def test_simple_integration_forward_connected_initial(self):
p = om.Problem(model=om.Group())
traj = p.model.add_subsystem('traj', subsys=dm.Trajectory())
phase = dm.Phase(ode_class=TestODE, transcription=dm.RungeKutta(num_segments=200, method='RK4'))
traj.add_phase('phase0', phase)
phase.set_time_options(fix_initial=True, fix_duration=True, targets=['t'])
phase.add_state('y', fix_initial=False, connected_initial=True, targets=['y'], rate_source='ydot', units='m')
phase.add_timeseries_output('ydot', output_name='state_rate:y', units='m/s')
p.setup(check=True, force_alloc_complex=True)
p['traj.phase0.t_initial'] = 0.0
p['traj.phase0.t_duration'] = 2.0
# The initial guess of states at the segment boundaries
p['traj.phase0.states:y'] = 0.0
# The initial value of the states from which the integration proceeds
p['traj.phase0.initial_states:y'] = 0.5
p.run_model()
expected = _test_ode_solution(p['traj.phase0.ode.y'], p['traj.phase0.ode.t'])
assert_near_equal(p['traj.phase0.ode.y'], expected, tolerance=1.0E-3)
def test_simple_integration_backward_connected_initial(self):
p = om.Problem(model=om.Group())
phase = dm.Phase(ode_class=TestODE,
transcription=dm.RungeKutta(num_segments=200,
method='RK4'))
p.model.add_subsystem('phase0', subsys=phase)
phase.set_time_options(fix_initial=True, fix_duration=True)
phase.add_state('y', connected_initial=True)
phase.add_timeseries_output('ydot',
output_name='state_rate:y',
units='m/s')
p.setup(check=True, force_alloc_complex=True)
p['phase0.t_initial'] = 2.0
p['phase0.t_duration'] = -2.0
# The initial guess of state values at the segment boundaries
p['phase0.states:y'] = 0
# The initial value of the states from which the integration proceeds
p['phase0.initial_states:y'] = 5.305471950534675
p.run_model()
expected = np.atleast_2d(
_test_ode_solution(p['phase0.ode.y'], p['phase0.timeseries.time']))
assert_rel_error(self,
p['phase0.timeseries.states:y'],
expected,
tolerance=1.0E-3)
def test_simple_integration_forward_connected_initial_fixed_initial(self):
p = om.Problem(model=om.Group())
phase = dm.Phase(ode_class=TestODE,
transcription=dm.RungeKutta(num_segments=200,
method='RK4'))
p.model.add_subsystem('phase0', subsys=phase)
phase.set_time_options(fix_initial=True,
fix_duration=True,
targets=['t'])
phase.add_state('y',
fix_initial=True,
connected_initial=True,
targets=['y'],
rate_source='ydot',
units='m')
phase.add_timeseries_output('ydot',
output_name='state_rate:y',
units='m/s')
with self.assertRaises(ValueError) as e:
p.setup(check=True, force_alloc_complex=True)
expected = "Cannot specify 'fix_initial=True' and specify 'connected_initial=True' for " \
"state y in phase phase0."
self.assertEqual(str(e.exception), expected)
def test_load_case_rk4_to_lgl(self):
import openmdao.api as om
import dymos as dm
from openmdao.utils.assert_utils import assert_near_equal
p = setup_problem(dm.RungeKutta(num_segments=50))
# Solve for the optimal trajectory
dm.run_problem(p)
# Load the solution
case = om.CaseReader('dymos_solution.db').get_case('final')
# create a problem with a different transcription with a different number of variables
q = setup_problem(dm.GaussLobatto(num_segments=10))
# Load the values from the previous solution
dm.load_case(q, case)
# Run the model to ensure we find the same output values as those that we recorded
q.run_driver()
outputs = dict([
(o[0], o[1])
for o in case.list_outputs(units=True, shape=True, out_stream=None)
])
time_val = outputs['phase0.timeseries.time']['value']
theta_val = outputs['phase0.timeseries.controls:theta']['value']
assert_near_equal(q['phase0.timeseries.controls:theta'],
q.model.phase0.interpolate(xs=time_val,
ys=theta_val,
nodes='all'),
tolerance=1.0E-1)
def test_single_phase_reverse_propagation_rk(self):
prob = om.Problem()
num_seg = 10
seg_ends, _ = lgl(num_seg + 1)
# First phase: normal operation.
transcription = dm.RungeKutta(num_segments=num_seg)
phase0 = dm.Phase(ode_class=BatteryODE, transcription=transcription)
traj_p0 = prob.model.add_subsystem('phase0', phase0)
traj_p0.set_time_options(fix_initial=True, fix_duration=True)
traj_p0.add_state('state_of_charge',
fix_initial=True,
fix_final=False,
targets=['SOC'],
rate_source='dXdt:SOC')
prob.setup()
prob['phase0.t_initial'] = 0
prob['phase0.t_duration'] = -1.0 * 3600
prob['phase0.states:state_of_charge'][:] = 0.63464982
prob.set_solver_print(level=0)
prob.run_model()
soc0 = prob['phase0.states:state_of_charge']
assert_near_equal(soc0[-1], 1.0, 1e-6)
def test_simple_integration_forward(self):
p = om.Problem(model=om.Group())
phase = dm.Phase(ode_class=TestODE,
transcription=dm.RungeKutta(num_segments=200,
method='RK4'))
p.model.add_subsystem('phase0', subsys=phase)
phase.set_time_options(fix_initial=True,
fix_duration=True,
targets=['t'])
phase.add_state('y',
fix_initial=True,
targets=['y'],
rate_source='ydot',
units='m')
phase.add_timeseries_output('ydot',
output_name='state_rate:y',
units='m/s')
p.setup(check=True, force_alloc_complex=True)
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 2.0
p['phase0.states:y'] = 0.5
p.run_model()
expected = _test_ode_solution(p['phase0.ode.y'], p['phase0.ode.t'])
assert_near_equal(p['phase0.ode.y'], expected, tolerance=1.0E-3)
def _make_problem(self, transcription, num_seg, transcription_order=3):
p = om.Problem(model=om.Group())
p.driver = om.ScipyOptimizeDriver()
# Compute sparsity/coloring when run_driver is called
p.driver.declare_coloring()
t = {
'gauss-lobatto':
dm.GaussLobatto(num_segments=num_seg, order=transcription_order),
'radau-ps':
dm.Radau(num_segments=num_seg, order=transcription_order),
'runge-kutta':
dm.RungeKutta(num_segments=num_seg)
}
phase = dm.Phase(ode_class=_BrachistochroneTestODE,
transcription=t[transcription])
p.model.add_subsystem('phase0', phase)
phase.set_time_options(initial_bounds=(1, 1), duration_bounds=(.5, 10))
phase.add_state('x', fix_initial=True)
phase.add_state('y', fix_initial=True)
phase.add_state('v', fix_initial=True)
phase.add_control('theta',
units='deg',
rate_continuity=True,
lower=0.01,
upper=179.9)
phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665)
phase.add_boundary_constraint('x', loc='final', equals=10)
phase.add_boundary_constraint('y', loc='final', equals=5)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', scaler=10)
p.model.linear_solver = om.DirectSolver()
p.setup()
p['phase0.t_initial'] = 1.0
p['phase0.t_duration'] = 3.0
p['phase0.states:x'] = phase.interpolate(ys=[0, 10],
nodes='state_input')
p['phase0.states:y'] = phase.interpolate(ys=[10, 5],
nodes='state_input')
p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9],
nodes='state_input')
p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100.5],
nodes='control_input')
return p
def test_double_integrator_rk4(self, compressed=True):
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.declare_coloring()
t = dm.RungeKutta(num_segments=30, order=3, compressed=compressed)
traj = p.model.add_subsystem('traj', dm.Trajectory())
phase = traj.add_phase(
'phase0', dm.Phase(ode_class=DoubleIntegratorODE, transcription=t))
phase.set_time_options(fix_initial=True, fix_duration=True, units='s')
phase.add_state('v',
fix_initial=True,
fix_final=False,
rate_source='u',
shape=(1, ),
units='m/s')
phase.add_state('x', fix_initial=True, rate_source='v', units='m')
phase.add_control('u',
units='m/s**2',
scaler=0.01,
continuity=False,
rate_continuity=False,
rate2_continuity=False,
shape=(1, ),
lower=-1.0,
upper=1.0)
phase.add_boundary_constraint(name='v',
loc='final',
equals=0,
units='m/s')
