def test_two_burn_orbit_raise_gl_rk_gl_constrained(self):
import numpy as np
import matplotlib.pyplot as plt
from openmdao.api import Problem, Group, pyOptSparseDriver, DirectSolver
from openmdao.utils.assert_utils import assert_rel_error
from openmdao.utils.general_utils import set_pyoptsparse_opt
from dymos import Phase, GaussLobatto, RungeKutta, Trajectory
from dymos.examples.finite_burn_orbit_raise.finite_burn_eom import FiniteBurnODE
traj = Trajectory()
p = Problem(model=Group())
p.model.add_subsystem('traj', traj)
p.driver = pyOptSparseDriver()
_, optimizer = set_pyoptsparse_opt('SNOPT', fallback=True)
p.driver.options['optimizer'] = optimizer
p.driver.options['dynamic_simul_derivs'] = True
traj.add_design_parameter('c', opt=False, val=1.5, units='DU/TU')
# First Phase (burn)
burn1 = Phase(ode_class=FiniteBurnODE,
transcription=GaussLobatto(num_segments=10, order=3, compressed=True))
burn1 = traj.add_phase('burn1', burn1)
burn1.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
burn1.set_state_options('r', fix_initial=True, fix_final=False)
burn1.set_state_options('theta', fix_initial=True, fix_final=False)
burn1.set_state_options('vr', fix_initial=True, fix_final=False)
burn1.set_state_options('vt', fix_initial=True, fix_final=False)
burn1.set_state_options('accel', fix_initial=True, fix_final=False)
burn1.set_state_options('deltav', fix_initial=True, fix_final=False)
burn1.add_control('u1', rate_continuity=True, rate2_continuity=True, units='deg',
scaler=0.01, lower=-30, upper=30)
# Second Phase (Coast)
coast = Phase(ode_class=FiniteBurnODE,
transcription=RungeKutta(num_segments=20, compressed=True))
traj.add_phase('coast', coast)
coast.set_time_options(initial_bounds=(0.5, 20), duration_bounds=(.5, 10), duration_ref=10)
coast.set_state_options('r', fix_initial=False, fix_final=False)
coast.set_state_options('theta', fix_initial=False, fix_final=False)
coast.set_state_options('vr', fix_initial=False, fix_final=False)
coast.set_state_options('vt', fix_initial=False, fix_final=False)
coast.set_state_options('accel', fix_initial=True, fix_final=False)
coast.set_state_options('deltav', fix_initial=False, fix_final=False)
coast.add_design_parameter('u1', opt=False, val=0.0)
# Third Phase (burn)
burn2 = Phase(ode_class=FiniteBurnODE,
transcription=GaussLobatto(num_segments=10, order=3, compressed=True))
traj.add_phase('burn2', burn2)
burn2.set_time_options(initial_bounds=(0.5, 20), duration_bounds=(.5, 10), initial_ref=10)
burn2.set_state_options('r', fix_initial=False, fix_final=True)
burn2.set_state_options('theta', fix_initial=False, fix_final=False)
burn2.set_state_options('vr', fix_initial=False, fix_final=True)
burn2.set_state_options('vt', fix_initial=False, fix_final=True)
burn2.set_state_options('accel', fix_initial=False, fix_final=False, defect_scaler=1.0)
burn2.set_state_options('deltav', fix_initial=False, fix_final=False, defect_scaler=1.0)
burn2.add_control('u1', rate_continuity=True, rate2_continuity=True, units='deg',
scaler=0.01, lower=-30, upper=30)
burn2.add_objective('deltav', loc='final', scaler=1.0)
burn1.add_timeseries_output('pos_x', units='DU')
coast.add_timeseries_output('pos_x', units='DU')
burn2.add_timeseries_output('pos_x', units='DU')
burn1.add_timeseries_output('pos_y', units='DU')
coast.add_timeseries_output('pos_y', units='DU')
burn2.add_timeseries_output('pos_y', units='DU')
# Link Phases
traj.link_phases(phases=['burn1', 'coast', 'burn2'],
vars=['time', 'r', 'theta', 'vr', 'vt', 'deltav'])
