def plot(self, tof, N=60, units=AU, color="b", label=None, axes=None): from pykep.orbit_plots import plot_kepler plot_kepler(r0=self._r, v0=self._v, tof=tof, mu=self._mu, N=N, units=units, color=color, label=label, axes=axes)
def plot(self, x, axes=None): """ ax = prob.plot_trajectory(x, axes=None) - x: encoded trajectory - axes: matplotlib axis where to plot. If None figure and axis will be created - [out] ax: matplotlib axis where to plot Plots the trajectory represented by a decision vector x on the 3d axis ax Example:: ax = prob.plot(x) """ import matplotlib as mpl from mpl_toolkits.mplot3d import Axes3D import matplotlib.pyplot as plt from pykep.orbit_plots import plot_planet, plot_lambert, plot_kepler if axes is None: mpl.rcParams['legend.fontsize'] = 10 fig = plt.figure() axes = fig.gca(projection='3d') axes.scatter(0, 0, 0, color='y') # 1 - we 'decode' the chromosome recording the various deep space # manouvres timing (days) in the list T T = list([0] * (self.N_max - 1)) for i in range(len(T)): T[i] = log(x[2 + 4 * i]) total = sum(T) T = [x[1] * time / total for time in T] # 2 - We compute the starting and ending position r_start, v_start = self.start.eph(epoch(x[0])) if self.phase_free: r_target, v_target = self.target.eph(epoch(x[-1])) else: r_target, v_target = self.target.eph(epoch(x[0] + x[1])) plot_planet(self.start, t0=epoch(x[0]), color=(0.8, 0.6, 0.8), legend=True, units=AU, ax=axes, s=0) plot_planet(self.target, t0=epoch(x[0] + x[1]), color=(0.8, 0.6, 0.8), legend=True, units=AU, ax=axes, s=0) DV_list = x[5::4] maxDV = max(DV_list) DV_list = [s / maxDV * 30 for s in DV_list] colors = ['b', 'r'] * (len(DV_list) + 1) # 3 - We loop across inner impulses rsc = r_start vsc = v_start for i, time in enumerate(T[:-1]): theta = 2 * pi * x[3 + 4 * i] phi = acos(2 * x[4 + 4 * i] - 1) - pi / 2 Vinfx = x[5 + 4 * i] * cos(phi) * cos(theta) Vinfy = x[5 + 4 * i] * cos(phi) * sin(theta) Vinfz = x[5 + 4 * i] * sin(phi) # We apply the (i+1)-th impulse vsc = [a + b for a, b in zip(vsc, [Vinfx, Vinfy, Vinfz])] axes.scatter(rsc[0] / AU, rsc[1] / AU, rsc[2] / AU, color='k', s=DV_list[i]) plot_kepler(rsc, vsc, T[i] * DAY2SEC, self.__common_mu, N=200, color=colors[i], legend=False, units=AU, ax=axes) rsc, vsc = propagate_lagrangian(rsc, vsc, T[i] * DAY2SEC, self.__common_mu) cw = (ic2par(rsc, vsc, self.start.mu_central_body)[2] > pi / 2) # We now compute the remaining two final impulses # Lambert arc to reach seq[1] dt = T[-1] * DAY2SEC l = lambert_problem(rsc, r_target, dt, self.__common_mu, cw, False) plot_lambert(l, sol=0, color=colors[i + 1], legend=False, units=AU, ax=axes, N=200) v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] DV1 = norm([a - b for a, b in zip(v_beg_l, vsc)]) DV2 = norm([a - b for a, b in zip(v_end_l, v_target)]) axes.scatter(rsc[0] / AU, rsc[1] / AU, rsc[2] / AU, color='k', s=min(DV1 / maxDV * 30, 40)) axes.scatter(r_target[0] / AU, r_target[1] / AU, r_target[2] / AU, color='k', s=min(DV2 / maxDV * 30, 40)) return axes