# Maximize distance travelled in one second.
phase.add_objective('x', loc='final', scaler=-1)
p.model.linear_solver = om.DirectSolver()
p.setup(check=True)
p['traj.phase0.t_initial'] = 0.0
p['traj.phase0.t_duration'] = 1.0
p['traj.phase0.states:x'] = phase.interpolate(ys=[0, 0.25],
nodes='state_input')
p['traj.phase0.states:v'] = phase.interpolate(ys=[0, 0],
nodes='state_input')
p['traj.phase0.controls:u'] = phase.interpolate(ys=[1, -1],
nodes='control_input')
p.run_driver()
return p
def brachistochrone_min_time(transcription='gauss-lobatto', num_segments=8, transcription_order=3,
compressed=True, optimizer='SLSQP', simul_derivs=True):
p = Problem(model=Group())
# if optimizer == 'SNOPT':
p.driver = pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
p.driver.options['dynamic_simul_derivs'] = simul_derivs
if transcription == 'gauss-lobatto':
t = dm.GaussLobatto(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
elif transcription == 'radau-ps':
t = dm.Radau(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
elif transcription == 'runge-kutta':
t = dm.RungeKutta(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
phase = dm.Phase(ode_class=BrachistochroneODE, transcription=t)
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
phase.set_state_options('x', fix_initial=True, fix_final=False, solve_segments=False)
phase.set_state_options('y', fix_initial=True, fix_final=False, solve_segments=False)
phase.set_state_options('v', fix_initial=True, fix_final=False, solve_segments=False)
phase.add_control('theta', continuity=True, rate_continuity=True,
units='deg', lower=0.01, upper=179.9)
phase.add_input_parameter('g', units='m/s**2', val=9.80665)
phase.add_boundary_constraint('x', loc='final', equals=10)
phase.add_boundary_constraint('y', loc='final', equals=5)
# Minimize time at the end of the phase
phase.add_objective('time_phase', loc='final', scaler=10)
p.model.linear_solver = DirectSolver()
p.setup(check=True)
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 2.0
p['phase0.states:x'] = phase.interpolate(ys=[0, 10], nodes='state_input')
p['phase0.states:y'] = phase.interpolate(ys=[10, 5], nodes='state_input')
p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9], nodes='state_input')
p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100], nodes='control_input')
p['phase0.input_parameters:g'] = 9.80665
p.run_driver()
return p
def test_load_case_lgl_to_rk4(self):
import openmdao.api as om
import dymos as dm
from openmdao.utils.assert_utils import assert_rel_error
from scipy.interpolate import interp1d
import numpy as np
p = setup_problem(dm.GaussLobatto(num_segments=20))
# Solve for the optimal trajectory
p.run_driver()
# Load the solution
cr = om.CaseReader('brachistochrone_solution.db')
system_cases = cr.list_cases('root')
case = cr.get_case(system_cases[-1])
# create a problem with a different transcription with a different number of variables
q = setup_problem(dm.RungeKutta(num_segments=50))
# Load the values from the previous solution
dm.load_case(q, case)
# Run the model to ensure we find the same output values as those that we recorded
q.run_driver()
outputs = dict([
(o[0], o[1])
for o in case.list_outputs(units=True, shape=True, out_stream=None)
])
time_val = outputs['phase0.timeseries.time']['value'][:, 0]
theta_val = outputs['phase0.timeseries.controls:theta']['value'][:, 0]
nodup = np.insert(time_val[1:] != time_val[:-1], 0,
True) # remove duplicate times
time_val = time_val[nodup]
theta_val = theta_val[nodup]
q_time = q['phase0.timeseries.time'][:, 0]
q_theta = q['phase0.timeseries.controls:theta'][:, 0]
nodup = np.insert(q_time[1:] != q_time[:-1], 0,
True) # remove duplicate times
q_time = q_time[nodup]
q_theta = q_theta[nodup]
fq_theta = interp1d(q_time,
q_theta,
kind='cubic',
bounds_error=False,
fill_value='extrapolate')
assert_rel_error(self, fq_theta(time_val), theta_val, tolerance=1.0E-2)
def test_brachistochrone_undecorated_ode_rk(self):
import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
import openmdao.api as om
from openmdao.utils.assert_utils import assert_near_equal
import dymos as dm
p = om.Problem(model=om.Group())
p.driver = om.ScipyOptimizeDriver()
phase = dm.Phase(ode_class=BrachistochroneODE, transcription=dm.RungeKutta(num_segments=20))
p.model.add_subsystem('phase0', phase)
phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(.5, 10), units='s')
phase.add_state('x', fix_initial=True, rate_source='xdot', units='m')
phase.add_state('y', fix_initial=True, rate_source='ydot', units='m')
phase.add_state('v', fix_initial=True, rate_source='vdot', targets=['v'], units='m/s')
phase.add_control('theta', units='deg', rate_continuity=False, lower=0.01, upper=179.9, targets=['theta'])
phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665, targets=['g'])
phase.add_boundary_constraint('x', loc='final', equals=10)
phase.add_boundary_constraint('y', loc='final', equals=5)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', scaler=10)
p.model.linear_solver = om.DirectSolver()
p.setup()
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 2.0
p['phase0.states:x'] = phase.interpolate(ys=[0, 10], nodes='state_input')
p['phase0.states:y'] = phase.interpolate(ys=[10, 5], nodes='state_input')
p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9], nodes='state_input')
p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100.5], nodes='control_input')
# Solve for the optimal trajectory
p.run_driver()
# Test the results
assert_near_equal(p.get_val('phase0.timeseries.time')[-1], 1.8016, tolerance=1.0E-3)
def make_brachistochrone_phase(transcription='gauss-lobatto', num_segments=8, transcription_order=3,
compressed=True):
if transcription == 'gauss-lobatto':
t = dm.GaussLobatto(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
elif transcription == 'radau-ps':
t = dm.Radau(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
elif transcription == 'runge-kutta':
t = dm.RungeKutta(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
phase = dm.Phase(ode_class=BrachistochroneODE, transcription=t)
return phase
def test_ex_brachistochrone_vs_rungekutta_compressed(self):
import openmdao.api as om
import dymos as dm
from dymos.examples.brachistochrone.brachistochrone_vector_states_ode import \
BrachistochroneVectorStatesODE
p = om.Problem(model=om.Group())
p.driver = om.ScipyOptimizeDriver()
p.driver.declare_coloring()
phase = dm.Phase(ode_class=BrachistochroneVectorStatesODE,
transcription=dm.RungeKutta(num_segments=20,
compressed=True))
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
phase.add_state(
'pos',
shape=(2, ),
rate_source=BrachistochroneVectorStatesODE.states['pos']
['rate_source'],
units=BrachistochroneVectorStatesODE.states['pos']['units'],
fix_initial=True,
fix_final=False)
phase.add_state(
'v',
rate_source=BrachistochroneVectorStatesODE.states['v']
['rate_source'],
targets=BrachistochroneVectorStatesODE.states['v']['targets'],
units=BrachistochroneVectorStatesODE.states['v']['units'],
fix_initial=True,
fix_final=False)
phase.add_control(
'theta',
units='deg',
targets=BrachistochroneVectorStatesODE.parameters['theta']
['targets'],
rate_continuity=False,
lower=0.01,
upper=179.9)
phase.add_design_parameter(
'g',
targets=BrachistochroneVectorStatesODE.parameters['g']['targets'],
units='m/s**2',
opt=False,
val=9.80665)
phase.add_boundary_constraint('pos', loc='final', lower=[10, 5])
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', scaler=10)
p.model.linear_solver = om.DirectSolver()
p.setup(check=True, force_alloc_complex=True)
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 1.80162174
pos0 = [0, 10]
posf = [10, 5]
p['phase0.states:pos'] = phase.interpolate(ys=[pos0, posf],
nodes='state_input')
p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9],
nodes='state_input')
p['phase0.controls:theta'] = phase.interpolate(ys=[0.46, 100.22900215],
nodes='control_input')
p['phase0.design_parameters:g'] = 9.80665
p.run_driver()
self.assert_results(p)
self.tearDown()
def brachistochrone_min_time(transcription='gauss-lobatto',
num_segments=8,
transcription_order=3,
compressed=True,
optimizer='SLSQP'):
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
p.driver.declare_coloring()
if transcription == 'gauss-lobatto':
t = dm.GaussLobatto(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
elif transcription == 'radau-ps':
t = dm.Radau(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
elif transcription == 'runge-kutta':
t = dm.RungeKutta(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
traj = dm.Trajectory()
phase = dm.Phase(ode_class=BrachistochroneODE, transcription=t)
traj.add_phase('phase0', phase)
p.model.add_subsystem('traj0', traj)
phase.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
phase.add_state('x',
rate_source=BrachistochroneODE.states['x']['rate_source'],
units=BrachistochroneODE.states['x']['units'],
fix_initial=True,
fix_final=False,
solve_segments=False)
phase.add_state('y',
rate_source=BrachistochroneODE.states['y']['rate_source'],
units=BrachistochroneODE.states['y']['units'],
fix_initial=True,
fix_final=False,
solve_segments=False)
phase.add_state('v',
rate_source=BrachistochroneODE.states['v']['rate_source'],
targets=BrachistochroneODE.states['v']['targets'],
units=BrachistochroneODE.states['v']['units'],
fix_initial=True,
fix_final=False,
solve_segments=False)
phase.add_control(
'theta',
targets=BrachistochroneODE.parameters['theta']['targets'],
continuity=True,
rate_continuity=True,
units='deg',
lower=0.01,
upper=179.9)
phase.add_input_parameter(
'g',
targets=BrachistochroneODE.parameters['g']['targets'],
units='m/s**2',
val=9.80665)
phase.add_timeseries('timeseries2',
transcription=dm.Radau(num_segments=num_segments * 5,
order=transcription_order,
compressed=compressed),
subset='control_input')
phase.add_boundary_constraint('x', loc='final', equals=10)
phase.add_boundary_constraint('y', loc='final', equals=5)
# Minimize time at the end of the phase
phase.add_objective('time_phase', loc='final', scaler=10)
p.model.linear_solver = om.DirectSolver()
p.setup(check=['unconnected_inputs'])
p['traj0.phase0.t_initial'] = 0.0
p['traj0.phase0.t_duration'] = 2.0
p['traj0.phase0.states:x'] = phase.interpolate(ys=[0, 10],
nodes='state_input')
p['traj0.phase0.states:y'] = phase.interpolate(ys=[10, 5],
nodes='state_input')
p['traj0.phase0.states:v'] = phase.interpolate(ys=[0, 9.9],
nodes='state_input')
p['traj0.phase0.controls:theta'] = phase.interpolate(ys=[5, 100],
nodes='control_input')
p['traj0.phase0.input_parameters:g'] = 9.80665
p.final_setup()
return p
def test_brachistochrone_vector_state_path_constraints_rk_partial_indices(
self):
p = om.Problem(model=om.Group())
p.driver = om.ScipyOptimizeDriver()
p.driver.declare_coloring()
phase = dm.Phase(ode_class=BrachistochroneVectorStatesODE,
transcription=dm.RungeKutta(num_segments=50))
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
phase.add_state(
'pos',
shape=(2, ),
rate_source=BrachistochroneVectorStatesODE.states['pos']
['rate_source'],
