def _objfun_impl(self, x):
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T and the cartesian components of vinf
T, Vinfx, Vinfy, Vinfz = self._decode_times_and_vinf(x)
# 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
v0 = [a + b for a, b in zip(v_P[0], [Vinfx, Vinfy, Vinfz])]
r, v = propagate_lagrangian(r_P[0], v0, x[5] * T[0] * DAY2SEC,
self.common_mu)
# Lambert arc to reach seq[1]
dt = (1 - x[5]) * 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[8 + (i - 1) * 4] * self.seq[i].radius,
x[7 + (i - 1) * 4], self.seq[i].mu_self)
# s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out,
x[9 + (i - 1) * 4] * T[i] * DAY2SEC,
self.common_mu)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[9 + (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 _objfun_impl(self, x):
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T and the cartesian components of vinf
T, Vinfx, Vinfy, Vinfz = self._decode_times_and_vinf(x)
# 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
v0 = [a + b for a, b in zip(v_P[0], [Vinfx, Vinfy, Vinfz])]
r, v = propagate_lagrangian(r_P[0], v0, x[5] * T[0] * DAY2SEC, self.common_mu)
# Lambert arc to reach seq[1]
dt = (1 - x[5]) * 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[8 + (i - 1) * 4] * self.seq[i].radius, x[7 + (i - 1) * 4], self.seq[i].mu_self)
# s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out, x[9 + (i - 1) * 4] * T[i] * DAY2SEC, self.common_mu)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[9 + (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 plot_orbits(self, pop, ax=None):
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
A1, A2 = self._ast1, self._ast2
if ax is None:
fig = plt.figure()
axis = fig.add_subplot(111, projection='3d')
else:
axis = ax
plot_planet(A1, ax=axis, s=10, t0=epoch(self.lb[0]))
plot_planet(A2, ax=axis, s=10, t0=epoch(self.ub[0]))
for ind in pop:
if ind.cur_f[0] == self._UNFEASIBLE:
continue
dep, arr = ind.cur_x
rdep, vdep = A1.eph(epoch(dep))
rarr, varr = A2.eph(epoch(arr))
l = lambert_problem(rdep, rarr, (arr - dep) * DAY2SEC, A1.mu_central_body, False, 1)
axis = plot_lambert(l, ax=axis, alpha=0.8, color='k')
if ax is None:
plt.show()
return axis
def plot_orbits(self, pop, ax=None):
import matplotlib.pylab as plt
from mpl_toolkits.mplot3d import Axes3D
A1, A2 = self._ast1, self._ast2
if ax is None:
fig = plt.figure()
axis = fig.add_subplot(111, projection='3d')
else:
axis = ax
plot_planet(A1, ax=axis, s=10, t0=epoch(self.lb[0]))
plot_planet(A2, ax=axis, s=10, t0=epoch(self.ub[0]))
for ind in pop:
if ind.cur_f[0] == self._UNFEASIBLE:
continue
dep, arr = ind.cur_x
rdep, vdep = A1.eph(epoch(dep))
rarr, varr = A2.eph(epoch(arr))
l = lambert_problem(rdep, rarr, (arr - dep) * DAY2SEC,
A1.mu_central_body, False, 1)
axis = plot_lambert(l, ax=axis, alpha=0.8, color='k')
if ax is None:
plt.show()
return axis
def _objfun_impl(self, x):
from math import sqrt
# 1 - We check that the transfer time is positive
if x[0] >= x[1]:
if self.f_dimension == 1:
return (self._UNFEASIBLE, )
else:
return (self._UNFEASIBLE, self._UNFEASIBLE)
# 2 - We compute the asteroid positions
r1, v1 = self._ast1.eph(x[0])
r2, v2 = self._ast2.eph(x[1])
# 3 - We compute Lambert arc
l = lambert_problem(r1, r2, (x[1] - x[0]) * DAY2SEC,