def plot(self, x, ax=None): """ ax = prob.plot(x, ax=None) - x: encoded trajectory - ax: matplotlib axis where to plot. If None figure and axis will be created - [out] ax: matplotlib axis where to plot Plots the trajectory represented by a decision vector x on the 3d axis ax Example:: ax = prob.plot(x) """ import matplotlib as mpl from mpl_toolkits.mplot3d import Axes3D import matplotlib.pyplot as plt from pykep.orbit_plots import plot_planet, plot_lambert, plot_kepler if ax is None: mpl.rcParams['legend.fontsize'] = 10 fig = plt.figure() axis = fig.gca(projection='3d') else: axis = ax axis.scatter(0, 0, 0, color='y') # 1 - we 'decode' the chromosome recording the various times of flight # (days) in the list T and the cartesian components of vinf T, Vinfx, Vinfy, Vinfz = self._decode_times_and_vinf(x) # 2 - We compute the epochs and ephemerides of the planetary encounters t_P = list([None] * (self.n_legs + 1)) r_P = list([None] * (self.n_legs + 1)) v_P = list([None] * (self.n_legs + 1)) DV = list([None] * (self.n_legs + 1)) for i, planet in enumerate(self._seq): t_P[i] = epoch(x[0] + sum(T[0:i])) r_P[i], v_P[i] = planet.eph(t_P[i]) plot_planet(planet, t0=t_P[i], color=(0.8, 0.6, 0.8), legend=True, units=AU, axes=axis, N=150) # 3 - We start with the first leg v0 = [a + b for a, b in zip(v_P[0], [Vinfx, Vinfy, Vinfz])] r, v = propagate_lagrangian(r_P[0], v0, x[4] * T[0] * DAY2SEC, self.common_mu) plot_kepler(r_P[0], v0, x[4] * T[0] * DAY2SEC, self.common_mu, N=100, color='b', legend=False, units=AU, axes=axis) # Lambert arc to reach seq[1] dt = (1 - x[4]) * T[0] * DAY2SEC l = lambert_problem(r, r_P[1], dt, self.common_mu, False, False) plot_lambert(l, sol=0, color='r', legend=False, units=AU, axes=axis) v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] # First DSM occuring at time nu1*T1 DV[0] = norm([a - b for a, b in zip(v_beg_l, v)]) # 4 - And we proceed with each successive leg for i in range(1, self.n_legs): # Fly-by v_out = fb_prop(v_end_l, v_P[i], x[7 + (i - 1) * 4] * self._seq[i].radius, x[6 + (i - 1) * 4], self._seq[i].mu_self) # s/c propagation before the DSM r, v = propagate_lagrangian(r_P[i], v_out, x[8 + (i - 1) * 4] * T[i] * DAY2SEC, self.common_mu) plot_kepler(r_P[i], v_out, x[8 + (i - 1) * 4] * T[i] * DAY2SEC, self.common_mu, N=100, color='b', legend=False, units=AU, axes=axis) # Lambert arc to reach Earth during (1-nu2)*T2 (second segment) dt = (1 - x[8 + (i - 1) * 4]) * T[i] * DAY2SEC l = lambert_problem(r, r_P[i + 1], dt, self.common_mu, False, False) plot_lambert(l, sol=0, color='r', legend=False, units=AU, N=1000, axes=axis) v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] # DSM occuring at time nu2*T2 DV[i] = norm([a - b for a, b in zip(v_beg_l, v)]) plt.show() return axis