units=BrachistochroneVectorStatesODE.states['pos']['units'],
fix_initial=True,
fix_final=False)
phase.add_state(
'v',
rate_source=BrachistochroneVectorStatesODE.states['v']
['rate_source'],
targets=BrachistochroneVectorStatesODE.states['v']['targets'],
units=BrachistochroneVectorStatesODE.states['v']['units'],
fix_initial=True,
fix_final=False)
phase.add_control(
'theta',
units='deg',
targets=BrachistochroneVectorStatesODE.parameters['theta']
['targets'],
rate_continuity=True,
lower=0.01,
upper=179.9)
phase.add_parameter(
'g',
targets=BrachistochroneVectorStatesODE.parameters['g']['targets'],
units='m/s**2',
opt=False,
val=9.80665)
phase.add_boundary_constraint('pos', loc='final', equals=[10, 5])
phase.add_path_constraint('pos', indices=[1], lower=5)
phase.add_timeseries_output('pos_dot', shape=(2, ), units='m/s')
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', scaler=10)
p.model.linear_solver = om.DirectSolver()
p.setup(check=True, force_alloc_complex=True)
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 2.0
pos0 = [0, 10]
posf = [10, 5]
p['phase0.states:pos'] = phase.interpolate(ys=[pos0, posf],
nodes='state_input')
p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9],
nodes='state_input')
p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100],
nodes='control_input')
p['phase0.parameters:g'] = 9.80665
p.run_driver()
assert_near_equal(np.min(
p.get_val('phase0.timeseries.states:pos')[:, 1]),
5.0,
tolerance=1.0E-3)
# Plot results
if SHOW_PLOTS:
exp_out = phase.simulate(times_per_seg=20)
fig, ax = plt.subplots()
fig.suptitle('Brachistochrone Solution')
x_imp = p.get_val('phase0.timeseries.states:pos')[:, 0]
y_imp = p.get_val('phase0.timeseries.states:pos')[:, 1]
x_exp = exp_out.get_val('phase0.timeseries.states:pos')[:, 0]
y_exp = exp_out.get_val('phase0.timeseries.states:pos')[:, 1]
ax.plot(x_imp, y_imp, 'ro', label='implicit')
ax.plot(x_exp, y_exp, 'b-', label='explicit')
ax.set_xlabel('x (m)')
ax.set_ylabel('y (m)')
ax.grid(True)
ax.legend(loc='upper right')
fig, ax = plt.subplots()
fig.suptitle('Brachistochrone Solution\nVelocity')
t_imp = p.get_val('phase0.timeseries.time')
t_exp = exp_out.get_val('phase0.timeseries.time')
xdot_imp = p.get_val('phase0.timeseries.pos_dot')[:, 0]
ydot_imp = p.get_val('phase0.timeseries.pos_dot')[:, 1]
xdot_exp = exp_out.get_val('phase0.timeseries.pos_dot')[:, 0]
ydot_exp = exp_out.get_val('phase0.timeseries.pos_dot')[:, 1]
ax.plot(t_imp, xdot_imp, 'bo', label='implicit')
ax.plot(t_exp, xdot_exp, 'b-', label='explicit')
ax.plot(t_imp, ydot_imp, 'ro', label='implicit')
ax.plot(t_exp, ydot_exp, 'r-', label='explicit')
ax.set_xlabel('t (s)')
ax.set_ylabel('v (m/s)')
ax.grid(True)
ax.legend(loc='upper right')
fig, ax = plt.subplots()
fig.suptitle('Brachistochrone Solution')
x_imp = p.get_val('phase0.timeseries.time')
y_imp = p.get_val('phase0.timeseries.control_rates:theta_rate2')
x_exp = exp_out.get_val('phase0.timeseries.time')
y_exp = exp_out.get_val(
'phase0.timeseries.control_rates:theta_rate2')
ax.plot(x_imp, y_imp, 'ro', label='implicit')
ax.plot(x_exp, y_exp, 'b-', label='explicit')
ax.set_xlabel('time (s)')
ax.set_ylabel('theta rate2 (rad/s**2)')
ax.grid(True)
ax.legend(loc='lower right')
plt.show()
return p
def _run_transcription(self, transcription):
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.driver.declare_coloring()
#
# First Phase: Standard Brachistochrone
#
num_segments = 10
transcription_order = 3
compressed = False
if transcription == 'gauss-lobatto':
tx0 = dm.GaussLobatto(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
tx1 = dm.GaussLobatto(num_segments=num_segments * 2,
order=transcription_order * 3,
compressed=compressed)
elif transcription == 'radau-ps':
tx0 = dm.Radau(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
tx1 = dm.Radau(num_segments=num_segments * 2,
order=transcription_order * 3,
compressed=compressed)
elif transcription == 'runge-kutta':
tx0 = dm.RungeKutta(num_segments=20, compressed=compressed)
tx1 = dm.RungeKutta(num_segments=20 * 4, compressed=compressed)
phase0 = dm.Phase(ode_class=BrachistochroneODE, transcription=tx0)
p.model.add_subsystem('phase0', phase0)
phase0.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
phase0.add_state(
'x',
fix_initial=True,
fix_final=False,
rate_source=BrachistochroneODE.states['x']['rate_source'],
units=BrachistochroneODE.states['x']['units'])
phase0.add_state(
'y',
fix_initial=True,
fix_final=False,
rate_source=BrachistochroneODE.states['y']['rate_source'],
units=BrachistochroneODE.states['y']['units'])
phase0.add_state(
'v',
fix_initial=True,
rate_source=BrachistochroneODE.states['v']['rate_source'],
targets=BrachistochroneODE.states['v']['targets'],
units=BrachistochroneODE.states['v']['units'])
phase0.add_input_parameter(
'g',
targets=BrachistochroneODE.parameters['g']['targets'],
units=BrachistochroneODE.parameters['g']['units'],
val=9.80665)
phase0.add_control(
'theta',
units='deg',
targets=BrachistochroneODE.parameters['theta']['targets'],
rate_continuity=False,
lower=0.01,
upper=179.9)
phase0.add_boundary_constraint('x', loc='final', equals=10)
phase0.add_boundary_constraint('y', loc='final', equals=5)
# Add alternative timeseries output to provide control inputs for the next phase
phase0.add_timeseries('timeseries2',
transcription=tx1,
subset='control_input')
#
# Second Phase: Integration of ArcLength
#
phase1 = dm.Phase(ode_class=BrachistochroneArclengthODE,
transcription=tx1)
p.model.add_subsystem('phase1', phase1)
phase1.set_time_options(fix_initial=True, input_duration=True)
phase1.add_state('S',
fix_initial=True,
fix_final=False,
rate_source='Sdot',
units='m')
phase1.add_control('theta', opt=False, units='deg', targets=['theta'])
phase1.add_control('v', opt=False, units='m/s', targets=['v'])
#
# Connect the two phases
#
p.model.connect('phase0.t_duration', 'phase1.t_duration')
p.model.connect('phase0.timeseries2.controls:theta',
'phase1.controls:theta')
p.model.connect('phase0.timeseries2.states:v', 'phase1.controls:v')
# Minimize time at the end of the phase
# phase1.add_objective('time', loc='final', scaler=1)
# phase1.add_boundary_constraint('S', loc='final', upper=12)
phase1.add_objective('S', loc='final', ref=1)
p.model.linear_solver = om.DirectSolver()
p.setup(check=True)
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 2.0
p['phase0.states:x'] = phase0.interpolate(ys=[0, 10],
nodes='state_input')
p['phase0.states:y'] = phase0.interpolate(ys=[10, 5],
nodes='state_input')
p['phase0.states:v'] = phase0.interpolate(ys=[0, 9.9],
nodes='state_input')
p['phase0.controls:theta'] = phase0.interpolate(ys=[5, 100],
nodes='control_input')
p['phase0.input_parameters:g'] = 9.80665
p['phase1.states:S'] = 0.0
p.run_driver()
expected = np.sqrt((10 - 0)**2 + (10 - 5)**2)
assert_rel_error(self,
p['phase1.timeseries.states:S'][-1],
expected,
tolerance=1.0E-3)
def test_brachistochrone_for_docs_runge_kutta_polynomial_controls(self):
import openmdao.api as om
from openmdao.utils.assert_utils import assert_near_equal
import dymos as dm
from dymos.examples.plotting import plot_results
from dymos.examples.brachistochrone import BrachistochroneODE
#
# Initialize the Problem and the optimization driver
#
p = om.Problem(model=om.Group())
p.driver = om.ScipyOptimizeDriver()
p.driver.declare_coloring()
#
# Create a trajectory and add a phase to it
#
traj = p.model.add_subsystem('traj', dm.Trajectory())
phase = traj.add_phase(
'phase0',
dm.Phase(ode_class=BrachistochroneODE,
transcription=dm.RungeKutta(num_segments=10)))
#
# Set the variables
#
phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(.5, 10))
phase.add_state(
'x',
rate_source=BrachistochroneODE.states['x']['rate_source'],
units=BrachistochroneODE.states['x']['units'],
fix_initial=True,
fix_final=False,
solve_segments=False)
phase.add_state(
'y',
rate_source=BrachistochroneODE.states['y']['rate_source'],
units=BrachistochroneODE.states['y']['units'],
fix_initial=True,
fix_final=False,
solve_segments=False)
phase.add_state(
'v',
rate_source=BrachistochroneODE.states['v']['rate_source'],
targets=BrachistochroneODE.states['v']['targets'],
units=BrachistochroneODE.states['v']['units'],
fix_initial=True,
fix_final=False,
solve_segments=False)
phase.add_polynomial_control(
'theta',
order=1,
targets=BrachistochroneODE.parameters['theta']['targets'],
units='deg',
lower=0.01,
upper=179.9)
phase.add_input_parameter(
'g',
targets=BrachistochroneODE.parameters['g']['targets'],
units='m/s**2',
val=9.80665)
#
# Final state values are not optimization variables, so we must enforce final values
# with boundary constraints, not simple bounds.
#
phase.add_boundary_constraint('x', loc='final', equals=10)
phase.add_boundary_constraint('y', loc='final', equals=5)
#
# Minimize time at the end of the phase
#
phase.add_objective('time', loc='final', scaler=10)
p.model.linear_solver = om.DirectSolver()
#
# Setup the Problem
#
p.setup()
#
# Set the initial values
#
p['traj.phase0.t_initial'] = 0.0
p['traj.phase0.t_duration'] = 2.0
p['traj.phase0.states:x'] = phase.interpolate(ys=[0, 10],
nodes='state_input')
p['traj.phase0.states:y'] = phase.interpolate(ys=[10, 5],
nodes='state_input')
p['traj.phase0.states:v'] = phase.interpolate(ys=[0, 9.9],
nodes='state_input')
p['traj.phase0.polynomial_controls:theta'][:] = 5.0
#
# Solve for the optimal trajectory
#
dm.run_problem(p)
# Test the results
assert_near_equal(p.get_val('traj.phase0.timeseries.time')[-1],
1.8016,
tolerance=1.0E-3)
# Generate the explicitly simulated trajectory
exp_out = traj.simulate()
plot_results(
[('traj.phase0.timeseries.states:x',
'traj.phase0.timeseries.states:y', 'x (m)', 'y (m)'),
('traj.phase0.timeseries.time',
'traj.phase0.timeseries.polynomial_controls:theta', 'time (s)',
'theta (deg)')],
title=
'Brachistochrone Solution\nRK4 Shooting and Polynomial Controls',
p_sol=p,
p_sim=exp_out)
plt.show()
def brachistochrone_min_time(transcription='gauss-lobatto',
num_segments=8,
transcription_order=3,
compressed=True,
optimizer='SLSQP',
run_driver=True,
force_alloc_complex=False,
solve_segments=False):
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
p.driver.declare_coloring(tol=1.0E-12)
if transcription == 'gauss-lobatto':
t = dm.GaussLobatto(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
elif transcription == 'radau-ps':
t = dm.Radau(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
elif transcription == 'runge-kutta':
t = dm.RungeKutta(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
traj = dm.Trajectory()
phase = dm.Phase(ode_class=BrachistochroneODE, transcription=t)
p.model.add_subsystem('traj0', traj)
traj.add_phase('phase0', phase)
# p.model.add_subsystem('traj0', traj)
phase.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
phase.add_state('x',
rate_source=BrachistochroneODE.states['x']['rate_source'],
fix_initial=True,
fix_final=False,
solve_segments=solve_segments)
phase.add_state('y',
rate_source=BrachistochroneODE.states['y']['rate_source'],
fix_initial=True,
fix_final=False,
solve_segments=solve_segments)
