def pretty(self, x):
"""
prob.pretty(x)
- x: encoded trajectory
Prints human readable information on the trajectory represented by the decision vector x
"""
n_seg = self.__n_seg
m_i = self.__sc.mass
t0 = x[0]
T = x[1]
m_f = x[2]
thrusts = [np.linalg.norm(x[3 + 3 * i : 6 + 3 * i]) for i in range(n_seg)]
tf = t0 + T
mP = m_i - m_f
deltaV = self.__sc.isp * G0 * np.log(m_i / m_f)
dt = np.append(self.__fwd_dt, self.__bwd_dt) * T / DAY2SEC
time_thrusts_on = sum(dt[i] for i in range(len(thrusts)) if thrusts[i] > 0.1)
print("Departure:", epoch(t0), "(", t0, "mjd2000 )")
print("Time of flight:", T, "days")
print("Arrival:", epoch(tf), "(", tf, "mjd2000 )")
print("Delta-v:", deltaV, "m/s")
print("Propellant consumption:", mP, "kg")
print("Thrust-on time:", time_thrusts_on, "days")
def double_segments(self,x):
"""
new_prob, new_x = prob.double_segments(self,x)
- x: encoded trajectory
Returns the decision vector encoding a low trust trajectory having double the number of segments with respect to x
and a 'similar' throttle history. In case high fidelity is True, and x is a feasible trajectory, the returned decision vector
also encodes a feasible trajectory that can be further optimized
Returns the problem and the decision vector encoding a low-thrust trajectory having double the number of
segments with respect to x and the same throttle history. If x is a feasible trajectory, the new chromosome is "almost"
feasible, due to the new refined Earth gravity that is now different in the 2 halves of each segment).
"""
new_x = list(x[:3])
for i in range(self.__n_seg):
new_x.extend(x[3 + 3 * i : 6 + 3 * i] * 2)
new_prob = earth_gravity(
target = self.target,
n_seg = 2 * self.__n_seg,
grid_type = self.__grid_type,
t0 = [epoch(self.lb[0]), epoch(self.ub[0])],
tof = [self.lb[1], self.ub[1]],
m0 = self.__sc.mass,
Tmax = self.__sc.thrust,
Isp = self.__sc.isp,
earth_gravity = self.__earth_gravity,
start = self.__start
)
return new_prob, new_x
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 __init__(self,
seq=[jpl_lp('earth'),
jpl_lp('venus'),
jpl_lp('earth')],
t0=[epoch(0), epoch(1000)],
tof=[1.0, 5.0],
vinf=[0.5, 2.5],
add_vinf_dep=False,
add_vinf_arr=True,
multi_objective=False):
"""
PyKEP.trajopt.mga_1dsm(seq = [jpl_lp('earth'), jpl_lp('venus'), jpl_lp('earth')], t0 = [epoch(0),epoch(1000)], tof = [1.0,5.0], vinf = [0.5, 2.5], multi_objective = False, add_vinf_dep = False, add_vinf_arr=True)
- seq: list of PyKEP planets defining the encounter sequence (including the starting launch)
- t0: list of two epochs defining the launch window
- tof: list of two floats defining the minimum and maximum allowed mission lenght (years)
- vinf: list of two floats defining the minimum and maximum allowed initial hyperbolic velocity (at launch), in km/sec
- multi_objective: when True constructs a multiobjective problem (dv, T)
- add_vinf_dep: when True the computed Dv includes the initial hyperbolic velocity (at launch)
- add_vinf_arr: when True the computed Dv includes the final hyperbolic velocity (at the last planet)
"""
# Sanity checks ...... all planets need to have the same
# mu_central_body
if ([r.mu_central_body
for r in seq].count(seq[0].mu_central_body) != len(seq)):
raise ValueError(
'All planets in the sequence need to have exactly the same mu_central_body'
)
self.__add_vinf_dep = add_vinf_dep
self.__add_vinf_arr = add_vinf_arr
self.__n_legs = len(seq) - 1
dim = 7 + (self.__n_legs - 1) * 4
obj_dim = multi_objective + 1
# First we call the constructor for the base PyGMO problem
# As our problem is n dimensional, box-bounded (may be multi-objective), we write
# (dim, integer dim, number of obj, number of con, number of inequality con, tolerance on con violation)
super(mga_1dsm, self).__init__(dim, 0, obj_dim, 0, 0, 0)
# We then define all planets in the sequence and the common central
# body gravity as data members
self.seq = seq
self.common_mu = seq[0].mu_central_body
# And we compute the bounds
lb = [t0[0].mjd2000, tof[0] * 365.25] + [
0.0, 0.0, vinf[0] * 1000, 1e-5, 1e-5
] + [-2 * pi, 1.1, 1e-5, 1e-5] * (self.__n_legs - 1)
ub = [t0[1].mjd2000, tof[1] * 365.25] + [
1.0, 1.0, vinf[1] * 1000, 1.0 - 1e-5, 1.0 - 1e-5
] + [2 * pi, 30.0, 1.0 - 1e-5, 1.0 - 1e-5] * (self.__n_legs - 1)
# Accounting that each planet has a different safe radius......
for i, pl in enumerate(seq[1:-1]):
lb[8 + 4 * i] = pl.safe_radius / pl.radius
# And we set them
self.set_bounds(lb, ub)
def __init__(self,
seq=[jpl_lp('earth'),
jpl_lp('venus'),
jpl_lp('earth')],
t0=[epoch(0), epoch(1000)],
tof=[1.0, 5.0],
vinf=[0.5, 2.5],
mga_sol=None,
add_vinf_dep=False,
add_vinf_arr=True,
multi_objective=False,
avoid=[]):
"""
PyKEP.trajopt.mga_1dsm(seq = [jpl_lp('earth'), jpl_lp('venus'), jpl_lp('earth')], t0 = [epoch(0),epoch(1000)], tof = [1.0,5.0], vinf = [0.5, 2.5], multi_objective = False, add_vinf_dep = False, add_vinf_arr=True)
- seq: list of PyKEP planets defining the encounter sequence (including the starting launch)
- t0: list of two epochs defining the launch window
- tof: list of two floats defining the minimum and maximum allowed mission lenght (years)
- vinf: list of two floats defining the minimum and maximum allowed initial hyperbolic velocity (at launch), in km/sec
- multi_objective: when True constructs a multiobjective problem (dv, T)
- add_vinf_dep: when True the computed Dv includes the initial hyperbolic velocity (at launch)
- add_vinf_arr: when True the computed Dv includes the final hyperbolic velocity (at the last planet)
"""
# First we call the constructor for the base PyGMO problem
# As our problem is n dimensional, box-bounded (may be multi-objective), we write
# (dim, integer dim, number of obj, number of con, number of inequality con, tolerance on con violation)
dim = 7 + (len(seq) - 2) * 4
obj_dim = multi_objective + 1
super(mga_1dsm_transx, self).__init__(seq, dim, obj_dim, avoid)
self.__add_vinf_dep = add_vinf_dep
self.__add_vinf_arr = add_vinf_arr
# And we compute the bounds
lb = [t0[0].mjd2000, tof[0] * 365.25] + [
0.0, 0.0, vinf[0] * 1000, 1e-5, 1e-5
] + [-2 * pi, 1.1, 1e-5, 1e-5] * (self.n_legs - 1)
ub = [t0[1].mjd2000, tof[1] * 365.25] + [
1.0, 1.0, vinf[1] * 1000, 1.0 - 1e-5, 1.0 - 1e-5
] + [2 * pi, 30.0, 1.0 - 1e-5, 1.0 - 1e-5] * (self.n_legs - 1)