traj.link_phases(phases=['burn1', 'burn2'], vars=['accel'])
# Finish Problem Setup
p.model.linear_solver = DirectSolver()
p.setup(check=True, force_alloc_complex=True)
# Set Initial Guesses
p.set_val('traj.design_parameters:c', value=1.5)
p.set_val('traj.burn1.t_initial', value=0.0)
p.set_val('traj.burn1.t_duration', value=2.25)
p.set_val('traj.burn1.states:r',
value=burn1.interpolate(ys=[1, 1.5], nodes='state_input'))
p.set_val('traj.burn1.states:theta',
value=burn1.interpolate(ys=[0, 1.7], nodes='state_input'))
p.set_val('traj.burn1.states:vr',
value=burn1.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('traj.burn1.states:vt',
value=burn1.interpolate(ys=[1, 1], nodes='state_input'))
p.set_val('traj.burn1.states:accel',
value=burn1.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('traj.burn1.states:deltav',
value=burn1.interpolate(ys=[0, 0.1], nodes='state_input'), )
p.set_val('traj.burn1.controls:u1',
value=burn1.interpolate(ys=[-3.5, 13.0], nodes='control_input'))
p.set_val('traj.coast.t_initial', value=2.25)
p.set_val('traj.coast.t_duration', value=3.0)
p.set_val('traj.coast.states:r',
value=coast.interpolate(ys=[1.3, 1.5], nodes='state_input'))
p.set_val('traj.coast.states:theta',
value=coast.interpolate(ys=[2.1767, 1.7], nodes='state_input'))
p.set_val('traj.coast.states:vr',
value=coast.interpolate(ys=[0.3285, 0], nodes='state_input'))
p.set_val('traj.coast.states:vt',
value=coast.interpolate(ys=[0.97, 1], nodes='state_input'))
p.set_val('traj.coast.states:accel',
value=coast.interpolate(ys=[0, 0], nodes='state_input'))
# p.set_val('traj.coast.controls:u1',
# value=coast.interpolate(ys=[0, 0], nodes='control_input'))
p.set_val('traj.burn2.t_initial', value=5.25)
p.set_val('traj.burn2.t_duration', value=1.75)
p.set_val('traj.burn2.states:r',
value=burn2.interpolate(ys=[1.8, 3], nodes='state_input'))
p.set_val('traj.burn2.states:theta',
value=burn2.interpolate(ys=[3.2, 4.0], nodes='state_input'))
p.set_val('traj.burn2.states:vr',
value=burn2.interpolate(ys=[.5, 0], nodes='state_input'))
p.set_val('traj.burn2.states:vt',
value=burn2.interpolate(ys=[1, np.sqrt(1 / 3)], nodes='state_input'))
p.set_val('traj.burn2.states:accel',
value=burn2.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('traj.burn2.states:deltav',
value=burn2.interpolate(ys=[0.1, 0.2], nodes='state_input'))
p.set_val('traj.burn2.controls:u1',
value=burn2.interpolate(ys=[1, 1], nodes='control_input'))
p.run_driver()
assert_rel_error(self,
p.get_val('traj.burn2.timeseries.states:deltav')[-1],
0.3995,
tolerance=2.0E-3)
# Plot results
exp_out = traj.simulate()
fig = plt.figure(figsize=(8, 4))
fig.suptitle('Two Burn Orbit Raise Solution')
ax_u1 = plt.subplot2grid((2, 2), (0, 0))
ax_deltav = plt.subplot2grid((2, 2), (1, 0))
ax_xy = plt.subplot2grid((2, 2), (0, 1), rowspan=2)
span = np.linspace(0, 2 * np.pi, 100)
ax_xy.plot(np.cos(span), np.sin(span), 'k--', lw=1)
ax_xy.plot(3 * np.cos(span), 3 * np.sin(span), 'k--', lw=1)
ax_xy.set_xlim(-4.5, 4.5)
ax_xy.set_ylim(-4.5, 4.5)
ax_xy.set_xlabel('x ($R_e$)')
ax_xy.set_ylabel('y ($R_e$)')
ax_u1.set_xlabel('time ($TU$)')
ax_u1.set_ylabel('$u_1$ ($deg$)')
ax_u1.grid(True)
ax_deltav.set_xlabel('time ($TU$)')
ax_deltav.set_ylabel('${\Delta}v$ ($DU/TU$)')
ax_deltav.grid(True)
t_sol = dict((phs, p.get_val('traj.{0}.timeseries.time'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
x_sol = dict((phs, p.get_val('traj.{0}.timeseries.pos_x'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