def plot(self, x, axes=None): """ ax = prob.plot_trajectory(x, axes=None) - x: encoded trajectory - axes: matplotlib axis where to plot. If None figure and axis will be created - [out] ax: matplotlib axis where to plot Plots the trajectory represented by a decision vector x on the 3d axis ax Example:: ax = prob.plot(x) """ import matplotlib as mpl from mpl_toolkits.mplot3d import Axes3D import matplotlib.pyplot as plt from pykep.orbit_plots import plot_planet, plot_lambert, plot_kepler if axes is None: mpl.rcParams['legend.fontsize'] = 10 fig = plt.figure() axes = fig.gca(projection='3d') axes.scatter(0, 0, 0, color='y') # 1 - we 'decode' the chromosome recording the various deep space # manouvres timing (days) in the list T T = list([0] * (self.N_max - 1)) for i in range(len(T)): T[i] = log(x[2 + 4 * i]) total = sum(T) T = [x[1] * time / total for time in T] # 2 - We compute the starting and ending position r_start, v_start = self.start.eph(epoch(x[0])) if self.phase_free: r_target, v_target = self.target.eph(epoch(x[-1])) else: r_target, v_target = self.target.eph(epoch(x[0] + x[1])) plot_planet(self.start, t0=epoch(x[0]), color=( 0.8, 0.6, 0.8), legend=True, units=AU, ax=axes, s=0) plot_planet(self.target, t0=epoch( x[0] + x[1]), color=(0.8, 0.6, 0.8), legend=True, units=AU, ax=axes, s=0) DV_list = x[5::4] maxDV = max(DV_list) DV_list = [s / maxDV * 30 for s in DV_list] colors = ['b', 'r'] * (len(DV_list) + 1) # 3 - We loop across inner impulses rsc = r_start vsc = v_start for i, time in enumerate(T[:-1]): theta = 2 * pi * x[3 + 4 * i] phi = acos(2 * x[4 + 4 * i] - 1) - pi / 2 Vinfx = x[5 + 4 * i] * cos(phi) * cos(theta) Vinfy = x[5 + 4 * i] * cos(phi) * sin(theta) Vinfz = x[5 + 4 * i] * sin(phi) # We apply the (i+1)-th impulse vsc = [a + b for a, b in zip(vsc, [Vinfx, Vinfy, Vinfz])] axes.scatter(rsc[0] / AU, rsc[1] / AU, rsc[2] / AU, color='k', s=DV_list[i]) plot_kepler(rsc, vsc, T[i] * DAY2SEC, self.__common_mu, N=200, color=colors[i], legend=False, units=AU, ax=axes) rsc, vsc = propagate_lagrangian( rsc, vsc, T[i] * DAY2SEC, self.__common_mu) cw = (ic2par(rsc, vsc, self.start.mu_central_body)[2] > pi / 2) # We now compute the remaining two final impulses # Lambert arc to reach seq[1] dt = T[-1] * DAY2SEC l = lambert_problem(rsc, r_target, dt, self.__common_mu, cw, False) plot_lambert(l, sol=0, color=colors[ i + 1], legend=False, units=AU, ax=axes, N=200) v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] DV1 = norm([a - b for a, b in zip(v_beg_l, vsc)]) DV2 = norm([a - b for a, b in zip(v_end_l, v_target)]) axes.scatter(rsc[0] / AU, rsc[1] / AU, rsc[2] / AU, color='k', s=min(DV1 / maxDV * 30, 40)) axes.scatter(r_target[0] / AU, r_target[1] / AU, r_target[2] / AU, color='k', s=min(DV2 / maxDV * 30, 40)) return axes
def plot(self, x, ax=None): """ ax = prob.plot(x, ax=None) - x: encoded trajectory - ax: matplotlib axis where to plot. If None figure and axis will be created - [out] ax: matplotlib axis where to plot Plots the trajectory represented by a decision vector x on the 3d axis ax Example:: ax = prob.plot(x) """ import matplotlib as mpl from mpl_toolkits.mplot3d import Axes3D import matplotlib.pyplot as plt from pykep.orbit_plots import plot_planet, plot_lambert, plot_kepler if ax is None: mpl.rcParams['legend.fontsize'] = 10 fig = plt.figure() axis = fig.gca(projection='3d') else: axis = ax axis.scatter(0, 0, 0, color='y') # 1 - we 'decode' the chromosome recording the various times of flight # (days) in the list T and the cartesian components of vinf T, Vinfx, Vinfy, Vinfz = self._decode_times_and_vinf(x) # 2 - We compute the epochs and ephemerides of the planetary encounters t_P = list([None] * (self.