])]
self.__leg.set(t_P[i], x0, throttles, t_P[i + 1], xe)
# update mass!
m0 = x[4 + 8 * i]
ceq.extend(self.__leg.mismatch_constraints())
cineq.extend(self.__leg.throttles_constraints())
#outbound
self.__leg.set_spacecraft(self.__spacecrafts[1])
m0 = m0 - self.__dm # mass lost around ceres
for i in range(
len(self.seq1) - 1,
len(self.seq1) + len(self.seq2) - 2):
# First Leg
v = [a + b for a, b in zip(v_P[i + 1], x[(5 + i * 8):(8 + i * 8)])]
x0 = sc_state(r_P[i + 1], v, m0)
v = [
a + b for a, b in zip(v_P[i + 2], x[(8 + i * 8):(11 + i * 8)])
]
xe = sc_state(r_P[i + 2], v, x[4 + i * 8])
throttles = x[(3 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i])):(
3 + 8 * self.__n_legs + 3 * sum(self.__n_seg[:i]) +
3 * self.__n_seg[i])]
self.__leg.set(t_P[i + 1], x0, throttles, t_P[i + 2], xe)
# update mass!
m0 = x[4 + 8 * i]
ceq.extend(self.__leg.mismatch_constraints())
cineq.extend(self.__leg.throttles_constraints())
# Adding the boundary constraints
# departure1
v_dep_con1 = (x[5]**2 + x[6]**2 + x[7]**2 -
self.__vinf_dep1**2) / (EARTH_VELOCITY**2)
# arrival1
v_arr_con1 = (x[8 + (len(seq1) - 2) * 8]**2 +
x[9 +
(len(seq1) - 2) * 8]**2 + x[10 +
(len(seq1) - 2) * 8]**2 -
self.__vinf_arr1**2) / (EARTH_VELOCITY**2)
# departure2
v_dep_con2 = (x[5 + (len(seq1) - 1) * 8]**2 +
x[6 +
(len(seq1) - 1) * 8]**2 + x[7 +
(len(seq1) - 1) * 8]**2 -
self.__vinf_dep2**2) / (EARTH_VELOCITY**2)
# arrival2
v_arr_con2 = (x[8 + (len(seq1) - 1 + len(seq2) - 2) * 8]**2 +
x[9 + (len(seq1) - 1 + len(seq2) - 2)]**2 +
x[10 * (len(seq1) - 1 + len(seq2) - 2)]**2 -
self.__vinf_arr2**2) / (EARTH_VELOCITY**2)
cineq.append(v_dep_con1 * 100)
cineq.append(v_arr_con1 * 100)
cineq.append(v_dep_con2 * 100)
cineq.append(v_arr_con2 * 100)
# We add the fly-by constraints
for i in range(len(seq1) - 2):
DV_eq, alpha_ineq = fb_con(x[8 + i * 8:11 + i * 8],
x[13 + i * 8:16 + i * 8],
self.seq1[i + 1])
ceq.append(DV_eq / (EARTH_VELOCITY**2))
cineq.append(alpha_ineq)
for i in range(len(seq2) - 2):
DV_eq, alpha_ineq = fb_con(
x[8 + (i + len(seq1) - 1) * 8:11 + (i + len(seq1) - 1) * 8],
x[13 + (i + len(seq1) - 1) * 8:16 + (i + len(seq1) - 1) * 8],
self.seq2[i + 1])
ceq.append(DV_eq / (EARTH_VELOCITY**2))
cineq.append(alpha_ineq)
#Adding the mass constraint
mass_con = self.__mf - m0
ceq.append(mass_con / self.__mf)
# Making the mismatches non dimensional
for i in range(self.__n_legs):
ceq[0 + i * 7] /= AU
ceq[1 + i * 7] /= AU
ceq[2 + i * 7] /= AU
ceq[3 + i * 7] /= EARTH_VELOCITY
ceq[4 + i * 7] /= EARTH_VELOCITY
ceq[5 + i * 7] /= EARTH_VELOCITY
ceq[6 + i * 7] /= self.__mf
# We assemble the constraint vector
retval = list()
retval.extend(ceq)
retval.extend(cineq)
return retval