y_sol = dict((phs, p.get_val('traj.{0}.timeseries.pos_y'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
dv_sol = dict((phs, p.get_val('traj.{0}.timeseries.states:deltav'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
u1_sol = dict((phs, p.get_val('traj.{0}.timeseries.controls:u1'.format(phs), units='deg'))
for phs in ['burn1', 'burn2'])
t_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.time'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
x_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.pos_x'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
y_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.pos_y'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
dv_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.states:deltav'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
u1_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.controls:u1'.format(phs),
units='deg'))
for phs in ['burn1', 'burn2'])
for phs in ['burn1', 'coast', 'burn2']:
try:
ax_u1.plot(t_sol[phs], u1_sol[phs], 'ro', ms=3)
ax_u1.plot(t_exp[phs], u1_exp[phs], 'b-')
except KeyError:
pass
ax_deltav.plot(t_sol[phs], dv_sol[phs], 'ro', ms=3)
ax_deltav.plot(t_exp[phs], dv_exp[phs], 'b-')
ax_xy.plot(x_sol[phs], y_sol[phs], 'ro', ms=3, label='implicit')
ax_xy.plot(x_exp[phs], y_exp[phs], 'b-', label='explicit')
plt.show()
def test_two_burn_orbit_raise_for_docs(self):
import numpy as np
import matplotlib.pyplot as plt
from openmdao.api import Problem, pyOptSparseDriver, DirectSolver, SqliteRecorder
from openmdao.utils.assert_utils import assert_rel_error
from openmdao.utils.general_utils import set_pyoptsparse_opt
from dymos import Phase, Trajectory
from dymos.examples.finite_burn_orbit_raise.finite_burn_eom import FiniteBurnODE
traj = Trajectory()
p = Problem(model=traj)
p.driver = pyOptSparseDriver()
_, optimizer = set_pyoptsparse_opt('SNOPT', fallback=False)
p.driver.options['optimizer'] = 'SNOPT'
p.driver.options['dynamic_simul_derivs'] = True
traj.add_design_parameter('c', opt=False, val=1.5)
# First Phase (burn)
burn1 = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=3,
compressed=True)
burn1 = traj.add_phase('burn1', burn1)
burn1.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
burn1.set_state_options('r',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('theta',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('vr',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('vt',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('accel', fix_initial=True, fix_final=False)
burn1.set_state_options('deltav', fix_initial=True, fix_final=False)
burn1.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg',
scaler=0.01,
rate_continuity_scaler=0.001,
rate2_continuity_scaler=0.001,
lower=-30,
upper=30)
# Second Phase (Coast)
coast = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=3,
compressed=True)
traj.add_phase('coast', coast)
coast.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10),
duration_ref=10)
coast.set_state_options('r',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('theta',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('vr',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('vt',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('accel', fix_initial=True, fix_final=True)
coast.set_state_options('deltav', fix_initial=False, fix_final=False)
coast.add_control('u1', opt=False, val=0.0, units='deg')
# Third Phase (burn)
burn2 = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=3,