self._ast1.mu_central_body, False, 0)
# 4 - We compute the two impulses
v1l = l.get_v1()[0]
v2l = l.get_v2()[0]
DV1 = [a - b for a, b in zip(v1, v1l)]
DV2 = [a - b for a, b in zip(v2, v2l)]
a1, a2, tau, dv = damon(DV1, DV2, (x[1] - x[0]) * DAY2SEC)
Isp = self._Isp
g0 = 9.80665
Tmax = self._Tmax
ms = self._ms
MIMA = 2 * Tmax / norm(a1) / (1. +
exp(-norm(a1) *
(x[1] - x[0]) * DAY2SEC / Isp / g0))
DV1 = sum([l * l for l in DV1])
DV2 = sum([l * l for l in DV2])
totDV = sqrt(DV1) + sqrt(DV2)
totDT = x[1] - x[0]
if ms > MIMA:
if self.f_dimension == 1:
return (self._UNFEASIBLE, )
else:
return (self._UNFEASIBLE, self._UNFEASIBLE)
if self.f_dimension == 1:
return (totDV, )
else:
return (totDV, x[1])
def _objfun_impl(self, x):
# 1 - we 'decode' the chromosome recording the various deep space
# manouvres timing (days) in the list T
T = list([0] * (self.N_max - 1))
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]
# 2 - We compute the starting and ending position
r_start, v_start = self.start.eph(epoch(x[0]))
if self.phase_free:
r_target, v_target = self.target.eph(epoch(x[-1]))
else:
r_target, v_target = self.target.eph(epoch(x[0] + x[1]))
# 3 - We loop across inner impulses
rsc = r_start
vsc = v_start
for i, time in enumerate(T[:-1]):
theta = 2 * pi * x[3 + 4 * i]
phi = acos(2 * x[4 + 4 * i] - 1) - pi / 2
Vinfx = x[5 + 4 * i] * cos(phi) * cos(theta)
Vinfy = x[5 + 4 * i] * cos(phi) * sin(theta)
Vinfz = x[5 + 4 * i] * sin(phi)
# We apply the (i+1)-th impulse
vsc = [a + b for a, b in zip(vsc, [Vinfx, Vinfy, Vinfz])]
rsc, vsc = propagate_lagrangian(
rsc, vsc, T[i] * DAY2SEC, self.__common_mu)
cw = (ic2par(rsc, vsc, self.start.mu_central_body)[2] > pi / 2)
# We now compute the remaining two final impulses
# Lambert arc to reach seq[1]
dt = T[-1] * DAY2SEC
l = lambert_problem(rsc, r_target, dt, self.__common_mu, cw, False)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
DV1 = norm([a - b for a, b in zip(v_beg_l, vsc)])
DV2 = norm([a - b for a, b in zip(v_end_l, v_target)])
DV_others = sum(x[5::4])
if self.f_dimension == 1:
return (DV1 + DV2 + DV_others,)
else:
return (DV1 + DV2 + DV_others, x[1])
def _objfun_impl(self, x):
# 1 - we 'decode' the chromosome recording the various deep space
# manouvres timing (days) in the list T
T = list([0] * (self.N_max - 1))
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]
# 2 - We compute the starting and ending position
r_start, v_start = self.start.eph(epoch(x[0]))
if self.phase_free:
r_target, v_target = self.target.eph(epoch(x[-1]))
else:
r_target, v_target = self.target.eph(epoch(x[0] + x[1]))
# 3 - We loop across inner impulses
rsc = r_start
vsc = v_start
for i, time in enumerate(T[:-1]):
theta = 2 * pi * x[3 + 4 * i]
phi = acos(2 * x[4 + 4 * i] - 1) - pi / 2
Vinfx = x[5 + 4 * i] * cos(phi) * cos(theta)
Vinfy = x[5 + 4 * i] * cos(phi) * sin(theta)
Vinfz = x[5 + 4 * i] * sin(phi)
# We apply the (i+1)-th impulse
vsc = [a + b for a, b in zip(vsc, [Vinfx, Vinfy, Vinfz])]
rsc, vsc = propagate_lagrangian(rsc, vsc, T[i] * DAY2SEC,
self.__common_mu)
cw = (ic2par(rsc, vsc, self.start.mu_central_body)[2] > pi / 2)
# We now compute the remaining two final impulses
# Lambert arc to reach seq[1]
dt = T[-1] * DAY2SEC