self.__mga_sol = mga_sol
# Accounting that each planet has a different safe radius......
for i, pl in enumerate(seq[1:-1]):
lb[8 + 4 * i] = pl.safe_radius / pl.radius
# And we set them
self.set_bounds(lb, ub)
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 __init__(self, seq=[jpl_lp('earth'), jpl_lp('venus'), jpl_lp('earth')], t0=[epoch(0), epoch(1000)], tof=[1.0, 5.0], vinf=[0.5, 2.5], mga_sol = None, add_vinf_dep=False, add_vinf_arr=True, multi_objective=False, avoid = []):
"""
PyKEP.trajopt.mga_1dsm(seq = [jpl_lp('earth'), jpl_lp('venus'), jpl_lp('earth')], t0 = [epoch(0),epoch(1000)], tof = [1.0,5.0], vinf = [0.5, 2.5], multi_objective = False, add_vinf_dep = False, add_vinf_arr=True)
- seq: list of PyKEP planets defining the encounter sequence (including the starting launch)
- t0: list of two epochs defining the launch window
- tof: list of two floats defining the minimum and maximum allowed mission lenght (years)
- vinf: list of two floats defining the minimum and maximum allowed initial hyperbolic velocity (at launch), in km/sec
- multi_objective: when True constructs a multiobjective problem (dv, T)
- add_vinf_dep: when True the computed Dv includes the initial hyperbolic velocity (at launch)
- add_vinf_arr: when True the computed Dv includes the final hyperbolic velocity (at the last planet)
"""
# First we call the constructor for the base PyGMO problem
# As our problem is n dimensional, box-bounded (may be multi-objective), we write
# (dim, integer dim, number of obj, number of con, number of inequality con, tolerance on con violation)
dim = 7 + (len(seq) - 2) * 4
obj_dim = multi_objective + 1
super(mga_1dsm_transx, self).__init__(seq, dim, obj_dim, avoid)
self.__add_vinf_dep = add_vinf_dep
self.__add_vinf_arr = add_vinf_arr
# And we compute the bounds
lb = [t0[0].mjd2000, tof[0] * 365.25] + [0.0, 0.0, vinf[0] * 1000, 1e-5, 1e-5] + [-2 * pi, 1.1, 1e-5, 1e-5] * (self.n_legs - 1)
ub = [t0[1].mjd2000, tof[1] * 365.25] + [1.0, 1.0, vinf[1] * 1000, 1.0 - 1e-5, 1.0 - 1e-5] + [2 * pi, 30.0, 1.0 - 1e-5, 1.0 - 1e-5] * (self.n_legs - 1)
self.__mga_sol = mga_sol
# Accounting that each planet has a different safe radius......
for i, pl in enumerate(seq[1:-1]):
lb[8 + 4 * i] = pl.safe_radius / pl.radius
# And we set them
self.set_bounds(lb, ub)
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 __init__(self, seq=[jpl_lp('earth'), jpl_lp('venus'), jpl_lp('earth')], t0=[epoch(0), epoch(1000)], tof=[1.0, 5.0], vinf=[0.5, 2.5], add_vinf_dep=False, add_vinf_arr=True, multi_objective=False):
"""
PyKEP.trajopt.mga_1dsm(seq = [jpl_lp('earth'), jpl_lp('venus'), jpl_lp('earth')], t0 = [epoch(0),epoch(1000)], tof = [1.0,5.0], vinf = [0.5, 2.5], multi_objective = False, add_vinf_dep = False, add_vinf_arr=True)
- seq: list of PyKEP planets defining the encounter sequence (including the starting launch)
- t0: list of two epochs defining the launch window
- tof: list of two floats defining the minimum and maximum allowed mission lenght (years)
- vinf: list of two floats defining the minimum and maximum allowed initial hyperbolic velocity (at launch), in km/sec
- multi_objective: when True constructs a multiobjective problem (dv, T)
- add_vinf_dep: when True the computed Dv includes the initial hyperbolic velocity (at launch)
- add_vinf_arr: when True the computed Dv includes the final hyperbolic velocity (at the last planet)
"""
# Sanity checks ...... all planets need to have the same
# mu_central_body
if ([r.mu_central_body for r in seq].count(seq[0].mu_central_body) != len(seq)):
raise ValueError('All planets in the sequence need to have exactly the same mu_central_body')
self.__add_vinf_dep = add_vinf_dep
self.__add_vinf_arr = add_vinf_arr
self.__n_legs = len(seq) - 1
dim = 7 + (self.__n_legs - 1) * 4
obj_dim = multi_objective + 1
# First we call the constructor for the base PyGMO problem
# As our problem is n dimensional, box-bounded (may be multi-objective), we write
# (dim, integer dim, number of obj, number of con, number of inequality con, tolerance on con violation)
super(mga_1dsm, self).__init__(dim, 0, obj_dim, 0, 0, 0)
# We then define all planets in the sequence and the common central
# body gravity as data members
self.seq = seq
self.common_mu = seq[0].mu_central_body
# And we compute the bounds
lb = [t0[0].mjd2000, tof[0] * 365.25] + [0.0, 0.0, vinf[0] * 1000, 1e-5, 1e-5] + [-2 * pi, 1.1, 1e-5, 1e-5] * (self.__n_legs - 1)
ub = [t0[1].mjd2000, tof[1] * 365.25] + [1.0, 1.0, vinf[1] * 1000, 1.0 - 1e-5, 1.0 - 1e-5] + [2 * pi, 30.0, 1.0 - 1e-5, 1.0 - 1e-5] * (self.__n_legs - 1)