compressed=True)
traj.add_phase('burn2', burn2)
burn2.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10),
initial_ref=10)
burn2.set_state_options('r',
fix_initial=False,
fix_final=True,
defect_scaler=100.0)
burn2.set_state_options('theta',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
burn2.set_state_options('vr',
fix_initial=False,
fix_final=True,
defect_scaler=100.0)
burn2.set_state_options('vt',
fix_initial=False,
fix_final=True,
defect_scaler=100.0)
burn2.set_state_options('accel',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.set_state_options('deltav',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg',
scaler=0.01,
rate_continuity_scaler=0.001,
rate2_continuity_scaler=0.001,
lower=-30,
upper=30)
burn2.add_objective('deltav', loc='final', scaler=1.0)
# Link Phases
traj.link_phases(phases=['burn1', 'coast', 'burn2'],
vars=['time', 'r', 'theta', 'vr', 'vt', 'deltav'])
traj.link_phases(phases=['burn1', 'burn2'], vars=['accel'])
# Finish Problem Setup
p.model.options['assembled_jac_type'] = 'csc'
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.driver.add_recorder(
SqliteRecorder('two_burn_orbit_raise_example_for_docs.db'))
p.setup(check=True)
# Set Initial Guesses
p.set_val('design_parameters:c', value=1.5)
p.set_val('burn1.t_initial', value=0.0)
p.set_val('burn1.t_duration', value=2.25)
p.set_val('burn1.states:r',
value=burn1.interpolate(ys=[1, 1.5], nodes='state_input'))
p.set_val('burn1.states:theta',
value=burn1.interpolate(ys=[0, 1.7], nodes='state_input'))
p.set_val('burn1.states:vr',
value=burn1.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('burn1.states:vt',
value=burn1.interpolate(ys=[1, 1], nodes='state_input'))
p.set_val('burn1.states:accel',
value=burn1.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val(
'burn1.states:deltav',
value=burn1.interpolate(ys=[0, 0.1], nodes='state_input'),
)
p.set_val('burn1.controls:u1',
value=burn1.interpolate(ys=[-3.5, 13.0],
nodes='control_input'))
p.set_val('coast.t_initial', value=2.25)
p.set_val('coast.t_duration', value=3.0)
p.set_val('coast.states:r',
value=coast.interpolate(ys=[1.3, 1.5], nodes='state_input'))
p.set_val('coast.states:theta',
value=coast.interpolate(ys=[2.1767, 1.7],
nodes='state_input'))
p.set_val('coast.states:vr',
value=coast.interpolate(ys=[0.3285, 0], nodes='state_input'))
p.set_val('coast.states:vt',
value=coast.interpolate(ys=[0.97, 1], nodes='state_input'))
p.set_val('coast.states:accel',
value=coast.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('coast.controls:u1',
value=coast.interpolate(ys=[0, 0], nodes='control_input'))
p.set_val('burn2.t_initial', value=5.25)
p.set_val('burn2.t_duration', value=1.75)
p.set_val('burn2.states:r',
value=burn2.interpolate(ys=[1, 3], nodes='state_input'))
p.set_val('burn2.states:theta',
value=burn2.interpolate(ys=[0, 4.0], nodes='state_input'))
p.set_val('burn2.states:vr',
value=burn2.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('burn2.states:vt',
value=burn2.interpolate(ys=[1, np.sqrt(1 / 3)],
nodes='state_input'))
p.set_val('burn2.states:accel',
value=burn2.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('burn2.states:deltav',
value=burn2.interpolate(ys=[0.1, 0.2], nodes='state_input'))
p.set_val('burn2.controls:u1',
value=burn2.interpolate(ys=[1, 1], nodes='control_input'))
p.run_driver()
assert_rel_error(self,
traj.get_values('deltav', flat=True)[-1],
0.3995,
tolerance=2.0E-3)
# Plot results
exp_out = traj.simulate(times=50, num_procs=3)