# Note that by omitting the targets here Dymos will automatically attempt to connect
# to a top-level input named 'v' in the ODE, and connect to nothing if it's not found.
phase.add_state('v',
rate_source=BrachistochroneODE.states['v']['rate_source'],
fix_initial=True,
fix_final=False,
solve_segments=solve_segments)
phase.add_control('theta',
continuity=True,
rate_continuity=True,
units='deg',
lower=0.01,
upper=179.9)
phase.add_parameter('g', targets=['g'], units='m/s**2')
phase.add_timeseries('timeseries2',
transcription=dm.Radau(num_segments=num_segments * 5,
order=transcription_order,
compressed=compressed),
subset='control_input')
phase.add_boundary_constraint('x', loc='final', equals=10)
phase.add_boundary_constraint('y', loc='final', equals=5)
# Minimize time at the end of the phase
phase.add_objective('time_phase', loc='final', scaler=10)
p.setup(check=['unconnected_inputs'],
force_alloc_complex=force_alloc_complex)
p['traj0.phase0.t_initial'] = 0.0
p['traj0.phase0.t_duration'] = 2.0
p['traj0.phase0.states:x'] = phase.interpolate(ys=[0, 10],
nodes='state_input')
p['traj0.phase0.states:y'] = phase.interpolate(ys=[10, 5],
nodes='state_input')
p['traj0.phase0.states:v'] = phase.interpolate(ys=[0, 9.9],
nodes='state_input')
p['traj0.phase0.controls:theta'] = phase.interpolate(ys=[5, 100],
nodes='control_input')
p['traj0.phase0.parameters:g'] = 9.80665
dm.run_problem(p, run_driver=run_driver)
# Plot results
if SHOW_PLOTS:
exp_out = traj.simulate()
fig, ax = plt.subplots()
fig.suptitle('Brachistochrone Solution')
x_imp = p.get_val('traj0.phase0.timeseries.states:x')
y_imp = p.get_val('traj0.phase0.timeseries.states:y')
x_exp = exp_out.get_val('traj0.phase0.timeseries.states:x')
y_exp = exp_out.get_val('traj0.phase0.timeseries.states:y')
ax.plot(x_imp, y_imp, 'ro', label='implicit')
ax.plot(x_exp, y_exp, 'b-', label='explicit')
ax.set_xlabel('x (m)')
ax.set_ylabel('y (m)')
ax.grid(True)
ax.legend(loc='upper right')
fig, ax = plt.subplots()
fig.suptitle('Brachistochrone Solution')
x_imp = p.get_val('traj0.phase0.timeseries.time_phase')
y_imp = p.get_val('traj0.phase0.timeseries.controls:theta')
x_exp = exp_out.get_val('traj0.phase0.timeseries.time_phase')
y_exp = exp_out.get_val('traj0.phase0.timeseries.controls:theta')
ax.plot(x_imp, y_imp, 'ro', label='implicit')
ax.plot(x_exp, y_exp, 'b-', label='explicit')
ax.set_xlabel('time (s)')
ax.set_ylabel('theta (rad)')
ax.grid(True)
ax.legend(loc='lower right')
plt.show()
return p
def make_traj(transcription='gauss-lobatto',
transcription_order=3,
compressed=False,
connected=False):
t = {
'gauss-lobatto':
dm.GaussLobatto(num_segments=5,
order=transcription_order,
compressed=compressed),
'radau':
dm.Radau(num_segments=20,
order=transcription_order,
compressed=compressed),
'runge-kutta':
dm.RungeKutta(num_segments=5, compressed=compressed)
}
traj = dm.Trajectory()
traj.add_parameter('c',
opt=False,
val=1.5,
units='DU/TU',
targets={
'burn1': ['c'],
'burn2': ['c']
})
# First Phase (burn)
burn1 = dm.Phase(ode_class=FiniteBurnODE, transcription=t[transcription])
burn1 = traj.add_phase('burn1', burn1)
burn1.set_time_options(fix_initial=True,
duration_bounds=(.5, 10),
units='TU')
burn1.add_state('r',
fix_initial=True,
fix_final=False,
defect_scaler=100.0,
rate_source='r_dot',
targets=['r'],
units='DU')
burn1.add_state('theta',
fix_initial=True,
fix_final=False,
defect_scaler=100.0,
rate_source='theta_dot',
targets=['theta'],
units='rad')
burn1.add_state('vr',
fix_initial=True,
fix_final=False,
defect_scaler=100.0,
rate_source='vr_dot',
targets=['vr'],
units='DU/TU')
burn1.add_state('vt',
fix_initial=True,
fix_final=False,
defect_scaler=100.0,
rate_source='vt_dot',
targets=['vt'],
units='DU/TU')
burn1.add_state('accel',
fix_initial=True,
fix_final=False,
rate_source='at_dot',
targets=['accel'],
units='DU/TU**2')
burn1.add_state('deltav',
fix_initial=True,
fix_final=False,
rate_source='deltav_dot',
units='DU/TU')
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,
targets=['u1'])
# Second Phase (Coast)
coast = dm.Phase(ode_class=FiniteBurnODE, transcription=t[transcription])
coast.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 50),
duration_ref=50,
units='TU')
coast.add_state('r',
fix_initial=False,
fix_final=False,
defect_scaler=100.0,
rate_source='r_dot',
targets=['r'],
units='DU')
coast.add_state('theta',
fix_initial=False,
fix_final=False,
defect_scaler=100.0,
rate_source='theta_dot',
targets=['theta'],
units='rad')
coast.add_state('vr',
fix_initial=False,
fix_final=False,
defect_scaler=100.0,
rate_source='vr_dot',
targets=['vr'],
units='DU/TU')
coast.add_state('vt',
fix_initial=False,
fix_final=False,
defect_scaler=100.0,
rate_source='vt_dot',
targets=['vt'],
units='DU/TU')
coast.add_state('accel',
fix_initial=True,
fix_final=True,
rate_source='at_dot',
targets=['accel'],
units='DU/TU**2')
coast.add_state('deltav',
fix_initial=False,
fix_final=False,
rate_source='deltav_dot',
units='DU/TU')
coast.add_parameter('u1', opt=False, val=0.0, units='deg', targets=['u1'])
coast.add_parameter('c', val=0.0, units='DU/TU', targets=['c'])
# Third Phase (burn)
burn2 = dm.Phase(ode_class=FiniteBurnODE, transcription=t[transcription])
if connected:
traj.add_phase('burn2', burn2)
traj.add_phase('coast', coast)
burn2.set_time_options(initial_bounds=(1.0, 60),
duration_bounds=(-10.0, -0.5),
initial_ref=10,
units='TU')
burn2.add_state('r',
fix_initial=True,
fix_final=False,
defect_scaler=100.0,
rate_source='r_dot',
targets=['r'],
units='DU')
burn2.add_state('theta',
fix_initial=False,
fix_final=False,
defect_scaler=100.0,
rate_source='theta_dot',
targets=['theta'],
units='rad')
burn2.add_state('vr',
fix_initial=True,
fix_final=False,
defect_scaler=1000.0,
rate_source='vr_dot',
targets=['vr'],
units='DU/TU')
burn2.add_state('vt',
fix_initial=True,
fix_final=False,
defect_scaler=1000.0,
rate_source='vt_dot',
targets=['vt'],
units='DU/TU')
burn2.add_state('accel',
fix_initial=False,
fix_final=False,
defect_scaler=1.0,
rate_source='at_dot',
targets=['accel'],
units='DU/TU**2')
burn2.add_state('deltav',
fix_initial=False,
fix_final=False,
defect_scaler=1.0,
rate_source='deltav_dot',
units='DU/TU')
burn2.add_objective('deltav', loc='initial', scaler=100.0)
burn2.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg',
scaler=0.01,
lower=-180,
upper=180,
targets=['u1'])
else:
traj.add_phase('coast', coast)
traj.add_phase('burn2', burn2)
burn2.set_time_options(initial_bounds=(0.5, 50),
duration_bounds=(.5, 10),
initial_ref=10,
units='TU')
burn2.add_state('r',
fix_initial=False,
fix_final=True,
defect_scaler=100.0,
rate_source='r_dot',
targets=['r'],
units='DU')
burn2.add_state('theta',
fix_initial=False,
fix_final=False,
defect_scaler=100.0,
rate_source='theta_dot',
targets=['theta'],
units='rad')
burn2.add_state('vr',
fix_initial=False,
fix_final=True,
defect_scaler=1000.0,
rate_source='vr_dot',
targets=['vr'],
units='DU/TU')
burn2.add_state('vt',
fix_initial=False,
fix_final=True,
defect_scaler=1000.0,
rate_source='vt_dot',
targets=['vt'],
units='DU/TU')
burn2.add_state('accel',
fix_initial=False,
fix_final=False,
defect_scaler=1.0,
rate_source='at_dot',
targets=['accel'],
units='DU/TU**2')
burn2.add_state('deltav',
fix_initial=False,
fix_final=False,
defect_scaler=1.0,
rate_source='deltav_dot',
units='DU/TU')
burn2.add_objective('deltav', loc='final', scaler=100.0)
burn2.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg',
scaler=0.01,
lower=-180,
upper=180,
targets=['u1'])
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
if connected:
traj.link_phases(phases=['burn1', 'coast'],
vars=['time', 'r', 'theta', 'vr', 'vt', 'deltav'],
connected=True)
