def plot(self, tof, N=60, units=AU, color="b", label=None, axes=None):
from pykep.orbit_plots import plot_kepler
plot_kepler(r0=self._r,
v0=self._v,
tof=tof,
mu=self._mu,
N=N,
units=units,
color=color,
label=label,
axes=axes)
def plot(self, x, axes=None):
"""
ax = prob.plot_trajectory(x, axes=None)
- x: encoded trajectory
- axes: 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 axes is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axes = fig.gca(projection='3d')
axes.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=axes,
s=0)
plot_planet(self.target,
t0=epoch(x[0] + x[1]),
color=(0.8, 0.6, 0.8),
legend=True,
units=AU,
ax=axes,
s=0)
DV_list = x[5::4]
maxDV = max(DV_list)
DV_list = [s / maxDV * 30 for s in DV_list]
colors = ['b', 'r'] * (len(DV_list) + 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])]
axes.scatter(rsc[0] / AU,
rsc[1] / AU,
rsc[2] / AU,
color='k',
s=DV_list[i])
plot_kepler(rsc,
vsc,
T[i] * DAY2SEC,
self.__common_mu,
N=200,
color=colors[i],
legend=False,
units=AU,
ax=axes)
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=colors[i + 1],
legend=False,
units=AU,
ax=axes,
N=200)
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)])
axes.scatter(rsc[0] / AU,
rsc[1] / AU,
rsc[2] / AU,
color='k',
s=min(DV1 / maxDV * 30, 40))
axes.scatter(r_target[0] / AU,
r_target[1] / AU,
r_target[2] / AU,
color='k',
s=min(DV2 / maxDV * 30, 40))
return axes
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,
axes=axis,
N=150)
# 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[4] * T[0] * DAY2SEC,
self.common_mu)
plot_kepler(r_P[0],
v0,
x[4] * T[0] * DAY2SEC,
self.common_mu,
N=100,
color='b',
legend=False,
units=AU,
axes=axis)
# 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(l, sol=0, color='r', legend=False, units=AU, axes=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[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(r_P[i],
v_out,
x[8 + (i - 1) * 4] * T[i] * DAY2SEC,
self.common_mu,
N=100,
color='b',
legend=False,
units=AU,
axes=axis)
# 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(l,
sol=0,
color='r',
legend=False,
units=AU,
N=1000,
axes=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 plot(self, x, axes=None):
"""
ax = prob.plot_trajectory(x, axes=None)
- x: encoded trajectory
- axes: 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 axes is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axes = fig.gca(projection='3d')
axes.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=axes, s=0)
plot_planet(self.target, t0=epoch(
x[0] + x[1]), color=(0.8, 0.6, 0.8), legend=True, units=AU, ax=axes, s=0)
DV_list = x[5::4]
maxDV = max(DV_list)
DV_list = [s / maxDV * 30 for s in DV_list]
colors = ['b', 'r'] * (len(DV_list) + 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])]
axes.scatter(rsc[0] / AU, rsc[1] / AU, rsc[2] /
AU, color='k', s=DV_list[i])
plot_kepler(rsc, vsc, T[i] * DAY2SEC, self.__common_mu,
N=200, color=colors[i], legend=False, units=AU, ax=axes)
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=colors[
i + 1], legend=False, units=AU, ax=axes, N=200)
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)])
axes.scatter(rsc[0] / AU, rsc[1] / AU, rsc[2] / AU,
color='k', s=min(DV1 / maxDV * 30, 40))
axes.scatter(r_target[0] / AU, r_target[1] / AU,
r_target[2] / AU, color='k', s=min(DV2 / maxDV * 30, 40))
return axes
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 _fitness_impl(self, decoded_x, logging=False, plotting=False, ax=None):
""" Computation of the objective function. """
saturn_distance_violated = 0
# decode x
t0, u, v, dep_vinf, etas, T, betas, rps = decoded_x
# convert incoming velocity vector
theta, phi = 2.0 * pi * u, acos(2.0 * v - 1.0) - pi / 2.0