l = lambert_problem(rsc, r_target, dt, self.__common_mu, cw, False)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
DV1 = norm([a - b for a, b in zip(v_beg_l, vsc)])
DV2 = norm([a - b for a, b in zip(v_end_l, v_target)])
DV_others = sum(x[5::4])
if self.f_dimension == 1:
return (DV1 + DV2 + DV_others, )
else:
return (DV1 + DV2 + DV_others, x[1])
def _objfun_impl(self, x):
from math import sqrt
# 1 - We check that the transfer time is positive
if x[0] >= x[1]:
if self.f_dimension == 1:
return (self._UNFEASIBLE, )
else:
return (self._UNFEASIBLE, self._UNFEASIBLE)
# 2 - We compute the asteroid positions
r1, v1 = self._ast1.eph(x[0])
r2, v2 = self._ast2.eph(x[1])
# 3 - We compute Lambert arc
l = lambert_problem(r1, r2, (x[1] - x[0]) * DAY2SEC, self._ast1.mu_central_body, False, 0)
# 4 - We compute the two impulses
v1l = l.get_v1()[0]
v2l = l.get_v2()[0]
DV1 = [a - b for a, b in zip(v1, v1l)]
DV2 = [a - b for a, b in zip(v2, v2l)]
a1, a2, tau, dv = damon(DV1, DV2, (x[1] - x[0]) * DAY2SEC)
Isp = self._Isp
g0 = 9.80665
Tmax = self._Tmax
ms = self._ms
MIMA = 2 * Tmax / norm(a1) / (1. + exp(-norm(a1) * (x[1] - x[0]) * DAY2SEC / Isp / g0) )
DV1 = sum([l * l for l in DV1])
DV2 = sum([l * l for l in DV2])
totDV = sqrt(DV1) + sqrt(DV2)
totDT = x[1] - x[0]
if ms > MIMA:
if self.f_dimension == 1:
return (self._UNFEASIBLE, )
else:
return (self._UNFEASIBLE, self._UNFEASIBLE)
if self.f_dimension == 1:
return (totDV, )
else:
return (totDV, x[1])
def _objfun_impl(self, x):
from math import sqrt
# 1 - We check that the transfer time is positive
if x[0] >= x[1]:
if self.f_dimension == 1:
return (self._UNFEASIBLE, )
else:
return (self._UNFEASIBLE, self._UNFEASIBLE)
# 2 - We compute the asteroid positions
r1, v1 = self._ast1.eph(x[0])
r2, v2 = self._ast2.eph(x[1])
# 3 - We compute Lambert arc
l = lambert_problem(r1, r2, (x[1] - x[0]) * DAY2SEC, self._ast1.mu_central_body, False, 0)
# 4 - We compute the two impulses
v1l = l.get_v1()[0]
v2l = l.get_v2()[0]
DV1 = [a - b for a, b in zip(v1, v1l)]
DV2 = [a - b for a, b in zip(v2, v2l)]
DV1 = sum([l * l for l in DV1])
DV2 = sum([l * l for l in DV2])
totDV = sqrt(DV1) + sqrt(DV2)
totDT = x[1] - x[0]
if totDV >= self._max_acc * totDT * DAY2SEC:
if self.f_dimension == 1:
return (self._UNFEASIBLE, )
else:
return (self._UNFEASIBLE, self._UNFEASIBLE)
if self.f_dimension == 1:
return (totDV, )
else:
return (totDV, x[1])
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.orbit_plots import plot_planet, plot_lambert, plot_kepler
if ax is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axis = fig.gca(projection='3d')
else:
axis = ax
axis.scatter(0, 0, 0, color='y')
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T and the cartesian components of vinf
T, Vinfx, Vinfy, Vinfz = self._decode_times_and_vinf(x)
# 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(planet, t0=t_P[i], color=(0.8, 0.6, 0.8), legend=True, units = AU, ax=axis)
# 3 - We start with the first leg
v0 = [a + b for a, b in zip(v_P[0], [Vinfx, Vinfy, Vinfz])]
r, v = propagate_lagrangian(r_P[0], v0, x[5] * T[0] * DAY2SEC, self.common_mu)
plot_kepler(r_P[0], v0, x[5] * T[0] * DAY2SEC, self.common_mu, N=100, color='b', legend=False, units=AU, ax=axis)