# Accounting that each planet has a different safe radius......
for i, pl in enumerate(seq[1:-1]):
lb[8 + 4 * i] = pl.safe_radius / pl.radius
# And we set them
self.set_bounds(lb, ub)
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_trajectory(self, x, units=AU, plot_segments=True, ax=None):
"""
ax = prob.plot_trajectory(self, x, units=AU, plot_segments=True, ax=None)
- x: encoded trajectory
- units: the length unit to be used in the plot
- plot_segments: when true plots also the segments boundaries
- [out] ax: matplotlib axis where to plot
Plots the trajectory
"""
import matplotlib as mpl
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from PyKEP.orbit_plots import plot_planet, plot_taylor
# 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
n_seg = self.__n_seg
fwd_seg = self.__fwd_seg
bwd_seg = self.__bwd_seg
t0 = x[0]
T = x[1]
isp = self.__sc.isp
veff = isp * G0
fwd_grid = t0 + T * self.__fwd_grid # days
bwd_grid = t0 + T * self.__bwd_grid # days
throttles = [x[3 + 3 * i : 6 + 3 * i] for i in range(n_seg)]
alphas = [min(1., np.linalg.norm(t)) for t in throttles]
times = np.concatenate((fwd_grid, bwd_grid))
rfwd, rbwd, vfwd, vbwd, mfwd, mbwd, ufwd, ubwd, fwd_dt, bwd_dt = self._propagate(x)
# Plotting the Sun, the Earth and the target
axis.scatter([0], [0], [0], color='y')
plot_planet(self.__earth, epoch(t0), units=units, legend=True, color=(0.7, 0.7, 1), ax=axis)
plot_planet(self.target, epoch(t0 + T), units=units, legend=True, color=(0.7, 0.7, 1), ax=axis)
# Forward propagation
xfwd = [0.0] * (fwd_seg + 1)
yfwd = [0.0] * (fwd_seg + 1)
zfwd = [0.0] * (fwd_seg + 1)
xfwd[0] = rfwd[0][0] / units
yfwd[0] = rfwd[0][1] / units
zfwd[0] = rfwd[0][2] / units
for i in range(fwd_seg):
plot_taylor(rfwd[i], vfwd[i], mfwd[i], ufwd[i], fwd_dt[i], MU_SUN, veff, N=10, units=units, color=(alphas[i], 0, 1-alphas[i]), ax=axis)
xfwd[i+1] = rfwd[i+1][0] / units
yfwd[i+1] = rfwd[i+1][1] / units
zfwd[i+1] = rfwd[i+1][2] / units
if plot_segments:
axis.scatter(xfwd[:-1], yfwd[:-1], zfwd[:-1], label='nodes', marker='o', s=1)
# Backward propagation
xbwd = [0.0] * (bwd_seg + 1)
ybwd = [0.0] * (bwd_seg + 1)
zbwd = [0.0] * (bwd_seg + 1)
xbwd[-1] = rbwd[-1][0] / units
ybwd[-1] = rbwd[-1][1] / units
zbwd[-1] = rbwd[-1][2] / units
for i in range(bwd_seg):
plot_taylor(rbwd[-i-1], vbwd[-i-1], mbwd[-i-1], ubwd[-i-1], -bwd_dt[-i-1], MU_SUN, veff, N=10, units=units, color=(alphas[-i-1], 0, 1-alphas[-i-1]), ax=axis)
xbwd[-i-2] = rbwd[-i-2][0] / units
ybwd[-i-2] = rbwd[-i-2][1] / units
zbwd[-i-2] = rbwd[-i-2][2] / units
if plot_segments:
axis.scatter(xbwd[1:], ybwd[1:], zbwd[1:], marker='o', s=1)
if ax is None: # show only if axis is not set
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 __init__(self,
seq=[jpl_lp('earth'),
jpl_lp('venus'),
jpl_lp('earth')],
n_seg=[10] * 2,
t0=[epoch(0), epoch(1000)],
tof=[[200, 500], [200, 500]],
vinf_dep=2.5,
vinf_arr=2.0,
mass=4000.0,
Tmax=1.0,
Isp=2000.0,
fb_rel_vel=6,
multi_objective=False,
high_fidelity=False):
"""
prob = mga_lt_nep(seq = [jpl_lp('earth'),jpl_lp('venus'),jpl_lp('earth')], n_seg = [10]*2,
t0 = [epoch(0),epoch(1000)], tof = [[200,500],[200,500]], vinf_dep=2.5, vinf_arr=2.0, mass=4000.0, Tmax=1.0, Isp=2000.0,
multi_objective = False, fb_rel_vel = 6, high_fidelity=False)
- seq: list of PyKEP.planet defining the encounter sequence for the trajectoty (including the initial planet)
- n_seg: list of integers containing the number of segments to be used for each leg (len(n_seg) = len(seq)-1)
- t0: list of PyKEP epochs defining the launch window
- tof: minimum and maximum time of each leg (days)
- vinf_dep: maximum launch hyperbolic velocity allowed (in km/sec)
- vinf_arr: maximum arrival hyperbolic velocity allowed (in km/sec)
- mass: spacecraft starting mass
- Tmax: maximum thrust
- Isp: engine specific impulse
- fb_rel_vel = determines the bounds on the maximum allowed relative velocity at all fly-bys (in km/sec)
- multi-objective: when True defines the problem as a multi-objective problem, returning total DV and time of flight
- high_fidelity = makes the trajectory computations slower, but actually dynamically feasible.
"""
# 1) We compute the problem dimensions .... and call the base problem constructor
self.__n_legs = len(seq) - 1
n_fb = self.__n_legs - 1
# 1a) The decision vector length
dim = 1 + self.__n_legs * 8 + sum(n_seg) * 3
# 1b) The total number of constraints (mismatch + fly-by + boundary + throttles
c_dim = self.__n_legs * 7 + n_fb * 2 + 2 + sum(n_seg)
# 1c) The number of inequality constraints (boundary + fly-by angle + throttles)
c_ineq_dim = 2 + n_fb + sum(n_seg)
# 1d) the number of objectives
f_dim = multi_objective + 1
# First we call the constructor for the base PyGMO problem
# As our problem is n dimensional, box-bounded (may be multi-objective), we write
# (dim, integer dim, number of obj, number of con, number of inequality con, tolerance on con violation)
super(mga_lt_nep, self).__init__(dim, 0, f_dim, c_dim, c_ineq_dim,
1e-4)
# 2) We then define some class data members
# public:
self.seq = seq
# private:
self.__n_seg = n_seg
self.__vinf_dep = vinf_dep * 1000
self.__vinf_arr = vinf_arr * 1000
self.__sc = spacecraft(mass, Tmax, Isp)
self.__leg = leg()
self.__leg.set_mu(MU_SUN)
self.__leg.set_spacecraft(self.__sc)
self.__leg.high_fidelity = high_fidelity
fb_rel_vel *= 1000
# 3) We compute the bounds
lb = [t0[0].mjd2000] + [
0, mass / 2, -fb_rel_vel, -fb_rel_vel, -fb_rel_vel, -fb_rel_vel,
-fb_rel_vel, -fb_rel_vel
] * self.__n_legs + [-1, -1, -1] * sum(self.__n_seg)
ub = [t0[1].mjd2000] + [
1, mass, fb_rel_vel, fb_rel_vel, fb_rel_vel, fb_rel_vel,
fb_rel_vel, fb_rel_vel
] * self.__n_legs + [1, 1, 1] * sum(self.__n_seg)
# 3a ... and account for the bounds on the vinfs......
lb[3:6] = [-self.__vinf_dep] * 3
ub[3:6] = [self.__vinf_dep] * 3
lb[-sum(self.__n_seg) * 3 - 3:-sum(self.__n_seg) *
3] = [-self.__vinf_arr] * 3
ub[-sum(self.__n_seg) * 3 - 3:-sum(self.__n_seg) *
3] = [self.__vinf_arr] * 3
# 3b... and for the time of flight
lb[1:1 + 8 * self.__n_legs:8] = [el[0] for el in tof]
ub[1:1 + 8 * self.__n_legs:8] = [el[1] for el in tof]
# 4) And we set the bounds
self.set_bounds(lb, ub)
def ic_from_mga_1dsm(self, x):
"""
x_lt = prob.ic_from_mga_1dsm(x_mga)
- x_mga: compatible trajectory as encoded by an mga_1dsm problem
Returns an initial guess for the low-thrust trajectory, converting the mga_1dsm solution x_dsm. The user
is responsible that x_mga makes sense (i.e. it is a viable mga_1dsm representation). The conversion is done by importing in the
low-thrust encoding a) the launch date b) all the legs durations, c) the in and out relative velocities at each planet.