# No direct connections to the end of a phase.
traj.link_phases(phases=['burn2', 'coast'],
vars=['r', 'theta', 'vr', 'vt', 'deltav'],
locs=('++', '++'))
traj.link_phases(phases=['burn2', 'coast'],
vars=['time'],
locs=('++', '++'))
traj.link_phases(phases=['burn1', 'burn2'],
vars=['accel'],
locs=('++', '++'))
else:
traj.link_phases(phases=['burn1', 'coast', 'burn2'],
vars=['time', 'r', 'theta', 'vr', 'vt', 'deltav'])
traj.link_phases(phases=['burn1', 'burn2'], vars=['accel'])
return traj
def test_promotes_parameter(self):
transcription = 'radau-ps'
optimizer = 'SNOPT'
num_segments = 10
transcription_order = 3
compressed = False
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
OPT, OPTIMIZER = set_pyoptsparse_opt(optimizer, fallback=True)
p.driver.options['optimizer'] = OPTIMIZER
p.driver.declare_coloring()
if transcription == 'gauss-lobatto':
t = dm.GaussLobatto(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
elif transcription == 'radau-ps':
t = dm.Radau(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
elif transcription == 'runge-kutta':
t = dm.RungeKutta(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
traj = dm.Trajectory()
phase = dm.Phase(ode_class=BrachistochroneODE, transcription=t)
traj.add_phase(
'phase0',
phase,
promotes_inputs=['t_initial', 't_duration', 'parameters:g'])
p.model.add_subsystem('traj', traj)
phase.set_time_options(fix_initial=True,
duration_bounds=(.5, 10),
units='s')
phase.add_state('x',
fix_initial=True,
fix_final=False,
solve_segments=False,
units='m',
rate_source='xdot')
phase.add_state('y',
fix_initial=True,
fix_final=False,
solve_segments=False,
units='m',
rate_source='ydot')
phase.add_state('v',
fix_initial=True,
fix_final=False,
solve_segments=False,
units='m/s',
rate_source='vdot',
targets=['v'])
phase.add_control('theta',
continuity=True,
rate_continuity=True,
units='deg',
lower=0.01,
upper=179.9,
targets=['theta'])
phase.add_parameter('g', units='m/s**2', val=9.80665, targets=['g'])
phase.add_boundary_constraint('x', loc='final', equals=10)
phase.add_boundary_constraint('y', loc='final', equals=5)
# Minimize time at the end of the phase
phase.add_objective('time_phase', loc='final', scaler=10)
p.model.linear_solver = om.DirectSolver()
p.setup(check=True)
p['traj.t_initial'] = 0.0
p['traj.t_duration'] = 2.0
p['traj.phase0.states:x'] = phase.interpolate(ys=[0, 10],
nodes='state_input')
p['traj.phase0.states:y'] = phase.interpolate(ys=[10, 5],
nodes='state_input')
p['traj.phase0.states:v'] = phase.interpolate(ys=[0, 9.9],
nodes='state_input')
p['traj.phase0.controls:theta'] = phase.interpolate(
ys=[5, 100], nodes='control_input')
p['traj.parameters:g'] = 9.80665
p.run_driver()
assert_near_equal(p['traj.t_duration'], 1.8016, tolerance=1.0E-4)
def test_static_ode_output_runge_kutta(self):
#
# Define the OpenMDAO problem
#
p = om.Problem(model=om.Group())
#
# Define a Trajectory object
#
traj = dm.Trajectory()
p.model.add_subsystem('traj', subsys=traj)
#
# Define a Dymos Phase object with GaussLobatto Transcription
#
phase = dm.Phase(ode_class=BrachODEStaticOutput,
transcription=dm.RungeKutta(num_segments=10))
traj.add_phase(name='phase0', phase=phase)
#
# Set the time options
# Time has no targets in our ODE.
# We fix the initial time so that the it is not a design variable in the optimization.
# The duration of the phase is allowed to be optimized, but is bounded on [0.5, 10].
#
phase.set_time_options(fix_initial=True, duration_bounds=(1.0, 10.0), units='s')
#
# Set the time options
# Initial values of positions and velocity are all fixed.
# The final value of position are fixed, but the final velocity is a free variable.
# The equations of motion are not functions of position, so 'x' and 'y' have no targets.
# The rate source points to the output in the ODE which provides the time derivative of the
# given state.
phase.add_state('x', fix_initial=True)
phase.add_state('y', fix_initial=True)
phase.add_state('v', fix_initial=True)
# Define theta as a control.
phase.add_control(name='theta', units='rad', lower=0.01, upper=np.pi-0.01, shape=(1,))
phase.add_timeseries_output('*')
phase.add_boundary_constraint('x', loc='final', equals=10)
phase.add_boundary_constraint('y', loc='final', equals=5)
# Minimize final time.
phase.add_objective('time', loc='final')
# Set the driver.
p.driver = om.ScipyOptimizeDriver()
# Allow OpenMDAO to automatically determine our sparsity pattern.
# Doing so can significant speed up the execution of Dymos.
p.driver.declare_coloring()
# Setup the problem
with warnings.catch_warnings(record=True) as ctx:
warnings.simplefilter('always')
p.setup(check=True)
expected_warning = "Cannot add ODE output foo to the timeseries output. It is sized " \
"such that its first dimension != num_nodes."
self.assertIn(expected_warning, [str(w.message) for w in ctx])
# Now that the OpenMDAO problem is setup, we can set the values of the states.
p.set_val('traj.phase0.t_initial', 0.0, units='s')
p.set_val('traj.phase0.t_duration', 5.0, units='s')
p.set_val('traj.phase0.states:x',
phase.interpolate(ys=[0, 10], nodes='state_input'),
units='m')
p.set_val('traj.phase0.states:y',
phase.interpolate(ys=[10, 5], nodes='state_input'),
units='m')
p.set_val('traj.phase0.states:v',
phase.interpolate(ys=[0, 5], nodes='state_input'),
units='m/s')
p.set_val('traj.phase0.controls:theta',
phase.interpolate(ys=[0.01, 90], nodes='control_input'),
units='deg')
# Run the driver to solve the problem
with warnings.catch_warnings(record=True) as ctx:
warnings.simplefilter('always')
dm.run_problem(p, simulate=True, make_plots=False)
expected_warning = "Cannot add ODE output foo to the timeseries output. It is sized " \
"such that its first dimension != num_nodes."
self.assertIn(expected_warning, [str(w.message) for w in ctx])
sol = om.CaseReader('dymos_solution.db').get_case('final')
sim = om.CaseReader('dymos_simulation.db').get_case('final')
with self.assertRaises(expected_exception=KeyError) as e:
sol.get_val('traj.phase0.timeseries.foo')
self.assertEqual(str(e.exception), "'Variable name \"traj.phase0.timeseries.foo\" not found.'")
with self.assertRaises(expected_exception=KeyError) as e:
sim.get_val('traj.phase0.timeseries.foo')
self.assertEqual(str(e.exception), "'Variable name \"traj.phase0.timeseries.foo\" not found.'")
def brachistochrone_min_time(transcription='gauss-lobatto',
num_segments=8,
transcription_order=3,
compressed=True,
optimizer='SLSQP',
dynamic_simul_derivs=True,
force_alloc_complex=False,
solve_segments=False,
run_driver=True):
p = om.Problem(model=om.Group())
if optimizer == 'SNOPT':
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
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 = om.ScipyOptimizeDriver()
if dynamic_simul_derivs:
p.driver.declare_coloring()
if transcription == 'runge-kutta':
transcription = dm.RungeKutta(num_segments=num_segments,
compressed=compressed)
fix_final = False
elif transcription == 'gauss-lobatto':
transcription = dm.GaussLobatto(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
fix_final = not solve_segments
elif transcription == 'radau-ps':
transcription = dm.Radau(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
fix_final = not solve_segments
traj = dm.Trajectory()
phase = dm.Phase(ode_class=BrachistochroneVectorStatesODE,
transcription=transcription)
traj.add_phase('phase0', phase)
p.model.add_subsystem('traj0', traj)
phase.set_time_options(fix_initial=True,
duration_bounds=(.5, 10),
units='s')
# can't fix final position if you're solving the segments
phase.add_state(
'pos',
rate_source=BrachistochroneVectorStatesODE.states['pos']
['rate_source'],
units=BrachistochroneVectorStatesODE.states['pos']['units'],
shape=BrachistochroneVectorStatesODE.states['pos']['shape'],
fix_initial=True,
fix_final=fix_final,
solve_segments=solve_segments)
#
phase.add_state(
'v',
rate_source=BrachistochroneVectorStatesODE.states['v']['rate_source'],
targets=BrachistochroneVectorStatesODE.states['v']['targets'],
units=BrachistochroneVectorStatesODE.states['v']['units'],
fix_initial=True,
fix_final=False,
solve_segments=solve_segments)
#
phase.add_control(
'theta',
targets=BrachistochroneVectorStatesODE.parameters['theta']['targets'],
continuity=True,
rate_continuity=True,
units='deg',
lower=0.01,
upper=179.9)
phase.add_design_parameter(
'g',
targets=BrachistochroneVectorStatesODE.parameters['g']['targets'],
opt=False,
units='m/s**2',
val=9.80665)
if not fix_final:
phase.add_boundary_constraint('pos',
loc='final',
units='m',
shape=(2, ),
equals=[10, 5])
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', scaler=10)
p.model.linear_solver = om.DirectSolver()
p.setup(check=True, force_alloc_complex=force_alloc_complex)
p['traj0.phase0.t_initial'] = 0.0
p['traj0.phase0.t_duration'] = 1.8016
pos0 = [0, 10]
posf = [10, 5]
p['traj0.phase0.states:pos'] = phase.interpolate(ys=[pos0, posf],
nodes='state_input')
p['traj0.phase0.states:v'] = phase.interpolate(ys=[0, 9.9],
nodes='state_input')
p['traj0.phase0.controls:theta'] = phase.interpolate(ys=[5, 100],
nodes='control_input')
p['traj0.phase0.design_parameters:g'] = 9.80665
p.run_model()
if run_driver:
p.run_driver()
return p
def test_brachistochrone_forward_shooting(self):
import openmdao.api as om
from openmdao.utils.assert_utils import assert_near_equal
import dymos as dm
from dymos.examples.brachistochrone.brachistochrone_ode import BrachistochroneODE
p = om.Problem(model=om.Group())
p.driver = om.ScipyOptimizeDriver()
p.driver.declare_coloring()
with warnings.catch_warnings(record=True) as w:
# Cause all warnings to always be triggered.
warnings.simplefilter("always")
# Trigger a warning.
phase = dm.Phase(ode_class=BrachistochroneODE,
transcription=dm.RungeKutta(num_segments=20))
assert issubclass(w[-1].category, DeprecationWarning)
expected_msg = 'The RungeKutta transcription is deprecated and ' \
'will be removed in Dymos v1.0.0.\nFor equivalent behavior, users ' \
'should switch to GaussLobatto(order=3, solve_segments=True)'
self.assertEqual(str(w[-1].message), expected_msg)
p.model.add_subsystem('phase0', phase)
phase.set_time_options(initial_bounds=(0, 0),
duration_bounds=(0.5, 2.0))
phase.add_state(
'x',
rate_source=BrachistochroneODE.states['x']['rate_source'],
fix_initial=True,
fix_final=False,
solve_segments=False)
phase.add_state(
'y',
rate_source=BrachistochroneODE.states['y']['rate_source'],
fix_initial=True,
fix_final=False,
solve_segments=False)
phase.add_state(
'v',
rate_source=BrachistochroneODE.states['v']['rate_source'],
fix_initial=True,
fix_final=False,
solve_segments=False)
phase.add_control('theta',
continuity=True,
rate_continuity=True,
units='deg',
lower=0.01,
upper=179.9)
phase.add_parameter('g', units='m/s**2', opt=False, val=9.80665)
# Final state values can't be controlled with simple bounds in ExplicitPhase,
# so use nonlinear boundary constraints instead.
phase.add_boundary_constraint('x', loc='final', equals=10)
phase.add_boundary_constraint('y', loc='final', equals=5)
# Minimize time at the end of the phase
phase.add_objective('time_phase', loc='final', scaler=10)
p.model.linear_solver = om.DirectSolver()
p.setup(check=True)
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 2.0
p['phase0.states:x'] = 0
p['phase0.states:y'] = 10
p['phase0.states:v'] = 0
p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100.5],
nodes='control_input')
# Solve for the optimal trajectory
p.run_driver()
# Test the results
assert_near_equal(p['phase0.time'][-1], 1.8016, tolerance=1.0E-3)
# Generate the explicitly simulated trajectory
exp_out = phase.simulate()
assert_near_equal(exp_out.get_val('phase0.timeseries.states:x')[-1, 0],
10,
tolerance=1.0E-3)
assert_near_equal(exp_out.get_val('phase0.timeseries.states:y')[-1, 0],
5,
tolerance=1.0E-3)
def test_connected_linkages_rk(self):
prob = om.Problem()
if optimizer == 'SNOPT':
opt = prob.driver = om.pyOptSparseDriver()
opt.options['optimizer'] = optimizer
opt.declare_coloring()
opt.opt_settings['Major iterations limit'] = 1000
opt.opt_settings['Major feasibility tolerance'] = 1.0E-6
opt.opt_settings['Major optimality tolerance'] = 1.0E-6
opt.opt_settings["Linesearch tolerance"] = 0.10
opt.opt_settings['iSumm'] = 6
else:
opt = prob.driver = om.ScipyOptimizeDriver()
opt.declare_coloring()
num_seg = 20
seg_ends, _ = lgl(num_seg + 1)
traj = prob.model.add_subsystem('traj', dm.Trajectory())
# First phase: normal operation.
transcription = dm.RungeKutta(num_segments=num_seg)
phase0 = dm.Phase(ode_class=BatteryODE, transcription=transcription)
traj_p0 = traj.add_phase('phase0', phase0)
traj_p0.set_time_options(fix_initial=True, fix_duration=True)
traj_p0.add_state('state_of_charge',
fix_initial=True,
fix_final=False,
targets=['SOC'],
rate_source='dXdt:SOC')
# Second phase: normal operation.
phase1 = dm.Phase(ode_class=BatteryODE, transcription=transcription)
traj_p1 = traj.add_phase('phase1', phase1)
traj_p1.set_time_options(fix_initial=False, fix_duration=True)
traj_p1.add_state('state_of_charge',
fix_initial=False,
fix_final=False,
targets=['SOC'],
rate_source='dXdt:SOC')
traj_p1.add_objective('time', loc='final')
# Second phase, but with battery failure.
phase1_bfail = dm.Phase(ode_class=BatteryODE,
ode_init_kwargs={'num_battery': 2},
transcription=transcription)
traj_p1_bfail = traj.add_phase('phase1_bfail', phase1_bfail)
traj_p1_bfail.set_time_options(fix_initial=False, fix_duration=True)
traj_p1_bfail.add_state('state_of_charge',
fix_initial=False,
fix_final=False,
targets=['SOC'],
rate_source='dXdt:SOC')
# Second phase, but with motor failure.
phase1_mfail = dm.Phase(ode_class=BatteryODE,
ode_init_kwargs={'num_motor': 2},
transcription=transcription)
traj_p1_mfail = traj.add_phase('phase1_mfail', phase1_mfail)
traj_p1_mfail.set_time_options(fix_initial=False, fix_duration=True)
traj_p1_mfail.add_state('state_of_charge',
fix_initial=False,
fix_final=False,
targets=['SOC'],
rate_source='dXdt:SOC')
traj.link_phases(phases=['phase0', 'phase1'],
vars=['state_of_charge', 'time'],
connected=True)
traj.link_phases(phases=['phase0', 'phase1_bfail'],
vars=['state_of_charge', 'time'],
connected=True)
traj.link_phases(phases=['phase0', 'phase1_mfail'],
vars=['state_of_charge', 'time'],
connected=True)
prob.model.options['assembled_jac_type'] = 'csc'
prob.model.linear_solver = om.DirectSolver(assemble_jac=True)
prob.setup()
prob['traj.phase0.t_initial'] = 0
prob['traj.phase0.t_duration'] = 1.0 * 3600
prob['traj.phase1.t_initial'] = 1.0 * 3600
prob['traj.phase1.t_duration'] = 1.0 * 3600
prob['traj.phase1_bfail.t_initial'] = 1.0 * 3600
prob['traj.phase1_bfail.t_duration'] = 1.0 * 3600
prob['traj.phase1_mfail.t_initial'] = 1.0 * 3600
prob['traj.phase1_mfail.t_duration'] = 1.0 * 3600
prob.set_solver_print(level=0)
dm.run_problem(prob)
soc0 = prob['traj.phase0.states:state_of_charge']
soc1 = prob['traj.phase1.states:state_of_charge']
soc1b = prob['traj.phase1_bfail.states:state_of_charge']
soc1m = prob['traj.phase1_mfail.states:state_of_charge']
# Final value for State of Chrage in each segment should be a good test.
assert_near_equal(soc0[-1], 0.63464982, 5e-5)
assert_near_equal(soc1[-1], 0.23794217, 5e-5)
assert_near_equal(soc1b[-1], 0.0281523, 5e-5)
assert_near_equal(soc1m[-1], 0.18625395, 5e-5)
def test_brachistochrone_forward_shooting_path_constrained_time(self):
import openmdao.api as om
from openmdao.utils.assert_utils import assert_near_equal
import dymos as dm
from dymos.examples.brachistochrone.brachistochrone_ode import BrachistochroneODE
p = om.Problem(model=om.Group())
p.driver = om.ScipyOptimizeDriver()
phase = dm.Phase(ode_class=BrachistochroneODE,
transcription=dm.RungeKutta(num_segments=20))
p.model.add_subsystem('phase0', phase)
phase.set_time_options(initial_bounds=(0, 0),
duration_bounds=(0.5, 2.0))
phase.add_state(
'x',
rate_source=BrachistochroneODE.states['x']['rate_source'],
fix_initial=True,
fix_final=False,
solve_segments=False)
phase.add_state(
'y',
rate_source=BrachistochroneODE.states['y']['rate_source'],
fix_initial=True,
fix_final=False,
solve_segments=False)
phase.add_state(
'v',
rate_source=BrachistochroneODE.states['v']['rate_source'],
fix_initial=True,
fix_final=False,
solve_segments=False)
phase.add_control('theta',
continuity=True,
rate_continuity=True,
units='deg',
lower=0.01,
upper=179.9)
phase.add_parameter('g', units='m/s**2', opt=False, val=9.80665)
