SSTO Lunar Ascent with Polynomial Controls#
This example demonstrates the use of polynomial controls in Dymos. Polynomial controls define the control profile as a single polynomial across the entire phase where the control values are specified at the Legendre Gauss Lobatto (LGL) nodes in phase dimensionless time. These controls can be of any arbitrary order greater than 1 (linear).
We’ve already demonstrated that the optimal single stage ascent in the absense of an atmosphere follows the linear tangent guidance law. In this example, we’ll change the control parameterization such that \(\tan \theta\) is provided by a polynomial control of order 1. The LGL nodes of a first order polynomial are the endpoints of the phase, thus the optimizer will be governing the value of \(\tan \theta\) at the initial and final times of the phase, and the Dymos will interpolate the values of \(\tan \theta\) to all other nodes in the Phase.
This example is equivalent to the previous linear tangent example in that we’ve reduced the problem from finding the appropriate control value at all nodes to that of finding the optimal value of just two quantities. But instead of optimizing the slope and intercept given by the parameters \(a\) and \(b\), we’re parameterizing the control using the endpoint values of the linear polynomial.
Now the guidance comp needs to convert the inverse tangent of the current value of the polynomial controls.
\[\theta = \arctan{p}\]
Solving the problem#
import numpy as np
import matplotlib.pyplot as plt
import openmdao.api as om
import dymos as dm
g = 1.61544 # lunar gravity, m/s**2
class LaunchVehicle2DEOM(om.ExplicitComponent):
"""
Simple 2D Cartesian Equations of Motion for a launch vehicle subject to thrust and drag.
"""
def initialize(self):
self.options.declare('num_nodes', types=int)
def setup(self):
nn = self.options['num_nodes']
# Inputs
self.add_input('vx',
val=np.zeros(nn),
desc='x velocity',
units='m/s')
self.add_input('vy',
val=np.zeros(nn),
desc='y velocity',
units='m/s')
self.add_input('m',
val=np.zeros(nn),
desc='mass',
units='kg')
self.add_input('theta',
val=np.zeros(nn),
desc='pitch angle',
units='rad')
self.add_input('thrust',
val=2100000 * np.ones(nn),
desc='thrust',
units='N')
self.add_input('Isp',
val=265.2 * np.ones(nn),
desc='specific impulse',
units='s')
# Outputs
self.add_output('xdot',
val=np.zeros(nn),
desc='velocity component in x',
units='m/s')
self.add_output('ydot',
val=np.zeros(nn),
desc='velocity component in y',
units='m/s')
self.add_output('vxdot',
val=np.zeros(nn),
desc='x acceleration magnitude',
units='m/s**2')
self.add_output('vydot',
val=np.zeros(nn),
desc='y acceleration magnitude',
units='m/s**2')
self.add_output('mdot',
val=np.zeros(nn),
desc='mass rate of change',
units='kg/s')
# Setup partials
ar = np.arange(self.options['num_nodes'])
self.declare_partials(of='xdot', wrt='vx', rows=ar, cols=ar, val=1.0)
self.declare_partials(of='ydot', wrt='vy', rows=ar, cols=ar, val=1.0)
self.declare_partials(of='vxdot', wrt='vx', rows=ar, cols=ar)
self.declare_partials(of='vxdot', wrt='m', rows=ar, cols=ar)
self.declare_partials(of='vxdot', wrt='theta', rows=ar, cols=ar)
self.declare_partials(of='vxdot', wrt='thrust', rows=ar, cols=ar)
self.declare_partials(of='vydot', wrt='m', rows=ar, cols=ar)
self.declare_partials(of='vydot', wrt='theta', rows=ar, cols=ar)
self.declare_partials(of='vydot', wrt='vy', rows=ar, cols=ar)
self.declare_partials(of='vydot', wrt='thrust', rows=ar, cols=ar)
self.declare_partials(of='mdot', wrt='thrust', rows=ar, cols=ar)
self.declare_partials(of='mdot', wrt='Isp', rows=ar, cols=ar)
def compute(self, inputs, outputs):
theta = inputs['theta']
cos_theta = np.cos(theta)
sin_theta = np.sin(theta)
vx = inputs['vx']
vy = inputs['vy']
m = inputs['m']
F_T = inputs['thrust']
Isp = inputs['Isp']
outputs['xdot'] = vx
outputs['ydot'] = vy
outputs['vxdot'] = F_T * cos_theta / m
outputs['vydot'] = F_T * sin_theta / m - g
outputs['mdot'] = -F_T / (g * Isp)
def compute_partials(self, inputs, jacobian):
theta = inputs['theta']
cos_theta = np.cos(theta)
sin_theta = np.sin(theta)
m = inputs['m']
F_T = inputs['thrust']
Isp = inputs['Isp']
# jacobian['vxdot', 'vx'] = -CDA * rho * vx / m
jacobian['vxdot', 'm'] = -(F_T * cos_theta) / m ** 2
jacobian['vxdot', 'theta'] = -(F_T / m) * sin_theta
jacobian['vxdot', 'thrust'] = cos_theta / m
# jacobian['vydot', 'vy'] = -CDA * rho * vy / m
jacobian['vydot', 'm'] = -(F_T * sin_theta) / m ** 2
jacobian['vydot', 'theta'] = (F_T / m) * cos_theta
jacobian['vydot', 'thrust'] = sin_theta / m
jacobian['mdot', 'thrust'] = -1.0 / (g * Isp)
jacobian['mdot', 'Isp'] = F_T / (g * Isp ** 2)
class LaunchVehicleLinearTangentODE(om.Group):
"""
The LaunchVehicleLinearTangentODE for this case consists of a guidance component and
the EOM. Guidance is simply an OpenMDAO ExecComp which computes the arctangent of the
tan_theta variable.