All throttles are put to zero.
Example::
x_lt= prob.ic_from_mga_1dsm(x_mga)
"""
from math import pi, cos, sin, acos
from scipy.linalg import norm
from PyKEP import propagate_lagrangian, lambert_problem, DAY2SEC, fb_prop
retval = list([0.0] * self.dimension)
# 1 - we 'decode' the chromosome recording the various times of flight (days) in the list T
T = list([0] * (self.__n_legs))
for i in range(len(T)):
T[i] = log(x[2 + 4 * i])
total = sum(T)
T = [x[1] * time / total for time in T]
retval[0] = x[0]
for i in range(self.__n_legs):
retval[1 + 8 * i] = T[i]
retval[2 + 8 * i] = self.__sc.mass
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n_legs + 1))
r_P = list([None] * (self.__n_legs + 1))
v_P = list([None] * (self.__n_legs + 1))
DV = list([None] * (self.__n_legs + 1))
for i, planet in enumerate(self.seq):
t_P[i] = epoch(x[0] + sum(T[0:i]))
r_P[i], v_P[i] = self.seq[i].eph(t_P[i])
# 3 - We start with the first leg
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
Vinfx = x[3] * cos(phi) * cos(theta)
Vinfy = x[3] * cos(phi) * sin(theta)
Vinfz = x[3] * sin(phi)
retval[3:6] = [Vinfx, Vinfy, Vinfz]
v0 = [a + b for a, b in zip(v_P[0], [Vinfx, Vinfy, Vinfz])]
r, v = propagate_lagrangian(r_P[0], v0, x[4] * T[0] * DAY2SEC, MU_SUN)
# Lambert arc to reach seq[1]
dt = (1 - x[4]) * T[0] * DAY2SEC
l = lambert_problem(r, r_P[1], dt, MU_SUN)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
retval[6:9] = [a - b for a, b in zip(v_end_l, v_P[1])]
# 4 - And we proceed with each successive leg
for i in range(1, self.__n_legs):
# Fly-by
v_out = fb_prop(v_end_l, v_P[i],
x[7 + (i - 1) * 4] * self.seq[i].radius,
x[6 + (i - 1) * 4], self.seq[i].mu_self)
retval[3 + i * 8:6 +
i * 8] = [a - b for a, b in zip(v_out, v_P[i])]
# s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out,
x[8 + (i - 1) * 4] * T[i] * DAY2SEC,
MU_SUN)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[8 + (i - 1) * 4]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt, MU_SUN)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# DSM occuring at time nu2*T2
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
retval[6 + i * 8:9 +
i * 8] = [a - b for a, b in zip(v_end_l, v_P[i + 1])]
return retval
def _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 __init__(self,
seq=[jpl_lp('earth'), jpl_lp('venus'), jpl_lp('earth')],
n_seg=[10] * 2,
t0=[epoch(0), epoch(1000)],
tof=[[200, 500], [200, 500]],
vinf_dep=2.5,
vinf_arr=2.0,
mass=4000.0,
Tmax=1.0,
Isp=2000.0,
fb_rel_vel=6,
multi_objective=False,
high_fidelity=False):
"""
prob = mga_lt_nep(seq = [jpl_lp('earth'),jpl_lp('venus'),jpl_lp('earth')], n_seg = [10]*2,
t0 = [epoch(0),epoch(1000)], tof = [[200,500],[200,500]], Vinf_dep=2.5, Vinf_arr=2.0, mass=4000.0, Tmax=1.0, Isp=2000.0,
multi_objective = False, fb_rel_vel = 6, high_fidelity=False)
- seq: list of PyKEP.planet defining the encounter sequence for the trajectoty (including the initial planet)
- n_seg: list of integers containing the number of segments to be used for each leg (len(n_seg) = len(seq)-1)
- t0: list of PyKEP epochs defining the launch window
- tof: minimum and maximum time of each leg (days)
- vinf_dep: maximum launch hyperbolic velocity allowed (in km/sec)
- vinf_arr: maximum arrival hyperbolic velocity allowed (in km/sec)
- mass: spacecraft starting mass
- Tmax: maximum thrust
- Isp: engine specific impulse
- fb_rel_vel = determines the bounds on the maximum allowed relative velocity at all fly-bys (in km/sec)
- multi-objective: when True defines the problem as a multi-objective problem, returning total DV and time of flight
- high_fidelity = makes the trajectory computations slower, but actually dynamically feasible.
"""
# 1) We compute the problem dimensions .... and call the base problem constructor
self.__n_legs = len(seq) - 1
n_fb = self.__n_legs - 1
# 1a) The decision vector length
dim = 1 + self.__n_legs * 8 + sum(n_seg) * 3
# 1b) The total number of constraints (mismatch + fly-by + boundary + throttles
c_dim = self.__n_legs * 7 + n_fb * 2 + 2 + sum(n_seg)
# 1c) The number of inequality constraints (boundary + fly-by angle + throttles)
c_ineq_dim = 2 + n_fb + sum(n_seg)
# 1d) the number of objectives
f_dim = multi_objective + 1
# First we call the constructor for the base PyGMO problem
# As our problem is n dimensional, box-bounded (may be multi-objective), we write
# (dim, integer dim, number of obj, number of con, number of inequality con, tolerance on con violation)
super(mga_lt_nep, self).__init__(dim, 0, f_dim, c_dim, c_ineq_dim, 1e-4)
# 2) We then define some class data members
# public:
self.seq = seq
# private:
self.__n_seg = n_seg
self.__vinf_dep = vinf_dep * 1000
self.__vinf_arr = vinf_arr * 1000
self.__sc = spacecraft(mass, Tmax, Isp)
self.__leg = leg()
self.__leg.set_mu(MU_SUN)
self.__leg.set_spacecraft(self.__sc)
self.__leg.high_fidelity = high_fidelity
fb_rel_vel *= 1000
# 3) We compute the bounds
lb = [t0[0].mjd2000] + [0, mass / 2, -fb_rel_vel, -fb_rel_vel, -fb_rel_vel, -fb_rel_vel, -fb_rel_vel, -fb_rel_vel] * self.__n_legs + [-1, -1, -1] * sum(self.__n_seg)
ub = [t0[1].mjd2000] + [1, mass, fb_rel_vel, fb_rel_vel, fb_rel_vel, fb_rel_vel, fb_rel_vel, fb_rel_vel] * self.__n_legs + [1, 1, 1] * sum(self.__n_seg)
