def fitness(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._obj_dim == 1:
return (sum(DV), )
else:
return (sum(DV), sum(T))
def fitness(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._obj_dim == 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 _dv_mga(pl1,
pl2,
tof,
max_revs,
rvt_outs,
rvt_ins,
rvt_pls,
dvs,
lps=None):
rvt_pl = rvt_pls[-1] # current planet
v_in = rvt_pl._v if rvt_ins[-1] is None else rvt_ins[-1]._v
rvt_pl2 = rvt_planet(pl2, rvt_pl._t + tof)
rvt_pls.append(rvt_pl2)
r = rvt_pl._r
vpl = rvt_pl._v
r2 = rvt_pl2._r
lp = lambert_problem(r, r2, tof, rvt_pl._mu, False, max_revs)
lp = lambert_problem_multirev_ga(v_in, lp, pl1, vpl)
if not lps is None:
lps.append(lp)
v_out = lp.get_v1()[0]
rvt_out = rvt(r, v_out, rvt_pl._t, rvt_pl._mu)
rvt_outs.append(rvt_out)
rvt_in = rvt(r2, lp.get_v2()[0], rvt_pl._t + tof, rvt_pl._mu)
rvt_ins.append(rvt_in)
vr_in = [a - b for a, b in zip(v_in, vpl)]
vr_out = [a - b for a, b in zip(v_out, vpl)]
dv = fb_vel(vr_in, vr_out, pl1)
dvs.append(dv)
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, axes=axis, s=10, t0=epoch(self.lb[0]))
plot_planet(A2, axes=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, axes=axis, alpha=0.8, color='k')
if ax is None:
plt.show()
return axis
def _compute_dvs(self, x: List[float]) -> Tuple[
float, # DVlaunch
List[float], # DVs
float, # DVarrival,
List[Any], # Lambert legs
float, #DVlaunch_tot
List[float], # T
List[Tuple[List[float], List[float]]], # ballistic legs
List[float], # epochs of ballistic legs
]:
# 1 - we 'decode' the times of flights and compute epochs (mjd2000)
T: List[float] = self._decode_tofs(x) # [T1, T2 ...]
ep = np.insert(T, 0, x[0]) # [t0, T1, T2 ...]
ep = np.cumsum(ep) # [t0, t1, t2, ...]
# 2 - we compute the ephemerides
r = [0] * len(self.seq)
v = [0] * len(self.seq)
for i in range(len(self.seq)):
r[i], v[i] = self.seq[i].eph(float(ep[i]))
l = list()
ballistic_legs: List[Tuple[List[float], List[float]]] = []
ballistic_ep: List[float] = []
# 3 - we solve the lambert problems
vi = v[0]
for i in range(self._n_legs):
lp = lambert_problem_multirev(
vi,
lambert_problem(r[i], r[i + 1], T[i] * DAY2SEC,
self._common_mu, False, self.max_revs))
l.append(lp)
vi = lp.get_v2()[0]
ballistic_legs.append((r[i], lp.get_v1()[0]))
ballistic_ep.append(ep[i])
# 4 - we compute the various dVs needed at fly-bys to match incoming
# and outcoming
DVfb = list()
for i in range(len(l) - 1):
vin = [a - b for a, b in zip(l[i].get_v2()[0], v[i + 1])]
vout = [a - b for a, b in zip(l[i + 1].get_v1()[0], v[i + 1])]
DVfb.append(fb_vel(vin, vout, self.seq[i + 1]))
# 5 - we add the departure and arrival dVs
DVlaunch_tot = np.linalg.norm(
[a - b for a, b in zip(v[0], l[0].get_v1()[0])])
DVlaunch = max(0, DVlaunch_tot - self.vinf)
DVarrival = np.linalg.norm(
[a - b for a, b in zip(v[-1], l[-1].get_v2()[0])])
if self.orbit_insertion:
# In this case we compute the insertion DV as a single pericenter
# burn
DVper = np.sqrt(DVarrival * DVarrival +
2 * self.seq[-1].mu_self / self.rp_target)
DVper2 = np.sqrt(2 * self.seq[-1].mu_self / self.rp_target -
self.seq[-1].mu_self / self.rp_target *
(1. - self.e_target))
DVarrival = np.abs(DVper - DVper2)
return (DVlaunch, DVfb, DVarrival, l, DVlaunch_tot, T, ballistic_legs,
ballistic_ep)
def pretty(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 = list(x[5::4])
DV_others.extend([DV1, DV2])
print("Total DV (m/s): ", sum(DV_others))
print("Dvs (m/s): ", DV_others)
print("Tofs (days): ", T)
def fitness(self, x):
# 1 - we 'decode' the chromosome into the various deep space
# manouvres times (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.obj_dim == 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)]
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 _compute_dvs(self, x):
# 1 - we 'decode' the times of flights and compute epochs (mjd2000)
T = self._decode_tofs(x) # [T1, T2 ...]
ep = np.insert(T, 0, x[0]) # [t0, T1, T2 ...]
ep = np.cumsum(ep) # [t0, t1, t2, ...]