# Final state values can't be controlled with simple bounds in ExplicitPhase,
# so use nonlinear boundary constraints instead.
phase.add_boundary_constraint('x', loc='final', equals=10)
phase.add_boundary_constraint('y', loc='final', equals=5)
phase.add_path_constraint('time', lower=0.0, upper=2.0)
phase.add_path_constraint('time_phase', lower=0.0, upper=2.0)
# Minimize time at the end of the phase
phase.add_objective('time_phase', loc='final', scaler=10)
p.model.linear_solver = om.DirectSolver()
p.setup(check=True)
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 2.0
p['phase0.states:x'] = 0
p['phase0.states:y'] = 10
p['phase0.states:v'] = 0
p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100.5],
nodes='control_input')
# Solve for the optimal trajectory
p.run_driver()
# Test the results
assert_near_equal(p['phase0.time'][-1], 1.8016, tolerance=1.0E-3)
# Generate the explicitly simulated trajectory
exp_out = phase.simulate()
assert_near_equal(exp_out.get_val('phase0.timeseries.states:x')[-1, 0],
10,
tolerance=1.0E-3)
assert_near_equal(exp_out.get_val('phase0.timeseries.states:y')[-1, 0],
5,
tolerance=1.0E-3)
def test_two_burn_orbit_raise_gl_rk_gl_constrained(self):
import numpy as np
import matplotlib.pyplot as plt
import openmdao.api as om
from openmdao.utils.assert_utils import assert_rel_error
from openmdao.utils.general_utils import set_pyoptsparse_opt
import dymos as dm
from dymos.examples.finite_burn_orbit_raise.finite_burn_eom import FiniteBurnODE
traj = dm.Trajectory()
p = om.Problem(model=om.Group())
p.model.add_subsystem('traj', traj)
p.driver = om.pyOptSparseDriver()
_, optimizer = set_pyoptsparse_opt('SNOPT', fallback=True)
p.driver.options['optimizer'] = optimizer
p.driver.declare_coloring()
traj.add_design_parameter('c',
opt=False,
val=1.5,
units='DU/TU',
targets={
'burn1': ['c'],
'coast': ['c'],
'burn2': ['c']
})
# First Phase (burn)
burn1 = dm.Phase(ode_class=FiniteBurnODE,
transcription=dm.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),
units='TU')
burn1.add_state('r',
fix_initial=True,
fix_final=False,
defect_scaler=100.0,
rate_source='r_dot',
targets=['r'],
units='DU')
burn1.add_state('theta',
fix_initial=True,
fix_final=False,
defect_scaler=100.0,
rate_source='theta_dot',
targets=['theta'],
units='rad')
burn1.add_state('vr',
fix_initial=True,
fix_final=False,
defect_scaler=100.0,
rate_source='vr_dot',
targets=['vr'],
units='DU/TU')
burn1.add_state('vt',
fix_initial=True,
fix_final=False,
defect_scaler=100.0,
rate_source='vt_dot',
targets=['vt'],
units='DU/TU')
burn1.add_state('accel',
fix_initial=True,
fix_final=False,
rate_source='at_dot',
targets=['accel'],
units='DU/TU**2')
burn1.add_state('deltav',
fix_initial=True,
fix_final=False,
rate_source='deltav_dot',
units='DU/TU')
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,
targets=['u1'])
# Second Phase (Coast)
coast = dm.Phase(ode_class=FiniteBurnODE,
transcription=dm.RungeKutta(num_segments=20))
traj.add_phase('coast', coast)
coast.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10),
duration_ref=10,
units='TU')
# TODO Moving add_state('theta'... after add_state('r',... causes the
# coloring to be invalid with scipy > 1.0.1
coast.add_state('theta',
fix_initial=False,
fix_final=False,
defect_scaler=100.0,
units='rad',
rate_source='theta_dot',
targets=['theta'])
coast.add_state('r',
fix_initial=False,
fix_final=False,
defect_scaler=100.0,
rate_source='r_dot',
targets=['r'],
units='DU')
coast.add_state('vr',
fix_initial=False,
fix_final=False,
defect_scaler=100.0,
rate_source='vr_dot',
targets=['vr'],
units='DU/TU')
coast.add_state('vt',
fix_initial=False,
fix_final=False,
defect_scaler=100.0,
rate_source='vt_dot',
targets=['vt'],
units='DU/TU')
coast.add_state('accel',
fix_initial=True,
fix_final=False,
ref=1.0E-12,
defect_ref=1.0E-12,
rate_source='at_dot',
targets=['accel'],
units='DU/TU**2')
coast.add_state('deltav',
fix_initial=False,
fix_final=False,
rate_source='deltav_dot',
units='DU/TU')
coast.add_control('u1',
targets=['u1'],
opt=False,
val=0.0,
units='deg')
# Third Phase (burn)
burn2 = dm.Phase(ode_class=FiniteBurnODE,
transcription=dm.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,
units='TU')
burn2.add_state('r',
fix_initial=False,
fix_final=True,
rate_source='r_dot',
targets=['r'],
units='DU')
burn2.add_state('theta',
fix_initial=False,
fix_final=False,
rate_source='theta_dot',
targets=['theta'],
units='rad')
burn2.add_state('vr',
fix_initial=False,
fix_final=True,
rate_source='vr_dot',
targets=['vr'],
units='DU/TU')
burn2.add_state('vt',
fix_initial=False,
fix_final=True,
rate_source='vt_dot',
targets=['vt'],
units='DU/TU')
burn2.add_state('accel',
fix_initial=False,
fix_final=False,
defect_ref=1.0E-6,
rate_source='at_dot',
targets=['accel'],
units='DU/TU**2')
burn2.add_state('deltav',
fix_initial=False,
fix_final=False,
rate_source='deltav_dot',
units='DU/TU')
burn2.add_control('u1',
targets=['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 = om.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_static_params(self):
prob = om.Problem(model=om.Group())
traj = prob.model.add_subsystem('traj', dm.Trajectory())
# First phase: normal operation.
# NOTE: using RK4 integration here
P_DEMAND = 2.0
phase0 = dm.Phase(ode_class=BatteryODE,
transcription=dm.RungeKutta(num_segments=200))
phase0.set_time_options(fix_initial=True, fix_duration=True)
phase0.add_state('state_of_charge',
fix_initial=True,
fix_final=False,
targets=['SOC'],
rate_source='dXdt:SOC')
phase0.add_timeseries_output('battery.V_oc', output_name='V_oc')
phase0.add_timeseries_output('battery.V_pack', output_name='V_pack')
phase0.add_timeseries_output('pwr_balance.I_Li', output_name='I_Li')
traj.add_phase('phase0', phase0)
# Second phase: normal operation.
transcription = dm.Radau(num_segments=5, order=5, compressed=True)
phase1 = dm.Phase(ode_class=BatteryODE, transcription=transcription)
phase1.set_time_options(fix_initial=False, fix_duration=True)
phase1.add_state('state_of_charge',
fix_initial=False,
fix_final=False,
solve_segments='forward',
targets=['SOC'],
rate_source='dXdt:SOC')
phase1.add_timeseries_output('battery.V_oc', output_name='V_oc')
phase1.add_timeseries_output('battery.V_pack', output_name='V_pack')
phase1.add_timeseries_output('pwr_balance.I_Li', output_name='I_Li')
traj.add_phase('phase1', phase1)
# Second phase, but with battery failure.
phase1_bfail = dm.Phase(ode_class=BatteryODE,
ode_init_kwargs={'num_battery': 2},
transcription=transcription)
phase1_bfail.set_time_options(fix_initial=False, fix_duration=True)
phase1_bfail.add_state('state_of_charge',
fix_initial=False,
fix_final=False,
solve_segments='forward',
targets=['SOC'],
rate_source='dXdt:SOC')
phase1_bfail.add_timeseries_output('battery.V_oc', output_name='V_oc')
phase1_bfail.add_timeseries_output('battery.V_pack',
output_name='V_pack')
phase1_bfail.add_timeseries_output('pwr_balance.I_Li',
output_name='I_Li')
traj.add_phase('phase1_bfail', phase1_bfail)
# Second phase, but with motor failure.
phase1_mfail = dm.Phase(ode_class=BatteryODE,
ode_init_kwargs={'num_motor': 2},
transcription=transcription)
phase1_mfail.set_time_options(fix_initial=False, fix_duration=True)
phase1_mfail.add_state('state_of_charge',
fix_initial=False,
fix_final=False,
solve_segments='forward',
targets=['SOC'],
rate_source='dXdt:SOC')
phase1_mfail.add_timeseries_output('battery.V_oc', output_name='V_oc')
phase1_mfail.add_timeseries_output('battery.V_pack',
output_name='V_pack')
phase1_mfail.add_timeseries_output('pwr_balance.I_Li',
output_name='I_Li')
traj.add_phase('phase1_mfail', phase1_mfail)
traj.link_phases(phases=['phase0', 'phase1'],
vars=['state_of_charge', 'time'],
connected=True)
traj.link_phases(phases=['phase0', 'phase1_bfail'],
vars=['state_of_charge', 'time'],
connected=True)
traj.link_phases(phases=['phase0', 'phase1_mfail'],
vars=['state_of_charge', 'time'],
connected=True)
# prob.model.linear_solver = om.DirectSolver(assemble_jac=True)
prob.setup()
prob.final_setup()
prob['traj.phases.phase0.time_extents.t_initial'] = 0
prob['traj.phases.phase0.time_extents.t_duration'] = 1.0 * 3600
# prob['traj.phases.phase1.time_extents.t_initial'] = 1.0*3600
prob['traj.phases.phase1.time_extents.t_duration'] = 1.0 * 3600
# prob['traj.phases.phase1_bfail.time_extents.t_initial'] = 1.0*3600
prob['traj.phases.phase1_bfail.time_extents.t_duration'] = 1.0 * 3600
# prob['traj.phases.phase1_mfail.time_extents.t_initial'] = 1.0*3600
prob['traj.phases.phase1_mfail.time_extents.t_duration'] = 1.0 * 3600
prob.set_solver_print(level=0)
prob.run_model()
plot = True
if plot:
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
t0 = prob['traj.phase0.timeseries.time']
t1 = prob['traj.phase1.timeseries.time']
t1b = prob['traj.phase1_bfail.timeseries.time']
t1m = prob['traj.phase1_mfail.timeseries.time']
soc0 = prob['traj.phase0.timeseries.states:state_of_charge']
soc1 = prob['traj.phase1.timeseries.states:state_of_charge']
soc1b = prob['traj.phase1_bfail.timeseries.states:state_of_charge']
soc1m = prob['traj.phase1_mfail.timeseries.states:state_of_charge']
plt.subplot(2, 2, 1)
plt.plot(t0, soc0, 'b')
plt.plot(t1, soc1, 'b')
plt.plot(t1b, soc1b, 'r')
plt.plot(t1m, soc1m, 'c')
plt.xlabel('Time (hour)')
plt.ylabel('State of Charge (percent)')
V_oc0 = prob['traj.phase0.timeseries.V_oc']
V_oc1 = prob['traj.phase1.timeseries.V_oc']
V_oc1b = prob['traj.phase1_bfail.timeseries.V_oc']
V_oc1m = prob['traj.phase1_mfail.timeseries.V_oc']
plt.subplot(2, 2, 2)
plt.plot(t0, V_oc0, 'b')
plt.plot(t1, V_oc1, 'b')
plt.plot(t1b, V_oc1b, 'r')
plt.plot(t1m, V_oc1m, 'c')
plt.xlabel('Time (hour)')
plt.ylabel('Open Circuit Voltage (V)')
V_pack0 = prob['traj.phase0.timeseries.V_pack']
V_pack1 = prob['traj.phase1.timeseries.V_pack']
V_pack1b = prob['traj.phase1_bfail.timeseries.V_pack']
V_pack1m = prob['traj.phase1_mfail.timeseries.V_pack']
plt.subplot(2, 2, 3)
plt.plot(t0, V_pack0, 'b')
plt.plot(t1, V_pack1, 'b')
plt.plot(t1b, V_pack1b, 'r')
plt.plot(t1m, V_pack1m, 'c')
plt.xlabel('Time (hour)')
plt.ylabel('Terminal Voltage (V)')
I_Li0 = prob['traj.phase0.timeseries.I_Li']
I_Li1 = prob['traj.phase1.timeseries.I_Li']
I_Li1b = prob['traj.phase1_bfail.timeseries.I_Li']
I_Li1m = prob['traj.phase1_mfail.timeseries.I_Li']
plt.subplot(2, 2, 4)
plt.plot(t0, I_Li0, 'b')
plt.plot(t1, I_Li1, 'b')
plt.plot(t1b, I_Li1b, 'r')
plt.plot(t1m, I_Li1m, 'c')
plt.xlabel('Time (hour)')
plt.ylabel('Line Current (A)')
plt.show()
def make_prob(self, transcription, num_segments, transcription_order,
compressed):
p = om.Problem(model=om.Group())
if transcription == 'gauss-lobatto':
t = dm.GaussLobatto(
num_segments=num_segments,
order=transcription_order,
compressed=compressed,
)
elif transcription == 'radau-ps':
t = dm.Radau(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
elif transcription == 'runge-kutta':
t = dm.RungeKutta(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
traj = dm.Trajectory()
phase = dm.Phase(ode_class=BrachistochroneODE, transcription=t)
p.model.add_subsystem('traj0', traj)
traj.add_phase('phase0', phase)
phase.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
phase.add_state('x',
fix_initial=True,
fix_final=False,
solve_segments='forward')
phase.add_state('y',
fix_initial=True,
fix_final=False,
solve_segments='forward')