# 3a ... and account for the bounds on the vinfs......
lb[3:6] = [-self.__vinf_dep] * 3
ub[3:6] = [self.__vinf_dep] * 3
lb[-sum(self.__n_seg) * 3 - 3:-sum(self.__n_seg) * 3] = [-self.__vinf_arr] * 3
ub[-sum(self.__n_seg) * 3 - 3:-sum(self.__n_seg) * 3] = [self.__vinf_arr] * 3
# 3b... and for the time of flight
lb[1:1 + 8 * self.__n_legs:8] = [el[0] for el in tof]
ub[1:1 + 8 * self.__n_legs:8] = [el[1] for el in tof]
# 4) And we set the bounds
self.set_bounds(lb, ub)
def ic_from_mga_1dsm(self, x):
"""
x_lt = prob.ic_from_mga_1dsm(x_mga)
- x_mga: compatible trajectory as encoded by an mga_1dsm problem
Returns an initial guess for the low-thrust trajectory, converting the mga_1dsm solution x_dsm. The user
is responsible that x_mga makes sense (i.e. it is a viable mga_1dsm representation). The conversion is done by importing in the
low-thrust encoding a) the launch date b) all the legs durations, c) the in and out relative velocities at each planet.
All throttles are put to zero.
Example::
x_lt= prob.ic_from_mga_1dsm(x_mga)
"""
from math import pi, cos, sin, acos
from scipy.linalg import norm
from PyKEP import propagate_lagrangian, lambert_problem, DAY2SEC, fb_prop
retval = list([0.0] * self.dimension)
# 1 - we 'decode' the chromosome recording the various times of flight (days) in the list T
T = list([0] * (self.__n_legs))
for i in range(len(T)):
T[i] = log(x[2 + 4 * i])
total = sum(T)
T = [x[1] * time / total for time in T]
retval[0] = x[0]
for i in range(self.__n_legs):
retval[1 + 8 * i] = T[i]
retval[2 + 8 * i] = self.__sc.mass
# 2 - We compute the epochs and ephemerides of the planetary encounters
t_P = list([None] * (self.__n_legs + 1))
r_P = list([None] * (self.__n_legs + 1))
v_P = list([None] * (self.__n_legs + 1))
DV = list([None] * (self.__n_legs + 1))
for i, planet in enumerate(self.seq):
t_P[i] = epoch(x[0] + sum(T[0:i]))
r_P[i], v_P[i] = self.seq[i].eph(t_P[i])
# 3 - We start with the first leg
theta = 2 * pi * x[1]
phi = acos(2 * x[2] - 1) - pi / 2
Vinfx = x[3] * cos(phi) * cos(theta)
Vinfy = x[3] * cos(phi) * sin(theta)
Vinfz = x[3] * sin(phi)
retval[3:6] = [Vinfx, Vinfy, Vinfz]
v0 = [a + b for a, b in zip(v_P[0], [Vinfx, Vinfy, Vinfz])]
r, v = propagate_lagrangian(r_P[0], v0, x[4] * T[0] * DAY2SEC, MU_SUN)
# Lambert arc to reach seq[1]
dt = (1 - x[4]) * T[0] * DAY2SEC
l = lambert_problem(r, r_P[1], dt, MU_SUN)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
retval[6:9] = [a - b for a, b in zip(v_end_l, v_P[1])]
# 4 - And we proceed with each successive leg
for i in range(1, self.__n_legs):
# Fly-by
v_out = fb_prop(v_end_l, v_P[i], x[7 + (i - 1) * 4] * self.seq[i].radius, x[6 + (i - 1) * 4], self.seq[i].mu_self)
retval[3 + i * 8:6 + i * 8] = [a - b for a, b in zip(v_out, v_P[i])]
# s/c propagation before the DSM
r, v = propagate_lagrangian(r_P[i], v_out, x[8 + (i - 1) * 4] * T[i] * DAY2SEC, MU_SUN)
# Lambert arc to reach Earth during (1-nu2)*T2 (second segment)
dt = (1 - x[8 + (i - 1) * 4]) * T[i] * DAY2SEC
l = lambert_problem(r, r_P[i + 1], dt, MU_SUN)
v_end_l = l.get_v2()[0]
v_beg_l = l.get_v1()[0]
# DSM occuring at time nu2*T2
DV[i] = norm([a - b for a, b in zip(v_beg_l, v)])
retval[6 + i * 8:9 + i * 8] = [a - b for a, b in zip(v_end_l, v_P[i + 1])]
return retval
def 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 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 plot_dists_thrust(self, x, ax=None):
"""
ax = prob.plot_dists_thrust(self, x, ax=None)
- x: encoded trajectory
- [out] ax: matplotlib axis where to plot
Plots the distance of the spacecraft from the Earth/Sun and the thrust profile
"""
import matplotlib as mpl
import matplotlib.pyplot as plt
# Creating the axis if necessary
if ax is None:
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
axis = fig.add_subplot(111)
else:
axis = ax
n_seg = self.__n_seg
fwd_seg = self.__fwd_seg
bwd_seg = self.__bwd_seg
t0 = x[0]
T = x[1]
fwd_grid = t0 + T * self.__fwd_grid # days
bwd_grid = t0 + T * self.__bwd_grid # days
throttles = [x[3 + 3 * i : 6 + 3 * i] for i in range(n_seg)]
thrusts = [min(1., np.linalg.norm(t)) for t in throttles]
thrusts.append(thrusts[-1]) # duplicate the last for plotting
dist_earth = [0.0] * (n_seg + 2) # distances spacecraft - Earth
dist_sun = [0.0] * (n_seg + 2) # distances spacecraft - Sun
times = np.concatenate((fwd_grid, bwd_grid))
rfwd, rbwd, vfwd, vbwd, mfwd, mbwd, ufwd, ubwd, fwd_dt, bwd_dt = self._propagate(x)
# Forward propagation
xfwd = [0.0] * (fwd_seg + 1)
yfwd = [0.0] * (fwd_seg + 1)
zfwd = [0.0] * (fwd_seg + 1)
xfwd[0] = rfwd[0][0] / AU
yfwd[0] = rfwd[0][1] / AU
zfwd[0] = rfwd[0][2] / AU
r_E = [ri/AU for ri in self.__earth.eph(epoch(fwd_grid[0]))[0]]
dist_earth[0] = np.linalg.norm([r_E[0]-xfwd[0], r_E[1]-yfwd[0], r_E[2]-zfwd[0]])
dist_sun[0] = np.linalg.norm([xfwd[0], yfwd[0], zfwd[0]])
for i in range(fwd_seg):
xfwd[i+1] = rfwd[i+1][0] / AU
yfwd[i+1] = rfwd[i+1][1] / AU
zfwd[i+1] = rfwd[i+1][2] / AU
r_E = [ri/AU for ri in self.__earth.eph(epoch(fwd_grid[i+1]))[0]]
dist_earth[i+1] = np.linalg.norm([r_E[0]-xfwd[i+1], r_E[1]-yfwd[i+1], r_E[2]-zfwd[i+1]])
dist_sun[i+1] = np.linalg.norm([xfwd[i+1], yfwd[i+1], zfwd[i+1]])
# Backward propagation
xbwd = [0.0] * (bwd_seg + 1)
ybwd = [0.0] * (bwd_seg + 1)
zbwd = [0.0] * (bwd_seg + 1)
xbwd[-1] = rbwd[-1][0] / AU
ybwd[-1] = rbwd[-1][1] / AU
zbwd[-1] = rbwd[-1][2] / AU
r_E = [ri/AU for ri in self.__earth.eph(epoch(bwd_grid[-1]))[0]]
dist_earth[-1] = np.linalg.norm([r_E[0]-xbwd[-1], r_E[1]-ybwd[-1], r_E[2]-zbwd[-1]])
dist_sun[-1] = np.linalg.norm([xbwd[-1], ybwd[-1], zbwd[-1]])
for i in range(bwd_seg):
xbwd[-i-2] = rbwd[-i-2][0] / AU
ybwd[-i-2] = rbwd[-i-2][1] / AU
zbwd[-i-2] = rbwd[-i-2][2] / AU
r_E = [ri/AU for ri in self.__earth.eph(epoch(bwd_grid[-i-2]))[0]]
dist_earth[-i-2] = np.linalg.norm([r_E[0]-xbwd[-i-2], r_E[1]-ybwd[-i-2], r_E[2]-zbwd[-i-2]])
dist_sun[-i-2] = np.linalg.norm([xbwd[-i-2], ybwd[-i-2], zbwd[-i-2]])
axis.set_xlabel("t [mjd2000]")
# Plot Earth distance
axis.plot(times,dist_earth, c = 'b', label = "sc-Earth")
# Plot Sun distance
axis.plot(times,dist_sun, c = 'y', label = "sc-Sun")
axis.set_ylabel("distance [AU]", color = 'k')
axis.set_ylim(bottom = 0.)