# Lambert arc to reach seq[1]
dt = (1 - x[5]) * T[0] * DAY2SEC
l = lambert_problem(r, r_P[1], dt, self.common_mu, False, False)
plot_lambert(l, sol=0, color='r', legend=False, units=AU, ax=axis)
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[8 + (i - 1) * 4] * self.seq[i].radius, x[7 + (i - 1) * 4], self.seq[i].mu_self)
# s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out, x[9 + (i - 1) * 4] * T[i] * DAY2SEC, self.common_mu)
plot_kepler(r_P[i], v_out, x[9 + (i - 1) * 4] * T[i] * DAY2SEC, self.common_mu, N=100, color='b', legend=False, units=AU, ax=axis)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[9 + (i - 1) * 4]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt, self.common_mu, False, False)
plot_lambert(l, sol=0, color='r', legend=False, units=AU, N=1000, ax=axis)
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 axis
def calc_objective(self, x, should_print=False):
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T and the cartesian components of vinf
T, Vinfx, Vinfy, Vinfz = self._decode_times_and_vinf(x)
Vinf = [Vinfx, Vinfy, Vinfz]
# 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])
if should_print:
self.print_time_info(self.seq, t_P)
if self.__add_vinf_dep:
DV[0] += self.burn_cost(self.seq[0], Vinf)
if should_print:
self.print_escape(self.seq[0], v_P[0], r_P[0], Vinf,
t_P[0].mjd)
# 3 - We start with the first leg
v0 = [a + b for a, b in zip(v_P[0], Vinf)]
r, v = propagate_lagrangian(r_P[0], v0, x[5] * T[0] * DAY2SEC,
self.common_mu)
# Lambert arc to reach seq[1]
dt = (1 - x[5]) * T[0] * DAY2SEC
l = lambert_problem(r, r_P[1], dt, self.common_mu, False, False)
v_beg_l = l.get_v1()[0]
v_end_l = l.get_v2()[0]
# First DSM occuring at time nu1*T1
deltaV = [a - b for a, b in zip(v_beg_l, v)]
DV[0] += norm(deltaV)
if should_print:
self.print_dsm(v, r, deltaV, v_beg_l, t_P[0].mjd + dt / DAY2SEC)
# 4 - And we proceed with each successive leg
for i in range(1, self.n_legs):
# Fly-by
radius = x[8 + (i - 1) * 4] * self.seq[i].radius
beta = x[7 + (i - 1) * 4]
v_out = fb_prop(v_end_l, v_P[i], radius, beta, self.seq[i].mu_self)
if should_print:
v_rel_in = [a - b for a, b in zip(v_end_l, v_P[i])]
v_rel_out = [a - b for a, b in zip(v_out, v_P[i])]
self.print_flyby(self.seq[i], v_P[i], r_P[i], v_rel_in,
v_rel_out, t_P[i].mjd)
# s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out,
x[9 + (i - 1) * 4] * T[i] * DAY2SEC,
self.common_mu)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[9 + (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
deltaV = [a - b for a, b in zip(v_beg_l, v)]
DV[i] = norm(deltaV)
if should_print:
self.print_dsm(v, r, deltaV, v_beg_l,
t_P[i].mjd + dt / DAY2SEC)
# Last Delta-v
if self.__add_vinf_arr:
Vexc_arr = [a - b for a, b in zip(v_end_l, v_P[-1])]
DV[-1] = self.burn_cost(self.seq[-1], Vexc_arr)
if should_print:
self.print_arrival(self.seq[-1], Vexc_arr, t_P[-1].mjd)
fuelCost = sum(DV)
if should_print:
print("Total fuel cost: %10.3f m/s" % round(fuelCost, 3))
if self.f_dimension == 1:
return (fuelCost, )
else:
return (fuelCost, sum(T))
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.orbit_plots import plot_planet, plot_lambert, plot_kepler
if ax is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axis = fig.gca(projection='3d')