# 2 - we compute the ephemerides
r = [0] * len(self.seq)
v = [0] * len(self.seq)
for i in range(len(self.seq)):
r[i], v[i] = self.seq[i].eph(ep[i])
# 3 - we solve the lambert problems
l = list()
for i in range(self._n_legs):
l.append(
lambert_problem(r[i], r[i + 1], T[i] * DAY2SEC,
self._common_mu, False, 0))
# 4 - we compute the various dVs needed at fly-bys to match incoming
# and outcoming
DVfb = list()
for i in range(len(l) - 1):
vin = [a - b for a, b in zip(l[i].get_v2()[0], v[i + 1])]
vout = [a - b for a, b in zip(l[i + 1].get_v1()[0], v[i + 1])]
DVfb.append(fb_vel(vin, vout, self.seq[i + 1]))
# 5 - we add the departure and arrival dVs
DVlaunch_tot = np.linalg.norm(
[a - b for a, b in zip(v[0], l[0].get_v1()[0])])
DVlaunch = max(0, DVlaunch_tot - self.vinf)
DVarrival = np.linalg.norm(
[a - b for a, b in zip(v[-1], l[-1].get_v2()[0])])
if self.orbit_insertion:
# In this case we compute the insertion DV as a single pericenter
# burn
DVper = np.sqrt(DVarrival * DVarrival +
2 * self.seq[-1].mu_self / self.rp_target)
DVper2 = np.sqrt(2 * self.seq[-1].mu_self / self.rp_target -
self.seq[-1].mu_self / self.rp_target *
(1. - self.e_target))
DVarrival = np.abs(DVper - DVper2)
return (DVlaunch, DVfb, DVarrival, l, DVlaunch_tot)
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 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([0.0] * (self.n_legs + 1))
for i in range(len(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[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,
cw=False,
max_revs=0)
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,
cw=False,
max_revs=0)
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")
if self._orbit_insertion:
# In this case we compute the insertion DV as a single pericenter
# burn
DVper = np.sqrt(DV[-1] * DV[-1] +
2 * self._seq[-1].mu_self / self._rp_target)
DVper2 = np.sqrt(2 * self._seq[-1].mu_self / self._rp_target -
self._seq[-1].mu_self / self._rp_target *
(1. - self._e_target))
DVinsertion = np.abs(DVper - DVper2)
print("Insertion DV: " + str(DVinsertion) + "m/s")
print("Total mission time: " + str(sum(T) / 365.25) + " years (" +
str(sum(T)) + " days)")
def fitness(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 in range(len(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[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,
cw=False,
max_revs=0)
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,
cw=False,
max_revs=0)
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._orbit_insertion:
# In this case we compute the insertion DV as a single pericenter
# burn
DVper = np.sqrt(DV[-1] * DV[-1] +
2 * self._seq[-1].mu_self / self._rp_target)
DVper2 = np.sqrt(2 * self._seq[-1].mu_self / self._rp_target -
self._seq[-1].mu_self / self._rp_target *
(1. - self._e_target))
DV[-1] = np.abs(DVper - DVper2)
if self._add_vinf_dep:
DV[0] += x[3]
if not self._multi_objective:
return (sum(DV), )
else:
return (sum(DV), sum(T))
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 _compute_dvs(self, x: List[float]) -> Tuple[
List[float], # DVs
List[Any], # Lambert legs
List[float], # T
List[Tuple[List[float], List[float]]], # ballistic legs
List[float], # epochs of ballistic legs
]:
# 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 in range(len(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])
ballistic_legs: List[Tuple[List[float], List[float]]] = []
ballistic_ep: List[float] = []
lamberts = []
# 3 - We start with the first leg
v0 = [a + b for a, b in zip(v_P[0], [Vinfx, Vinfy, Vinfz])]
ballistic_legs.append((r_P[0], v0))
ballistic_ep.append(t_P[0].mjd2000)
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_multirev(
v,
lambert_problem(r,
r_P[1],
dt,
self.common_mu,
cw=False,
max_revs=self.max_revs))
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
lamberts.append(l)
ballistic_legs.append((r, v_beg_l))
ballistic_ep.append(t_P[0].mjd2000 + x[4] * T[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)
ballistic_legs.append((r_P[i], v_out))
ballistic_ep.append(t_P[i].mjd2000)
# 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_multirev(
v,
lambert_problem(r,
r_P[i + 1],
dt,
self.common_mu,
cw=False,
max_revs=self.max_revs))
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
lamberts.append(l)
# DSM occuring at time nu2*T2
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
ballistic_legs.append((r, v_beg_l))
ballistic_ep.append(t_P[i].mjd2000 + x[8 + (i - 1) * 4] * T[i])
# 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._orbit_insertion:
# In this case we compute the insertion DV as a single pericenter
# burn
DVper = np.sqrt(DV[-1] * DV[-1] +
2 * self._seq[-1].mu_self / self._rp_target)
DVper2 = np.sqrt(2 * self._seq[-1].mu_self / self._rp_target -
self._seq[-1].mu_self / self._rp_target *
(1. - self._e_target))
DV[-1] = np.abs(DVper - DVper2)
if self._add_vinf_dep:
DV[0] += x[3]
return (DV, lamberts, T, ballistic_legs, ballistic_ep)
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)
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 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")