# Note that by omitting the targets here Dymos will automatically attempt to connect
# to a top-level input named 'v' in the ODE, and connect to nothing if it's not found.
phase.add_state('v',
fix_initial=True,
fix_final=False,
solve_segments='forward')
phase.add_control('theta',
continuity=True,
rate_continuity=True,
units='deg',
lower=0.01,
upper=179.9)
phase.add_parameter('g', targets=['g'], units='m/s**2')
phase.add_boundary_constraint('x', loc='final', equals=10)
phase.add_boundary_constraint('y', loc='final', equals=5)
# Minimize time at the end of the phase
phase.add_objective('time_phase', loc='final', scaler=10)
p.setup(force_alloc_complex=True)
p['traj0.phase0.t_initial'] = 0.0
p['traj0.phase0.t_duration'] = 2.0
p['traj0.phase0.states:x'] = phase.interpolate(ys=[0, 10],
nodes='state_input')
p['traj0.phase0.states:y'] = phase.interpolate(ys=[10, 5],
nodes='state_input')
p['traj0.phase0.states:v'] = phase.interpolate(ys=[0, 9.9],
nodes='state_input')
p['traj0.phase0.controls:theta'] = phase.interpolate(
ys=[5, 100], nodes='control_input')
p['traj0.phase0.parameters:g'] = 9.80665
return p
def vanderpol(transcription='gauss-lobatto', num_segments=8, transcription_order=3,
compressed=True, optimizer='SLSQP', use_pyoptsparse=False, delay=None):
"""Dymos problem definition for optimal control of a Van der Pol oscillator"""
# define the OpenMDAO problem
p = om.Problem(model=om.Group())
if not use_pyoptsparse:
p.driver = om.ScipyOptimizeDriver()
else:
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
if use_pyoptsparse and optimizer == 'SNOPT':
p.driver.opt_settings['iSumm'] = 6 # show detailed SNOPT output
p.driver.declare_coloring()
# define a Trajectory object and add to model
traj = dm.Trajectory()
p.model.add_subsystem('traj', subsys=traj)
# define a Transcription
if transcription == 'gauss-lobatto':
t = dm.GaussLobatto(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
elif transcription == 'radau-ps':
t = dm.Radau(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
elif transcription == 'runge-kutta':
t = dm.RungeKutta(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
# define a Phase as specified above and add to Phase
if not delay:
phase = dm.Phase(ode_class=vanderpol_ode, transcription=t)
else:
phase = dm.Phase(ode_class=vanderpol_ode_group, transcription=t) # distributed component group
traj.add_phase(name='phase0', phase=phase)
t_final = 15.0
phase.set_time_options(fix_initial=True, fix_duration=True, duration_val=t_final, units='s')
# set the State time options
phase.add_state('x0', fix_initial=False, fix_final=False,
rate_source='x0dot',
units='V/s',
targets='x0') # target required because x0 is an input
phase.add_state('x1', fix_initial=False, fix_final=False,
rate_source='x1dot',
units='V',
targets='x1') # target required because x1 is an input
phase.add_state('J', fix_initial=False, fix_final=False,
rate_source='Jdot',
units=None)
# define the control
phase.add_control(name='u', units=None, lower=-0.75, upper=1.0, continuity=True,
rate_continuity=True, targets='u') # target required because u is an input
# add constraints
phase.add_boundary_constraint('x0', loc='initial', equals=1.0)
phase.add_boundary_constraint('x1', loc='initial', equals=1.0)
phase.add_boundary_constraint('J', loc='initial', equals=0.0)
phase.add_boundary_constraint('x0', loc='final', equals=0.0)
phase.add_boundary_constraint('x1', loc='final', equals=0.0)
# define objective to minimize
phase.add_objective('J', loc='final')
# setup the problem
p.setup(check=True)
# TODO - Dymos API will soon provide a way to specify this.
# the linear solver used to compute derivatives is not working on MPI, so switch to LinearRunOnce
for phase in traj._phases.values():
phase.linear_solver = om.LinearRunOnce()
p['traj.phase0.t_initial'] = 0.0
p['traj.phase0.t_duration'] = t_final
# add a linearly interpolated initial guess for the state and control curves
p['traj.phase0.states:x0'] = phase.interpolate(ys=[1, 0], nodes='state_input')
p['traj.phase0.states:x1'] = phase.interpolate(ys=[1, 0], nodes='state_input')
p['traj.phase0.states:J'] = phase.interpolate(ys=[0, 1], nodes='state_input')
p['traj.phase0.controls:u'] = phase.interpolate(ys=[-0.75, -0.75], nodes='control_input')
p.final_setup()
# debugging helpers:
# om.n2(p) # show n2 diagram
#
# with np.printoptions(linewidth=1024): # display partials for manual checking
# p.check_partials(compact_print=True)
return p
def min_time_climb(optimizer='SLSQP',
num_seg=3,
transcription='gauss-lobatto',
transcription_order=3):
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
p.driver.declare_coloring()
p.driver.add_recorder(
om.SqliteRecorder(f'min_time_climb_solution_{transcription}.sql'))
p.driver.recording_options['includes'] = ['*']
p.driver.recording_options['record_objectives'] = True
p.driver.recording_options['record_constraints'] = True
p.driver.recording_options['record_desvars'] = True
if optimizer == 'SNOPT':
p.driver.opt_settings['Major iterations limit'] = 1000
p.driver.opt_settings['iSumm'] = 6
p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-6
p.driver.opt_settings['Major optimality tolerance'] = 1.0E-6
p.driver.opt_settings['Function precision'] = 1.0E-12
p.driver.opt_settings['Linesearch tolerance'] = 0.1
p.driver.opt_settings['Major step limit'] = 0.5
t = {
'gauss-lobatto':
dm.GaussLobatto(num_segments=num_seg, order=transcription_order),
'radau-ps':
dm.Radau(num_segments=num_seg, order=transcription_order),
'runge-kutta':
dm.RungeKutta(num_segments=num_seg)
}
traj = dm.Trajectory()
phase = dm.Phase(ode_class=MinTimeClimbODE, transcription=t[transcription])
traj.add_phase('phase0', phase)
p.model.add_subsystem('traj', traj)
phase.set_time_options(fix_initial=True,
duration_bounds=(50, 400),
duration_ref=100.0)
phase.add_state('r',
fix_initial=True,
lower=0,
upper=1.0E6,
ref=1.0E3,
defect_ref=1.0E3,
units='m',
rate_source='flight_dynamics.r_dot')
phase.add_state('h',
fix_initial=True,
lower=0,
upper=20000.0,
ref=1.0E2,
defect_ref=1.0E2,
units='m',
rate_source='flight_dynamics.h_dot',
targets=['h'])
phase.add_state('v',
fix_initial=True,
lower=10.0,
ref=1.0E2,
defect_ref=1.0E2,
units='m/s',
rate_source='flight_dynamics.v_dot',
targets=['v'])
phase.add_state('gam',
fix_initial=True,
lower=-1.5,
upper=1.5,
ref=1.0,
defect_ref=1.0,
units='rad',
rate_source='flight_dynamics.gam_dot',
targets=['gam'])
phase.add_state('m',
fix_initial=True,
lower=10.0,
upper=1.0E5,
ref=1.0E3,
defect_ref=1.0E3,
units='kg',
rate_source='prop.m_dot',
targets=['m'])
phase.add_control('alpha',
units='deg',
lower=-8.0,
upper=8.0,
scaler=1.0,
rate_continuity=True,
rate_continuity_scaler=100.0,
rate2_continuity=False,
targets=['alpha'])
phase.add_design_parameter('S',
val=49.2386,
units='m**2',
opt=False,
targets=['S'])
phase.add_design_parameter('Isp',
val=1600.0,
units='s',
opt=False,
targets=['Isp'])
phase.add_design_parameter('throttle',
val=1.0,
opt=False,
targets=['throttle'])
phase.add_boundary_constraint('h',
loc='final',
equals=20000,
scaler=1.0E-3,
units='m')
phase.add_boundary_constraint('aero.mach', loc='final', equals=1.0)
phase.add_boundary_constraint('gam', loc='final', equals=0.0, units='rad')
phase.add_path_constraint(name='h', lower=100.0, upper=20000, ref=20000)
phase.add_path_constraint(name='aero.mach', lower=0.1, upper=1.8)
phase.add_timeseries('timeseries2',
transcription=dm.GaussLobatto(num_segments=50,
order=3))
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', ref=1.0)
p.model.linear_solver = om.DirectSolver()
p.setup()
p['traj.phase0.t_initial'] = 0.0
p['traj.phase0.t_duration'] = 300.0
p['traj.phase0.states:r'] = phase.interpolate(ys=[0.0, 111319.54],
nodes='state_input')
p['traj.phase0.states:h'] = phase.interpolate(ys=[100.0, 20000.0],
nodes='state_input')
p['traj.phase0.states:v'] = phase.interpolate(ys=[135.964, 283.159],
nodes='state_input')
p['traj.phase0.states:gam'] = phase.interpolate(ys=[0.0, 0.0],
nodes='state_input')
p['traj.phase0.states:m'] = phase.interpolate(ys=[19030.468, 16841.431],
nodes='state_input')
p['traj.phase0.controls:alpha'] = phase.interpolate(ys=[0.0, 0.0],
nodes='control_input')
p.run_driver()
traj.simulate(record_file=f'min_time_climb_simulation_{transcription}.sql')
return p