else:
axis = ax
axis.scatter(0, 0, 0, color='y')
# 1 - we 'decode' the chromosome recording the various deep space
# manouvres timing (days) in the list T
T = list([0] * (self.N_max - 1))
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]
# 2 - We compute the starting and ending position
r_start, v_start = self.start.eph(epoch(x[0]))
if self.phase_free:
r_target, v_target = self.target.eph(epoch(x[-1]))
else:
r_target, v_target = self.target.eph(epoch(x[0] + x[1]))
plot_planet(self.start, t0=epoch(x[0]), color=(0.8, 0.6, 0.8), legend=True, units = AU, ax=axis)
plot_planet(self.target, t0=epoch(x[0] + x[1]), color=(0.8, 0.6, 0.8), legend=True, units = AU, ax=axis)
# 3 - We loop across inner impulses
rsc = r_start
vsc = v_start
for i, time in enumerate(T[:-1]):
theta = 2 * pi * x[3 + 4 * i]
phi = acos(2 * x[4 + 4 * i] - 1) - pi / 2
Vinfx = x[5 + 4 * i] * cos(phi) * cos(theta)
Vinfy = x[5 + 4 * i] * cos(phi) * sin(theta)
Vinfz = x[5 + 4 * i] * sin(phi)
# We apply the (i+1)-th impulse
vsc = [a + b for a, b in zip(vsc, [Vinfx, Vinfy, Vinfz])]
plot_kepler(rsc, vsc, T[
i] * DAY2SEC, self.__common_mu, N=200, color='b', legend=False, units=AU, ax=axis)
rsc, vsc = propagate_lagrangian(
rsc, vsc, T[i] * DAY2SEC, self.__common_mu)
cw = (ic2par(rsc, vsc, self.start.mu_central_body)[2] > pi / 2)
# We now compute the remaining two final impulses
# Lambert arc to reach seq[1]
dt = T[-1] * DAY2SEC
l = lambert_problem(rsc, r_target, dt, self.__common_mu, cw, False)
plot_lambert(
l, sol=0, color='r', legend=False, units=AU, ax=axis, N=200)
plt.show()
return axis
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.orbit_plots import plot_planet, plot_lambert, plot_kepler
if ax is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axis = fig.gca(projection='3d')
else:
axis = ax
axis.scatter(0, 0, 0, color='y')
# 1 - we 'decode' the chromosome recording the various deep space
# manouvres timing (days) in the list T
T = list([0] * (self.N_max - 1))
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]
# 2 - We compute the starting and ending position
r_start, v_start = self.start.eph(epoch(x[0]))
if self.phase_free:
r_target, v_target = self.target.eph(epoch(x[-1]))
else:
r_target, v_target = self.target.eph(epoch(x[0] + x[1]))
plot_planet(self.start,
t0=epoch(x[0]),
color=(0.8, 0.6, 0.8),
legend=True,
units=AU,
ax=axis)
plot_planet(self.target,
t0=epoch(x[0] + x[1]),
color=(0.8, 0.6, 0.8),
legend=True,
units=AU,
ax=axis)
# 3 - We loop across inner impulses
rsc = r_start
vsc = v_start
for i, time in enumerate(T[:-1]):
theta = 2 * pi * x[3 + 4 * i]
phi = acos(2 * x[4 + 4 * i] - 1) - pi / 2
Vinfx = x[5 + 4 * i] * cos(phi) * cos(theta)
Vinfy = x[5 + 4 * i] * cos(phi) * sin(theta)
Vinfz = x[5 + 4 * i] * sin(phi)
# We apply the (i+1)-th impulse
vsc = [a + b for a, b in zip(vsc, [Vinfx, Vinfy, Vinfz])]
plot_kepler(rsc,
vsc,
T[i] * DAY2SEC,
self.__common_mu,
N=200,
color='b',
legend=False,
units=AU,
ax=axis)
rsc, vsc = propagate_lagrangian(rsc, vsc, T[i] * DAY2SEC,
self.__common_mu)
cw = (ic2par(rsc, vsc, self.start.mu_central_body)[2] > pi / 2)
# We now compute the remaining two final impulses
# Lambert arc to reach seq[1]
dt = T[-1] * DAY2SEC
l = lambert_problem(rsc, r_target, dt, self.__common_mu, cw, False)