axis.tick_params('y', colors = 'k')
axis.legend(loc=2)
# draw threshold where Earth gravity equals 0.1*Tmax
axis.axhline(y = np.sqrt(MU_EARTH * self.__sc.mass / (self.__sc.thrust * 0.1)) / AU, c = 'g', ls = ":", lw = 1)
# Plot thrust profile
axis = axis.twinx()
axis.step(np.concatenate((fwd_grid, bwd_grid[1:])), thrusts, where = "post", c = 'r', linestyle = '--')
axis.set_ylabel("T/Tmax",color='r')
axis.tick_params('y',colors='r')
axis.set_xlim([times[0],times[-1]])
axis.set_ylim([0,1.2])
if ax is None: # show only if axis is not set
plt.show()
return axis
def __init__(self,
target = jpl_lp('mars'),
n_seg = 20,
grid_type = "uniform",
t0 = [epoch(0), epoch(1000)],
tof = [200, 500],
m0 = 50.0,
Tmax = 0.001,
Isp = 2000.0,
earth_gravity = False,
start = "earth"):
"""
prob = lt_margo(target = jpl_lp('mars'), n_seg = 20, grid_type = "uniform", t0 = [epoch(0), epoch(1000)],
tof = [200, 500], m0 = 50.0, Tmax = 0.001, Isp = 2000.0, earth_gravity = False, start = "earth")
- target: target PyKEP.planet
- n_seg: number of segments
- grid_type: "uniform" for uniform segments, "nonuniform" for a denser grid in the first part of the trajectory
- t0: list of two epochs defining the launch window
- tof: list of two floats definind the minimum and maximum time of flight (days)
- m0: initial mass of the spacecraft
- Tmax: maximum thrust
- Isp: engine specific impulse
- earth_gravity: boolean specifying whether to take Earth's gravity into account
- start: starting point ("earth", "l1", or "l2").
.. note::
L1 and L2 are approximated as the points on the line connecting the Sun and the Earth at a distance of, respectively, 0.99 and 1.01 AU from the Sun.
.. note::
If the Earth's gravity is enabled, the starting point cannot be the Earth
"""
# Various checks
if start not in ["earth", "l1", "l2"]:
raise ValueError("start must be either 'earth', 'l1' or 'l2'")
if grid_type not in ["uniform", "nonuniform"]:
raise ValueError("grid_type must be either 'uniform' or 'nonuniform'")
if earth_gravity and start == "earth":
raise ValueError("If Earth gravity is enabled the starting point cannot be the Earth")
# 1a) The decision vector length ([t0, tof, mf, [Tx,Ty,Tz] * n_seg])
dim = 3 + n_seg * 3
# 1b) The total number of constraints (mismatch + throttles)
c_dim = 7 + n_seg
# 1c) The number of inequality constraints (throttles)
c_ineq_dim = n_seg
# First we call the constructor for the base PyGMO problem
super(lt_margo, self).__init__(dim, 0, 1, c_dim, c_ineq_dim, 1e-4)
# 2) We then define some class data members
# public:
self.target = target
# private:
self.__n_seg = n_seg
self.__grid_type = grid_type # gridding function (must be 0 in 0, 1 in 1, and strictly increasing)
self.__sc = spacecraft(m0, Tmax, Isp)
self.__earth = jpl_lp('earth')
self.__earth_gravity = earth_gravity
self.__start = start
# grid construction
if grid_type == "uniform":
grid = np.array([i/n_seg for i in range(n_seg + 1)])
elif grid_type == "nonuniform":
grid_f = lambda x : x**2 if x<0.5 else 0.25+1.5*(x-0.5) # quadratic in [0,0.5], linear in [0.5,1]
grid = np.array([grid_f(i/n_seg) for i in range(n_seg + 1)])
fwd_seg = np.searchsorted(grid, 0.5, side='right') # index corresponding to the middle of the transfer
bwd_seg = n_seg - fwd_seg
fwd_grid = grid[:fwd_seg + 1]
bwd_grid = grid[fwd_seg:]
self.__fwd_seg = fwd_seg
self.__fwd_grid = fwd_grid
self.__fwd_dt = np.array([(fwd_grid[i+1] - fwd_grid[i]) for i in range(fwd_seg)]) * DAY2SEC
self.__bwd_seg = bwd_seg
self.__bwd_grid = bwd_grid
self.__bwd_dt = np.array([(bwd_grid[i+1] - bwd_grid[i]) for i in range(bwd_seg)]) * DAY2SEC
# 3) We compute the bounds
lb = [t0[0].mjd2000] + [tof[0]] + [0] + [-1, -1, -1] * n_seg
ub = [t0[1].mjd2000] + [tof[1]] + [m0] + [1, 1, 1] * n_seg
# 4) And we set the bounds
self.set_bounds(lb, ub)
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
def __init__(self,
start=jpl_lp('earth'),
target=jpl_lp('venus'),
N_max=3,
tof=[20., 400.],
vinf=[0., 4.],
phase_free=True,
multi_objective=False,
t0=None):
"""
prob = PyKEP.trajopt.pl2pl_N_impulses(start=jpl_lp('earth'), target=jpl_lp('venus'), N_max=3, tof=[20., 400.], vinf=[0., 4.], phase_free=True, multi_objective=False, t0=None)
- start: a PyKEP planet defining the starting orbit
- target: a PyKEP planet defining the target orbit
- N_max: maximum number of impulses
- tof: a list containing the box bounds [lower,upper] for the time of flight (days)
- vinf: a list containing the box bounds [lower,upper] for each DV magnitude (km/sec)
- phase_free: when True, no randezvous condition is enforced and the final orbit will be reached at an optimal true anomaly
- multi_objective: when True, a multi-objective problem is constructed with DV and time of flight as objectives
- t0: launch window defined as a list of two epochs [epoch,epoch]
"""
# Sanity checks
# 1) all planets need to have the same mu_central_body
if (start.mu_central_body != target.mu_central_body):
raise ValueError(
'Starting and ending PyKEP.planet must have the same mu_central_body'
)
# 2) Number of impulses must be at least 2
if N_max < 2:
raise ValueError('Number of impulses N is less than 2')
# 3) If phase_free is True, t0 does not make sense
if (t0 is None and not phase_free):
t0 = [epoch(0), epoch(1000)]
if (t0 is not None and phase_free):
raise ValueError('When phase_free is True no t0 can be specified')