fig = plt.figure(figsize=(8, 4))
fig.suptitle('Two Burn Orbit Raise Solution')
ax_u1 = plt.subplot2grid((2, 2), (0, 0))
ax_deltav = plt.subplot2grid((2, 2), (1, 0))
ax_xy = plt.subplot2grid((2, 2), (0, 1), rowspan=2)
span = np.linspace(0, 2 * np.pi, 100)
ax_xy.plot(np.cos(span), np.sin(span), 'k--', lw=1)
ax_xy.plot(3 * np.cos(span), 3 * np.sin(span), 'k--', lw=1)
ax_xy.set_xlim(-4.5, 4.5)
ax_xy.set_ylim(-4.5, 4.5)
ax_xy.set_xlabel('x ($R_e$)')
ax_xy.set_ylabel('y ($R_e$)')
ax_u1.set_xlabel('time ($TU$)')
ax_u1.set_ylabel('$u_1$ ($deg$)')
ax_u1.grid(True)
ax_deltav.set_xlabel('time ($TU$)')
ax_deltav.set_ylabel('${\Delta}v$ ($DU/TU$)')
ax_deltav.grid(True)
t_sol = traj.get_values('time')
x_sol = traj.get_values('pos_x')
y_sol = traj.get_values('pos_y')
dv_sol = traj.get_values('deltav')
u1_sol = traj.get_values('u1', units='deg')
t_exp = exp_out.get_values('time')
x_exp = exp_out.get_values('pos_x')
y_exp = exp_out.get_values('pos_y')
dv_exp = exp_out.get_values('deltav')
u1_exp = exp_out.get_values('u1', units='deg')
for phase_name in ['burn1', 'coast', 'burn2']:
ax_u1.plot(t_sol[phase_name], u1_sol[phase_name], 'ro', ms=3)
ax_u1.plot(t_exp[phase_name], u1_exp[phase_name], 'b-')
ax_deltav.plot(t_sol[phase_name], dv_sol[phase_name], 'ro', ms=3)
ax_deltav.plot(t_exp[phase_name], dv_exp[phase_name], 'b-')
ax_xy.plot(x_sol[phase_name],
y_sol[phase_name],
'ro',
ms=3,
label='implicit' if phase_name == 'burn1' else None)
ax_xy.plot(x_exp[phase_name],
y_exp[phase_name],
'b-',
label='explicit' if phase_name == 'burn1' else None)
plt.show()
def two_burn_orbit_raise_problem(transcription='gauss-lobatto',
optimizer='SNOPT',
transcription_order=3,
compressed=True,
show_plots=False):
traj = Trajectory()
p = Problem(model=traj)
if optimizer == 'SNOPT':
p.driver = pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
p.driver.options['dynamic_simul_derivs'] = True
p.driver.opt_settings['Major iterations limit'] = 100
p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-6
p.driver.opt_settings['Major optimality tolerance'] = 1.0E-6
p.driver.opt_settings['iSumm'] = 6
else:
p.driver = pyOptSparseDriver()
p.driver.options['dynamic_simul_derivs'] = True
traj.add_design_parameter('c', opt=False, val=1.5, units='DU/TU')
# First Phase (burn)
burn1 = Phase(transcription,
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=transcription_order,
compressed=compressed)
burn1 = traj.add_phase('burn1', burn1)
burn1.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
burn1.set_state_options('r',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('theta',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('vr',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('vt',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('accel', fix_initial=True, fix_final=False)
burn1.set_state_options('deltav', fix_initial=True, fix_final=False)
burn1.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg',
scaler=0.01,
rate_continuity_scaler=0.001,
rate2_continuity_scaler=0.001,
lower=-30,
upper=30)
# Second Phase (Coast)
coast = Phase(transcription,
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=transcription_order,
compressed=compressed)
traj.add_phase('coast', coast)
coast.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10),
duration_ref=10)
coast.set_state_options('r',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('theta',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('vr',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('vt',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('accel', fix_initial=True, fix_final=True)