plot_lambert(l,
sol=0,
color='r',
legend=False,
units=AU,
ax=axis,
N=200)
plt.show()
return axis
def pretty(self, x):
"""
prob.plot(x)
- x: encoded trajectory
Prints human readable information on the trajectory represented by the decision vector x
Example::
print(prob.pretty(x))
"""
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T and the cartesian components of vinf
T, Vinfx, Vinfy, Vinfz = self._decode_times_and_vinf(x)
# 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)
print("Departure: " + str(t_P[0]) + " (" + str(t_P[0].mjd2000) +
" mjd2000) ")
print("Duration: " + str(T[0]) + "days")
print("VINF: " + str(x[4] / 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[5] * T[0] * DAY2SEC,
self.common_mu)
print("DSM after " + str(x[5] * T[0]) + " days")
# Lambert arc to reach seq[1]
dt = (1 - x[5]) * 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[8 + (i - 1) * 4] * self.seq[i].radius,
x[7 + (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[8 + (i - 1) * 4]) +
" planetary radii")
# s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out,
x[9 + (i - 1) * 4] * T[i] * DAY2SEC,
self.common_mu)
print("DSM after " + str(x[9 + (i - 1) * 4] * T[i]) + " days")
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[9 + (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 pretty(self, x):
"""
prob.plot(x)
- x: encoded trajectory
Prints human readable information on the trajectory represented by the decision vector x
Example::
print(prob.pretty(x))
"""
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T and the cartesian components of vinf
T, Vinfx, Vinfy, Vinfz = self._decode_times_and_vinf(x)
# 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)
print("Departure: " + str(t_P[0]) + " (" + str(t_P[0].mjd2000) + " mjd2000) ")
print("Duration: " + str(T[0]) + "days")
print("VINF: " + str(x[4] / 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[5] * T[0] * DAY2SEC, self.common_mu)
print("DSM after " + str(x[5] * T[0]) + " days")
# Lambert arc to reach seq[1]
dt = (1 - x[5]) * 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[8 + (i - 1) * 4] * self.seq[i].radius, x[7 + (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[8 + (i - 1) * 4]) + " planetary radii")
# s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out, x[9 + (i - 1) * 4] * T[i] * DAY2SEC, self.common_mu)
print("DSM after " + str(x[9 + (i - 1) * 4] * T[i]) + " days")
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[9 + (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 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.orbit_plots import plot_planet, plot_lambert, plot_kepler
if ax is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axis = fig.gca(projection='3d')
else:
axis = ax
axis.scatter(0, 0, 0, color='y')
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T and the cartesian components of vinf
T, Vinfx, Vinfy, Vinfz = self._decode_times_and_vinf(x)
# 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(planet,
t0=t_P[i],
color=(0.8, 0.6, 0.8),
legend=True,
units=AU,
ax=axis)
# 3 - We start with the first leg
v0 = [a + b for a, b in zip(v_P[0], [Vinfx, Vinfy, Vinfz])]
r, v = propagate_lagrangian(r_P[0], v0, x[5] * T[0] * DAY2SEC,