# We compute the PyGMO problem dimensions
dim = 2 + 4 * (N_max - 2) + 1 + phase_free
obj_dim = multi_objective + 1
# First we call the constructor for the base PyGMO problem
# As our problem is n dimensional, box-bounded (may be multi-objective), we write
# (dim, integer dim, number of obj, number of con, number of inequality con, tolerance on con violation)
super(pl2pl_N_impulses, self).__init__(dim, 0, obj_dim, 0, 0, 0)
# We then define all class data members
self.start = start
self.target = target
self.N_max = N_max
self.phase_free = phase_free
self.multi_objective = multi_objective
self.__common_mu = start.mu_central_body
# And we compute the bounds
if phase_free:
lb = [start.ref_epoch.mjd2000, tof[0]
] + [0.0, 0.0, 0.0, vinf[0] * 1000] * (N_max - 2) + [0.0] + [
target.ref_epoch.mjd2000
]
ub = [
start.ref_epoch.mjd2000 + 2 * start.period * SEC2DAY, tof[1]
] + [1.0, 1.0, 1.0, vinf[1] * 1000] * (N_max - 2) + [1.0] + [
target.ref_epoch.mjd2000 + 2 * target.period * SEC2DAY
]
else:
lb = [t0[0].mjd2000, tof[0]
] + [0.0, 0.0, 0.0, vinf[0] * 1000] * (N_max - 2) + [0.0]
ub = [t0[1].mjd2000, tof[1]
] + [1.0, 1.0, 1.0, vinf[1] * 1000] * (N_max - 2) + [1.0]
# And we set them
self.set_bounds(lb, ub)
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 _propagate(self, x):
# 1 - We decode the chromosome
t0 = x[0]
T = x[1]
m_f = x[2]
# We extract the number of segments for forward and backward propagation
n_seg = self.__n_seg
fwd_seg = self.__fwd_seg
bwd_seg = self.__bwd_seg
# We extract information on the spacecraft
m_i = self.__sc.mass
max_thrust = self.__sc.thrust
isp = self.__sc.isp
veff = isp * G0
# And on the leg
throttles = [x[3 + 3 * i : 6 + 3 * i] for i in range(n_seg)]
# Return lists
n_points_fwd = fwd_seg + 1
n_points_bwd = bwd_seg + 1
rfwd = [[0.0] * 3] * (n_points_fwd)
vfwd = [[0.0] * 3] * (n_points_fwd)
mfwd = [0.0] * (n_points_fwd)
ufwd = [[0.0] * 3] * (fwd_seg)
rbwd = [[0.0] * 3] * (n_points_bwd)
vbwd = [[0.0] * 3] * (n_points_bwd)
mbwd = [0.0] * (n_points_bwd)
ubwd = [[0.0] * 3] * (bwd_seg)
# 2 - We compute the initial and final epochs and ephemerides
t_i = epoch(t0)
r_i, v_i = self.__earth.eph(t_i)
if self.__start == 'l1':
r_i = [r * 0.99 for r in r_i]
v_i = [v * 0.99 for v in v_i]
elif self.__start == 'l2':
r_i = [r * 1.01 for r in r_i]
v_i = [v * 1.01 for v in v_i]
t_f = epoch(t0 + T)
r_f, v_f = self.target.eph(t_f)
# 3 - Forward propagation
fwd_grid = t0 + T * self.__fwd_grid # days
fwd_dt = T * self.__fwd_dt # seconds
# Initial conditions
rfwd[0] = r_i
vfwd[0] = v_i
mfwd[0] = m_i
# Propagate
for i, t in enumerate(throttles[:fwd_seg]):
ufwd[i] = [max_thrust * thr for thr in t]
if self.__earth_gravity:
r_E, v_E = self.__earth.eph(epoch(fwd_grid[i]))
r_delta = [a - b for a,b in zip(r_E, rfwd[i])]
r3 = sum([r**2 for r in r_delta])**(3/2)
ufwd[i] = [ui + mfwd[i] * MU_EARTH / r3 * ri for ui,ri in zip(ufwd[i], r_delta)]
rfwd[i+1], vfwd[i+1], mfwd[i+1] = propagate_taylor(rfwd[i],vfwd[i],mfwd[i],ufwd[i],fwd_dt[i],MU_SUN,veff,-10,-10)
# 4 - Backward propagation
bwd_grid = t0 + T * self.__bwd_grid # days
bwd_dt = T * self.__bwd_dt # seconds
# Final conditions
rbwd[-1] = r_f
vbwd[-1] = v_f
mbwd[-1] = m_f
# Propagate
for i, t in enumerate(throttles[-1:-bwd_seg - 1:-1]):
ubwd[-i-1] = [max_thrust * thr for thr in t]
if self.__earth_gravity:
r_E, v_E = self.__earth.eph(epoch(bwd_grid[-i-1]))
r_delta = [a - b for a,b in zip(r_E, rbwd[-i-1])]
r3 = sum([r**2 for r in r_delta])**(3/2)
ubwd[-i-1] = [ui + mbwd[-i-1] * MU_EARTH / r3 * ri for ui,ri in zip(ubwd[-i-1], r_delta)]
rbwd[-i-2], vbwd[-i-2], mbwd[-i-2] = propagate_taylor(rbwd[-i-1],vbwd[-i-1],mbwd[-i-1],ubwd[-i-1],-bwd_dt[-i-1],MU_SUN,veff,-10,-10)
return rfwd, rbwd, vfwd, vbwd, mfwd, mbwd, ufwd, ubwd, fwd_dt, bwd_dt
def __init__(
self,
seq1=['earth', 'mars', 'ceres'],
seq2=['ceres', 'mars', 'earth'],
n_seg=[15] * 4,
t0=[epoch(11000), epoch(13000)],
tos=[200, 1000], # time of stay on planet
tof=[[40, 900]] * 4,
vinf_dep1=0.001,
vinf_arr1=0.001,
vinf_dep2=0.001,
vinf_arr2=5,
dm=400.0,
mass_end=700.0,
Tmax=0.4,
Isp=3800.0,
spacecrafts=None,
fb_rel_vel=6,
multi_objective=False,
high_fidelity=True,
solar_powered=True):
"""
prob = mga_lt_nep(seq = [jpl_lp('earth'),jpl_lp('venus'),jpl_lp('earth')], n_seg = [10]*2,
t0 = [epoch(0),epoch(1000)], tof = [[200,500],[200,500]], Vinf_dep=2.5, Vinf_arr=2.0, mass=4000.0, Tmax=1.0, Isp=2000.0,
multi_objective = False, fb_rel_vel = 6, high_fidelity=False)
- seq: list of PyKEP.planet defining the encounter sequence for the trajectoty (including the initial planet)
- n_seg: list of integers containing the number of segments to be used for each leg (len(n_seg) = len(seq)-1)
- t0: list of PyKEP epochs defining the launch window
- tof: minimum and maximum time of each leg (days)
- vinf_dep: maximum launch hyperbolic velocity allowed (in km/sec)
- vinf_arr: maximum arrival hyperbolic velocity allowed (in km/sec)
- mass: spacecraft starting mass
- Tmax: maximum thrust
- Isp: engine specific impulse
- fb_rel_vel = determines the bounds on the maximum allowed relative velocity at all fly-bys (in km/sec)
- multi-objective: when True defines the problem as a multi-objective problem, returning total DV and time of flight
- high_fidelity = makes the trajectory computations slower, but actually dynamically feasible.