Vinfx = dep_vinf * cos(phi) * cos(theta)
Vinfy = dep_vinf * cos(phi) * sin(theta)
Vinfz = dep_vinf * sin(phi)
# 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))
lamberts = list([None] * (self._n_legs))
v_outs = list([None] * (self._n_legs))
DV = list([0.0] * (self._n_legs + 1))
for i, planet in enumerate(self.seq):
t_P[i] = epoch(t0 + sum(T[0:i]))
r_P[i], v_P[i] = self.seq[i].eph(t_P[i])
# first leg
v_outs[0] = [Vinfx, Vinfy, Vinfz] # bug fixed
# check first leg up to DSM
saturn_distance_violated += self.check_distance(
r_P[0], v_outs[0], t0, etas[0] * T[0])
r, v = propagate_lagrangian(r_P[0], v_outs[0],
etas[0] * T[0] * DAY2SEC, self.common_mu)
# Lambert arc to reach seq[1]
dt = (1.0 - etas[0]) * T[0] * DAY2SEC
lamberts[0] = lambert_problem(r, r_P[1], dt, self.common_mu, self.cw,
0)
v_end_l = lamberts[0].get_v2()[0]
v_beg_l = lamberts[0].get_v1()[0]
# First DSM occuring at time eta0*T0
DV[0] = norm([a - b for a, b in zip(v_beg_l, v)])
# checking first leg after DSM
saturn_distance_violated += self.check_distance(
r, v_beg_l, etas[0] * T[0], T[0])
# successive legs
for i in range(1, self._n_legs):
# Fly-by
v_outs[i] = fb_prop(v_end_l, v_P[i],
rps[i - 1] * self.seq[i].radius, betas[i - 1],
self.seq[i].mu_self)
# checking next leg up to DSM
saturn_distance_violated += self.check_distance(
r_P[i], v_outs[i], T[i - 1], etas[i] * T[i])
# s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_outs[i],
etas[i] * T[i] * DAY2SEC,
self.common_mu)
# Lambert arc to reach next body
dt = (1 - etas[i]) * T[i] * DAY2SEC
lamberts[i] = lambert_problem(r, r_P[i + 1], dt, self.common_mu,
self.cw, 0)
v_end_l = lamberts[i].get_v2()[0]
v_beg_l = lamberts[i].get_v1()[0]
# DSM occuring at time eta_i*T_i
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
# checking next leg after DSM
saturn_distance_violated += self.check_distance(
r, v_beg_l, etas[i] * T[i], T[i])
# single dv penalty for now
if saturn_distance_violated > 0:
DV[-1] += DV_PENALTY
arr_vinf = norm([a - b for a, b in zip(v_end_l, v_P[-1])])
# last Delta-v
if self._add_vinf_arr:
DV[-1] = arr_vinf
if self._add_vinf_dep:
DV[0] += dep_vinf
# pretty printing
if logging:
print("First leg: {} to {}".format(self.seq[0].name,
self.seq[1].name))
print("Departure: {0} ({1:0.6f} mjd2000)".format(
t_P[0], t_P[0].mjd2000))
print("Duration: {0:0.6f}d".format(T[0]))
print("VINF: {0:0.3f}m/s".format(dep_vinf))
print("DSM after {0:0.6f}d".format(etas[0] * T[0]))
print("DSM magnitude: {0:0.6f}m/s".format(DV[0]))
for i in range(1, self._n_legs):
print("\nleg {}: {} to {}".format(i + 1, self.seq[i].name,
self.seq[i + 1].name))
print("Duration: {0:0.6f}d".format(T[i]))
print("Fly-by epoch: {0} ({1:0.6f} mjd2000)".format(
t_P[i], t_P[i].mjd2000))
print("Fly-by radius: {0:0.6f} planetary radii".format(rps[i -
1]))
print("DSM after {0:0.6f}d".format(etas[i] * T[i]))
print("DSM magnitude: {0:0.6f}m/s".format(DV[i]))
print("\nArrival at {}".format(self.seq[-1].name))
print("Arrival epoch: {0} ({1:0.6f} mjd2000)".format(
t_P[-1], t_P[-1].mjd2000))
print("Arrival Vinf: {0:0.3f}m/s".format(arr_vinf))
print("Total mission time: {0:0.6f}d ({1:0.3f} years)".format(
sum(T),
sum(T) / 365.25))
# plotting
if plotting:
ax.scatter(0, 0, 0, color='chocolate')
for i, planet in enumerate(self.seq):
plot_planet(planet,
t0=t_P[i],
color=pl2c[planet.name],
legend=True,
units=AU,
ax=ax)
for i in range(0, self._n_legs):
plot_kepler(r_P[i],
v_outs[i],
etas[i] * T[i] * DAY2SEC,
self.common_mu,
N=100,
color='b',
legend=False,
units=AU,
ax=ax)
for l in lamberts:
plot_lambert(l,
sol=0,
color='r',
legend=False,
units=AU,
N=1000,
ax=ax)
# returning building blocks for objectives
return (DV, T, arr_vinf, lamberts)