self.common_mu)
plot_kepler(r_P[0],
v0,
x[5] * T[0] * DAY2SEC,
self.common_mu,
N=100,
color='b',
legend=False,
units=AU,
ax=axis)
# Lambert arc to reach seq[1]
dt = (1 - x[5]) * T[0] * DAY2SEC
l = lambert_problem(r, r_P[1], dt, self.common_mu, False, False)
plot_lambert(l, sol=0, color='r', legend=False, units=AU, ax=axis)
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[8 + (i - 1) * 4] * self.seq[i].radius,
x[7 + (i - 1) * 4], self.seq[i].mu_self)
# s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out,
x[9 + (i - 1) * 4] * T[i] * DAY2SEC,
self.common_mu)
plot_kepler(r_P[i],
v_out,
x[9 + (i - 1) * 4] * T[i] * DAY2SEC,
self.common_mu,
N=100,
color='b',
legend=False,
units=AU,
ax=axis)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[9 + (i - 1) * 4]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt, self.common_mu, False,
False)
plot_lambert(l,
sol=0,
color='r',
legend=False,
units=AU,
N=1000,
ax=axis)
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 axis
def calc_objective(self, x, should_print = False):
# 1 - we 'decode' the chromosome recording the various times of flight
# (days) in the list T and the cartesian components of vinf
T, Vinfx, Vinfy, Vinfz = self._decode_times_and_vinf(x)
Vinf = [Vinfx, Vinfy, Vinfz]
# 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])
if should_print:
self.print_time_info(self.seq, t_P)
if self.__add_vinf_dep:
DV[0] += self.burn_cost(self.seq[0], Vinf)
if should_print:
self.print_escape(self.seq[0], v_P[0], r_P[0], Vinf, t_P[0].mjd)
# 3 - We start with the first leg
v0 = [a + b for a, b in zip(v_P[0], Vinf)]
r, v = propagate_lagrangian(r_P[0], v0, x[5] * T[0] * DAY2SEC, self.common_mu)
# Lambert arc to reach seq[1]
dt = (1 - x[5]) * T[0] * DAY2SEC
l = lambert_problem(r, r_P[1], dt, self.common_mu, False, False)
v_beg_l = l.get_v1()[0]
v_end_l = l.get_v2()[0]
# First DSM occuring at time nu1*T1
deltaV = [a - b for a, b in zip(v_beg_l, v)]
DV[0] += norm(deltaV)
if should_print:
self.print_dsm(v, r, deltaV, v_beg_l, t_P[0].mjd + dt / DAY2SEC)
# 4 - And we proceed with each successive leg
for i in range(1, self.n_legs):
# Fly-by
radius = x[8 + (i - 1) * 4] * self.seq[i].radius
beta = x[7 + (i - 1) * 4]
v_out = fb_prop(v_end_l, v_P[i],radius , beta, self.seq[i].mu_self)
if should_print:
v_rel_in = [a - b for a,b in zip(v_end_l, v_P[i])]
v_rel_out = [a - b for a,b in zip(v_out, v_P[i])]
self.print_flyby(self.seq[i], v_P[i], r_P[i], v_rel_in, v_rel_out, t_P[i].mjd)
# s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out, x[9 + (i - 1) * 4] * T[i] * DAY2SEC, self.common_mu)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[9 + (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
deltaV = [a - b for a, b in zip(v_beg_l, v)]
DV[i] = norm(deltaV)
if should_print:
self.print_dsm(v, r, deltaV, v_beg_l, t_P[i].mjd + dt / DAY2SEC)
# Last Delta-v
if self.__add_vinf_arr:
Vexc_arr = [a - b for a, b in zip(v_end_l, v_P[-1])]
DV[-1] = self.burn_cost(self.seq[-1], Vexc_arr)
if should_print:
self.print_arrival(self.seq[-1], Vexc_arr, t_P[-1].mjd)
fuelCost = sum(DV)
if should_print:
print("Total fuel cost: %10.3f m/s" % round(fuelCost, 3))
if self.f_dimension == 1:
return (fuelCost,)
else:
return (fuelCost, sum(T))