coast.set_state_options('deltav', fix_initial=False, fix_final=False)
coast.add_control('u1', opt=False, val=0.0, units='deg')
# Third Phase (burn)
burn2 = Phase(transcription,
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=transcription_order,
compressed=compressed)
traj.add_phase('burn2', burn2)
burn2.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10),
initial_ref=10)
burn2.set_state_options('r',
fix_initial=False,
fix_final=True,
defect_scaler=100.0)
burn2.set_state_options('theta',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
burn2.set_state_options('vr',
fix_initial=False,
fix_final=True,
defect_scaler=100.0)
burn2.set_state_options('vt',
fix_initial=False,
fix_final=True,
defect_scaler=100.0)
burn2.set_state_options('accel',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.set_state_options('deltav',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg',
scaler=0.01,
rate_continuity_scaler=0.001,
rate2_continuity_scaler=0.001,
lower=-10,
upper=10)
burn2.add_objective('deltav', loc='final', scaler=100.0)
# Link Phases
traj.link_phases(phases=['burn1', 'coast', 'burn2'],
vars=['time', 'r', 'theta', 'vr', 'vt', 'deltav'])
traj.link_phases(phases=['burn1', 'burn2'], vars=['accel'])
# Finish Problem Setup
p.model.options['assembled_jac_type'] = 'csc'
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.driver.add_recorder(SqliteRecorder('two_burn_orbit_raise_example.db'))
p.setup(check=True)
# Set Initial Guesses
p.set_val('design_parameters:c', value=1.5)
p.set_val('burn1.t_initial', value=0.0)
p.set_val('burn1.t_duration', value=2.25)
p.set_val('burn1.states:r',
value=burn1.interpolate(ys=[1, 1.5], nodes='state_input'))
p.set_val('burn1.states:theta',
value=burn1.interpolate(ys=[0, 1.7], nodes='state_input'))
p.set_val('burn1.states:vr',
value=burn1.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('burn1.states:vt',
value=burn1.interpolate(ys=[1, 1], nodes='state_input'))
p.set_val('burn1.states:accel',
value=burn1.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val(
'burn1.states:deltav',
value=burn1.interpolate(ys=[0, 0.1], nodes='state_input'),
)
p.set_val('burn1.controls:u1',
value=burn1.interpolate(ys=[-3.5, 13.0], nodes='control_input'))
p.set_val('coast.t_initial', value=2.25)
p.set_val('coast.t_duration', value=3.0)
p.set_val('coast.states:r',
value=coast.interpolate(ys=[1.3, 1.5], nodes='state_input'))
p.set_val('coast.states:theta',
value=coast.interpolate(ys=[2.1767, 1.7], nodes='state_input'))
p.set_val('coast.states:vr',
value=coast.interpolate(ys=[0.3285, 0], nodes='state_input'))
p.set_val('coast.states:vt',
value=coast.interpolate(ys=[0.97, 1], nodes='state_input'))
p.set_val('coast.states:accel',
value=coast.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('coast.controls:u1',
value=coast.interpolate(ys=[0, 0], nodes='control_input'))
p.set_val('burn2.t_initial', value=5.25)
p.set_val('burn2.t_duration', value=1.75)
p.set_val('burn2.states:r',
value=burn2.interpolate(ys=[1, 3], nodes='state_input'))
p.set_val('burn2.states:theta',
value=burn2.interpolate(ys=[0, 4.0], nodes='state_input'))
p.set_val('burn2.states:vr',
value=burn2.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('burn2.states:vt',
value=burn2.interpolate(ys=[1, np.sqrt(1 / 3)],
nodes='state_input'))
p.set_val('burn2.states:accel',
value=burn2.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('burn2.states:deltav',