"""
# We instanciate the sequences
if seq1[-1] != seq2[0]:
print 'Error : last planet of inbound and first planet of outbound must be the same'
else:
seq1 = self.make_sequence(seq1)
seq2 = self.make_sequence(seq2)
# 1) We compute the problem dimensions .... and call the base problem constructor
self.__n_legs = len(seq1) + len(seq2) - 2
n_fb = self.__n_legs - 2 # number of fylbys
# 1a) The decision vector length
dim = 1 + 1 + 1 + self.__n_legs * 8 + sum(n_seg) * 3
# 1b) The total number of constraints (mass + mismatch + fly-by + boundary + throttles
c_dim = 1 + self.__n_legs * 7 + n_fb * 2 + 4 + sum(n_seg)
# 1c) The number of inequality constraints (boundary + fly-by angle + throttles)
c_ineq_dim = 4 + n_fb + sum(n_seg)
# 1d) the number of objectives
f_dim = multi_objective + 1
# First we call the constructor for the base PyGMO problem
# As our problem is n dimensional, box-bounded (may be multi-objective), we write
# (dim, integer dim, number of obj, number of con, number of inequality con, tolerance on con violation)
super(mga_return_lt_nep, self).__init__(dim, 0, f_dim, c_dim,
c_ineq_dim, 1e-4)
# 2) We then define some class data members
# public:
self.seq1 = seq1
self.seq2 = seq2
# private:
self.__n_seg = n_seg
self.__vinf_dep1 = vinf_dep1 * 1000
self.__vinf_arr1 = vinf_arr1 * 1000
self.__vinf_dep2 = vinf_dep2 * 1000
self.__vinf_arr2 = vinf_arr2 * 1000
self.__mf = mass_end
self.__dm = dm
#Spacecaft(s)
if spacecrafts == None:
sc = spacecraft(mass_end, Tmax, Isp)
print "!!Spacecraft not defined (motors)!!"
#sc = spacecraft(mass_end, Tmax, Isp, 0.0000331,-0.0077, 9000, 2500, 29400, 300) #T6 x 2
#sc = spacecraft(mass_end, Tmax, Isp, 0.0000331,-0.0077, 9000, 2500, 25000, 300) #T6 x 2
self.__spacecrafts = [sc, sc]
elif len(spacecrafts) == 1:
print "Copying spacecraft twice"
self.__spacecrafts = [spacecrafts, spacecrafts]
elif len(spacecrafts) == 2:
self.__spacecrafts = spacecrafts
else:
print "!!Spacecraft definition does ot have the right size!!"
#sc = spacecraft(mass_end, Tmax, Isp, 0.0000331,-0.0077, 9000, 2500, 29400, 300) #T6 x 2
#sc = spacecraft(mass_end, Tmax, Isp, 0.0000331,-0.0077, 9000, 2500, 25000, 300) #T6 x 2
# T6 Qinetic x 2
#self.__sc = spacecraft(mass_end, Tmax, Isp, 0.0000331,-0.0077, 9000, 2500, 25000, 300)
#self.__sc = spacecraft(mass_end, Tmax, Isp, 0.00003333,-0.0072, 10000, 2000, 29400, 300)
#self.__sc = spacecraft(mass_end, Tmax, Isp,0.0000,0.2, 9000, 2500, 10000, 300)
self.__leg = leg()
self.__leg.set_mu(MU_SUN)
self.__leg.set_spacecraft(self.__spacecrafts[0])
self.__leg.high_fidelity = high_fidelity
self.__leg.solar_powered = solar_powered
fb_rel_vel *= 1000
# 3) We compute the bounds
lb = [t0[0].mjd2000] + [tos[0]] + [1000] + [
0, mass_end, -fb_rel_vel, -fb_rel_vel, -fb_rel_vel, -fb_rel_vel,
-fb_rel_vel, -fb_rel_vel
] * self.__n_legs + [-1, -1, -1] * sum(self.__n_seg)
ub = [t0[1].mjd2000] + [tos[1]] + [5000] + [
1, 5000, fb_rel_vel, fb_rel_vel, fb_rel_vel, fb_rel_vel,
fb_rel_vel, fb_rel_vel
] * self.__n_legs + [1, 1, 1] * sum(self.__n_seg)
# 3a ... and account for the bounds on the vinfs......
# 3a1 for departure 1
lb[5:8] = [-self.__vinf_dep1] * 3
ub[5:8] = [self.__vinf_dep1] * 3
# 3a2 for arrival 1
lb[5 + (len(seq1) - 2) * 8:8 +
(len(seq1) - 2) * 8] = [-self.__vinf_arr1] * 3
ub[5 + (len(seq1) - 2) * 8:8 +
(len(seq1) - 2) * 8] = [self.__vinf_arr1] * 3
# 3a3 for departure 2
lb[5 + (len(seq1) - 2 + 1) * 8:8 +
(len(seq1) - 2 + 1) * 8] = [-self.__vinf_dep2] * 3
ub[5 + (len(seq1) - 2 + 1) * 8:8 +
(len(seq1) - 2 + 1) * 8] = [self.__vinf_dep2] * 3
# 3a4 for arrival 2
lb[-sum(self.__n_seg) * 3 - 3:-sum(self.__n_seg) *
3] = [-self.__vinf_arr2] * 3
ub[-sum(self.__n_seg) * 3 - 3:-sum(self.__n_seg) *
3] = [self.__vinf_arr2] * 3
# 3b... and for the time of flight
lb[3:1 + 8 * self.__n_legs:8] = [el[0] for el in tof]
ub[3:1 + 8 * self.__n_legs:8] = [el[1] for el in tof]
# 4) And we set the bounds
self.set_bounds(lb, ub)