__n_legs + 1)) r_P = list([None] * (self.__n_legs + 1)) v_P = list([None] * (self.__n_legs + 1)) DV = list([None] * (self.__n_legs + 1)) for i, planet in enumerate(self.seq): t_P[i] = epoch(x[0] + sum(T[0:i])) r_P[i], v_P[i] = planet.eph(t_P[i]) plot_planet(planet, t0=t_P[i], color=( 0.8, 0.6, 0.8), legend=True, units=AU, ax=axis) # 3 - We start with the first leg v0 = [a + b for a, b in zip(v_P[0], [Vinfx, Vinfy, Vinfz])] r, v = propagate_lagrangian( r_P[0], v0, x[5] * T[0] * DAY2SEC, self.common_mu) plot_kepler(r_P[0], v0, x[5] * T[0] * DAY2SEC, self.common_mu, N=100, color='b', legend=False, units=AU, ax=axis) # Lambert arc to reach seq[1] dt = (1 - x[5]) * T[0] * DAY2SEC l = lambert_problem(r, r_P[1], dt, self.common_mu, False, False) plot_lambert(l, sol=0, color='r', legend=False, units=AU, ax=axis) v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] # First DSM occuring at time nu1*T1 DV[0] = norm([a - b for a, b in zip(v_beg_l, v)]) # 4 - And we proceed with each successive leg for i in range(1, self.__n_legs): # Fly-by v_out = fb_prop(v_end_l, v_P[i], x[ 8 + (i - 1) * 4] * self.seq[i].radius, x[7 + (i - 1) * 4], self.seq[i].mu_self) # s/c propagation before the DSM r, v = propagate_lagrangian( r_P[i], v_out, x[9 + (i - 1) * 4] * T[i] * DAY2SEC, self.common_mu) plot_kepler(r_P[i], v_out, x[9 + (i - 1) * 4] * T[i] * DAY2SEC, self.common_mu, N=100, color='b', legend=False, units=AU, ax=axis) # Lambert arc to reach Earth during (1-nu2)*T2 (second segment) dt = (1 - x[9 + (i - 1) * 4]) * T[i] * DAY2SEC l = lambert_problem(r, r_P[i + 1], dt, self.common_mu, False, False) plot_lambert(l, sol=0, color='r', legend=False, units=AU, N=1000, ax=axis) v_end_l = l.get_v2()[0] v_beg_l = l.get_v1()[0] # DSM occuring at time nu2*T2 DV[i] = norm([a - b for a, b in zip(v_beg_l, v)]) plt.show() return axis
def _fitness_impl(self, decoded_x, logging=False, plotting=False, ax=None): """ Computation of the objective function. """ saturn_distance_violated = 0 # decode x t0, u, v, dep_vinf, etas, T, betas, rps = decoded_x # convert incoming velocity vector theta, phi = 2.0 * pi * u, acos(2.0 * v - 1.0) - pi / 2.0 Vinfx = dep_vinf * cos(phi) * cos(theta) Vinfy = dep_vinf * cos(phi) * sin(theta) Vinfz = dep_vinf * sin(phi) # epochs and ephemerides of the planetary encounters t_P = list([None] * (self._n_legs + 1)) r_P = list([None] * (self._n_legs + 1)) v_P = list([None] * (self._n_legs + 1)) lamberts = list([None] * (self._n_legs)) v_outs = list([None] * (self._n_legs)) DV = list([0.0] * (self._n_legs + 1)) for i, planet in enumerate(self.seq): t_P[i] = epoch(t0 + sum(T[0:i])) r_P[i], v_P[i] = self.seq[i].eph(t_P[i]) # first leg v_outs[0] = [Vinfx, Vinfy, Vinfz] # bug fixed # check first leg up to DSM saturn_distance_violated += self.check_distance( r_P[0], v_outs[0], t0, etas[0] * T[0]) r, v = propagate_lagrangian(r_P[0], v_outs[0], etas[0] * T[0] * DAY2SEC, self.common_mu) # Lambert arc to reach seq[1] dt = (1.0 - etas[0]) * T[0] * DAY2SEC lamberts[0] = lambert_problem(r, r_P[1], dt, self.common_mu, self.cw, 0) v_end_l = lamberts[0].get_v2()[0] v_beg_l = lamberts[0].get_v1()[0] # First DSM occuring at time eta0*T0 DV[0] = norm([a - b for a, b in zip(v_beg_l, v)]) # checking first leg after DSM saturn_distance_violated += self.check_distance( r, v_beg_l, etas[0] * T[0], T[0]) # successive legs for i in range(1, self._n_legs): # Fly-by v_outs[i] = fb_prop(v_end_l, v_P[i], rps[i - 1] * self.seq[i].radius, betas[i - 1], self.seq[i].mu_self) # checking next leg up to DSM saturn_distance_violated += self.check_distance( r_P[i], v_outs[i], T[i - 1], etas[i] * T[i]) # s/c propagation before the DSM r, v = propagate_lagrangian(r_P[i], v_outs[i], etas[i] * T[i] * DAY2SEC, self.common_mu) # Lambert arc to reach next body dt = (1 - etas[i]) * T[i] * DAY2SEC lamberts[i] = lambert_problem(r, r_P[i + 1], dt, self.common_mu, self.cw, 0) v_end_l = lamberts[i].get_v2()[0] v_beg_l = lamberts[i].get_v1()[0] # DSM occuring at time eta_i*T_i DV[i] = norm([a - b for a, b in zip(v_beg_l, v)]) # checking next leg after DSM saturn_distance_violated += self.check_distance( r, v_beg_l, etas[i] * T[i], T[i]) # single dv penalty for now if saturn_distance_violated > 0: DV[-1] += DV_PENALTY arr_vinf = norm([a - b for a, b in zip(v_end_l, v_P[-1])]) # last Delta-v if self._add_vinf_arr: DV[-1] = arr_vinf if self._add_vinf_dep: DV[0] += dep_vinf # pretty printing if logging: print("First leg: {} to {}".format(self.seq[0].name, self.seq[1].name)) print("Departure: {0} ({1:0.6f} mjd2000)".format( t_P[0], t_P[0].mjd2000)) print("Duration: {0:0.6f}d".format(T[0])) print("VINF: {0:0.3f}m/s".format(dep_vinf)) print("DSM after {0:0.6f}d".format(etas[0] * T[0])) print("DSM magnitude: {0:0.6f}m/s".format(DV[0])) for i in range(1, self._n_legs): print("\nleg {}: {} to {}".format(i + 1, self.seq[i].name, self.seq[i + 1].name)) print("Duration: {0:0.6f}d".format(T[i])) print("Fly-by epoch: {0} ({1:0.6f} mjd2000)".format( t_P[i], t_P[i].mjd2000)) print("Fly-by radius: {0:0.6f} planetary radii".format(rps[i - 1])) print("DSM after {0:0.6f}d".format(etas[i] * T[i])) print("DSM magnitude: {0:0.6f}m/s".format(DV[i])) print("\nArrival at {}".format(self.seq[-1].name)) print("Arrival epoch: {0} ({1:0.6f} mjd2000)".format( t_P[-1], t_P[-1].mjd2000)) print("Arrival Vinf: {0:0.3f}m/s".format(arr_vinf)) print("Total mission time: {0:0.6f}d ({1:0.3f} years)".format( sum(T), sum(T) / 365.25)) # plotting if plotting: ax.scatter(0, 0, 0, color='chocolate') for i, planet in enumerate(self.seq): plot_planet(planet, t0=t_P[i], color=pl2c[planet.name], legend=True, units=AU, ax=ax) for i in range(0, self._n_legs): plot_kepler(r_P[i], v_outs[i], etas[i] * T[i] * DAY2SEC, self.common_mu, N=100, color='b', legend=False, units=AU, ax=ax) for l in lamberts: plot_lambert(l, sol=0, color='r', legend=False, units=AU, N=1000, ax=ax) # returning building blocks for objectives return (DV, T, arr_vinf, lamberts)