value=burn2.interpolate(ys=[0.1, 0.2], nodes='state_input'))
p.set_val('burn2.controls:u1',
value=burn2.interpolate(ys=[1, 1], nodes='control_input'))
p.run_driver()
# Plot results
exp_out = traj.simulate(times=50, num_procs=3)
fig = plt.figure(figsize=(8, 4))
fig.suptitle('Two Burn Orbit Raise Solution')
ax_u1 = plt.subplot2grid((2, 2), (0, 0))
ax_deltav = plt.subplot2grid((2, 2), (1, 0))
ax_xy = plt.subplot2grid((2, 2), (0, 1), rowspan=2)
span = np.linspace(0, 2 * np.pi, 100)
ax_xy.plot(np.cos(span), np.sin(span), 'k--', lw=1)
ax_xy.plot(3 * np.cos(span), 3 * np.sin(span), 'k--', lw=1)
ax_xy.set_xlim(-4.5, 4.5)
ax_xy.set_ylim(-4.5, 4.5)
ax_xy.set_xlabel('x ($R_e$)')
ax_xy.set_ylabel('y ($R_e$)')
ax_u1.set_xlabel('time ($TU$)')
ax_u1.set_ylabel('$u_1$ ($deg$)')
ax_u1.grid(True)
ax_deltav.set_xlabel('time ($TU$)')
ax_deltav.set_ylabel('${\Delta}v$ ($DU/TU$)')
ax_deltav.grid(True)
t_sol = traj.get_values('time', flat=True)
x_sol = traj.get_values('pos_x', flat=True)
y_sol = traj.get_values('pos_y', flat=True)
dv_sol = traj.get_values('deltav', flat=True)
u1_sol = traj.get_values('u1', units='deg', flat=True)
t_exp = exp_out.get_values('time', flat=True)
x_exp = exp_out.get_values('pos_x', flat=True)
y_exp = exp_out.get_values('pos_y', flat=True)
dv_exp = exp_out.get_values('deltav', flat=True)
u1_exp = exp_out.get_values('u1', units='deg', flat=True)
ax_u1.plot(t_sol, u1_sol, 'ro', ms=3)
ax_u1.plot(t_exp, u1_exp, 'b-')
ax_deltav.plot(t_sol, dv_sol, 'ro', ms=3)
ax_deltav.plot(t_exp, dv_exp, 'b-')
ax_xy.plot(x_sol, y_sol, 'ro', ms=3, label='implicit')
ax_xy.plot(x_exp, y_exp, 'b-', label='explicit')
if show_plots:
plt.show()
return p
def instantiate_problem(self, idx):
traj = Trajectory()
p = Problem(model=traj)
# First Phase (burn)
burn1 = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=4,
transcription_order=3,
compressed=True)
traj.add_phase('burn1', burn1)
burn1.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
burn1.set_state_options('r', fix_initial=True, fix_final=False)
burn1.set_state_options('theta', fix_initial=True, fix_final=False)
burn1.set_state_options('vr',
fix_initial=True,
fix_final=False,
defect_scaler=0.1)
burn1.set_state_options('vt',
fix_initial=True,
fix_final=False,
defect_scaler=0.1)
burn1.set_state_options('accel', fix_initial=True, fix_final=False)
burn1.set_state_options('deltav', fix_initial=True, fix_final=False)
burn1.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg')
burn1.add_design_parameter('c', opt=False, val=1.5)
# Second Phase (Coast)
coast = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=3,
compressed=True)
traj.add_phase('coast', coast)
coast.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10))
coast.set_state_options('r', fix_initial=False, fix_final=False)
coast.set_state_options('theta', fix_initial=False, fix_final=False)
coast.set_state_options('vr', fix_initial=False, fix_final=False)
coast.set_state_options('vt', fix_initial=False, fix_final=False)
coast.set_state_options('accel', fix_initial=True, fix_final=True)
coast.set_state_options('deltav', fix_initial=False, fix_final=False)
coast.add_control('u1', opt=False, val=0.0, units='deg')
coast.add_design_parameter('c', opt=False, val=1.5)
# Third Phase (burn)
burn2 = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=3,
transcription_order=3,
compressed=True)
traj.add_phase('burn2', burn2)
burn2.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10))
burn2.set_state_options('r',
fix_initial=False,
fix_final=True,
defect_scaler=1.0)
burn2.set_state_options('theta',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.set_state_options('vr',
fix_initial=False,
fix_final=True,
defect_scaler=0.1)
burn2.set_state_options('vt',
fix_initial=False,
fix_final=True,
defect_scaler=0.1)
burn2.set_state_options('accel',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.set_state_options('deltav',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg',
ref0=0,
ref=10)
burn2.add_design_parameter('c', opt=False, val=1.5)
burn2.add_objective('deltav', loc='final')
# Link Phases
traj.link_phases(phases=['burn1', 'coast', 'burn2'],
vars=['time', 'r', 'theta', 'vr', 'vt', 'deltav'])
traj.link_phases(phases=['burn1', 'burn2'], vars=['accel'])
# Finish Problem Setup
p.model.options['assembled_jac_type'] = 'csc'
p.model.linear_solver = DirectSolver(assemble_jac=True)
rec_file = 'two_burn_orbit_raise_example_{0}.db'.format(idx)
p.driver.add_recorder(SqliteRecorder(rec_file))
p.setup(check=True)
# Set Initial Guesses
p.set_val('burn1.t_initial', value=0.0)
p.set_val('burn1.t_duration', value=2.25)
p.set_val('burn1.states:r',
value=burn1.interpolate(ys=[1, 1.5], nodes='state_input'))
p.set_val('burn1.states:theta',
value=burn1.interpolate(ys=[0, 1.7], nodes='state_input'))
p.set_val('burn1.states:vr',
value=burn1.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('burn1.states:vt',
value=burn1.interpolate(ys=[1, 1], nodes='state_input'))
p.set_val('burn1.states:accel',
value=burn1.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('burn1.states:deltav',
value=burn1.interpolate(ys=[0, 0.1], nodes='state_input'))
p.set_val('burn1.controls:u1',
value=burn1.interpolate(ys=[-3.5, 13.0],
nodes='control_input'))
p.set_val('burn1.design_parameters:c', value=1.5)
p.set_val('coast.t_initial', value=2.25)
p.set_val('coast.t_duration', value=3.0)
p.set_val('coast.states:r',
value=coast.interpolate(ys=[1.3, 1.5], nodes='state_input'))
p.set_val('coast.states:theta',
value=coast.interpolate(ys=[2.1767, 1.7],
nodes='state_input'))
p.set_val('coast.states:vr',
value=coast.interpolate(ys=[0.3285, 0], nodes='state_input'))
p.set_val('coast.states:vt',
value=coast.interpolate(ys=[0.97, 1], nodes='state_input'))
p.set_val('coast.states:accel',
value=coast.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('coast.controls:u1',
value=coast.interpolate(ys=[0, 0], nodes='control_input'))
p.set_val('coast.design_parameters:c', value=1.5)
p.set_val('burn2.t_initial', value=5.25)
p.set_val('burn2.t_duration', value=1.75)
p.set_val('burn2.states:r',
value=burn2.interpolate(ys=[1, 3], nodes='state_input'))
p.set_val('burn2.states:theta',
value=burn2.interpolate(ys=[0, 4.0], nodes='state_input'))
p.set_val('burn2.states:vr',
value=burn2.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('burn2.states:vt',
value=burn2.interpolate(ys=[1, np.sqrt(1 / 3)],
nodes='state_input'))
p.set_val('burn2.states:accel',
value=burn2.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('burn2.states:deltav',
value=burn2.interpolate(ys=[0.1, 0.2], nodes='state_input'))
p.set_val('burn2.controls:u1',
value=burn2.interpolate(ys=[1, 1], nodes='control_input'))
p.set_val('burn2.design_parameters:c', value=1.5)
p.run_model()
# Plot results
sim_rec_file = 'traj_sim_{0}.db'.format(idx)
exp_out = traj.simulate(times=50, record_file=sim_rec_file)
loaded_exp_out = load_simulation_results(sim_rec_file)
return exp_out, loaded_exp_out, rec_file, sim_rec_file