"""
def initialize(self):
self.options.declare('num_nodes', types=int,
desc='Number of nodes to be evaluated in the RHS')
def setup(self):
nn = self.options['num_nodes']
self.add_subsystem('guidance', om.ExecComp('theta=arctan(tan_theta)',
theta={'val': np.ones(nn),
'units': 'rad'},
tan_theta={'val': np.ones(nn)}))
self.add_subsystem('eom', LaunchVehicle2DEOM(num_nodes=nn))
self.connect('guidance.theta', 'eom.theta')
#
# Setup and solve the optimal control problem
#
p = om.Problem(model=om.Group())
traj = p.model.add_subsystem('traj', dm.Trajectory())
phase = dm.Phase(ode_class=LaunchVehicleLinearTangentODE,
transcription=dm.Radau(num_segments=20, order=3, compressed=False))
traj.add_phase('phase0', phase)
phase.set_time_options(fix_initial=True, duration_bounds=(10, 1000), units='s')
#
# Set the state options. We include rate_source, units, and targets here since the ODE
# is not decorated with their default values.
#
phase.add_state('x', fix_initial=True, lower=0, rate_source='eom.xdot', units='m')
phase.add_state('y', fix_initial=True, lower=0, rate_source='eom.ydot', units='m')
phase.add_state('vx', fix_initial=True, lower=0, rate_source='eom.vxdot',
units='m/s', targets=['eom.vx'])
phase.add_state('vy', fix_initial=True, rate_source='eom.vydot',
units='m/s', targets=['eom.vy'])
phase.add_state('m', fix_initial=True, rate_source='eom.mdot',
units='kg', targets=['eom.m'])
#
# The tangent of theta is modeled as a linear polynomial over the duration of the phase.
#
phase.add_control('tan_theta', order=1, units=None, opt=True,
targets=['guidance.tan_theta'], control_type='polynomial')
#
# Parameters values for thrust and specific impulse are design parameters. They are
# provided by an IndepVarComp in the phase, but with opt=False their values are not
# design variables in the optimization problem.
#
phase.add_parameter('thrust', units='N', opt=False, val=3.0 * 50000.0 * 1.61544,
targets=['eom.thrust'])
phase.add_parameter('Isp', units='s', opt=False, val=1.0E6, targets=['eom.Isp'])
#
# Set the boundary constraints. These are all states which could also be handled
# by setting fix_final=True and including the correct final value in the initial guess.
#
phase.add_boundary_constraint('y', loc='final', equals=1.85E5, linear=True)
phase.add_boundary_constraint('vx', loc='final', equals=1627.0)
phase.add_boundary_constraint('vy', loc='final', equals=0)
phase.add_objective('time', index=-1, scaler=0.01)
#
# Add theta as a timeseries output since it's not included by default.
#
phase.add_timeseries_output('guidance.theta', units='deg')
#
# Set the optimizer
#
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.driver.declare_coloring()
#
# We don't strictly need to define a linear solver here since our problem is entirely
# feed-forward with no iterative loops. It's good practice to add one, however, since
# failing to do so can cause incorrect derivatives if iterative processes are ever
# introduced to the system.
#
p.model.linear_solver = om.DirectSolver()
p.setup(check=True)
#
# Assign initial guesses for the independent variables in the problem.
#
phase.set_time_val(initial=0.0, duration=500.0)
phase.set_state_val('x', [0, 350000.0])
phase.set_state_val('y', [0, 185000.0])
phase.set_state_val('vx', [0, 1627.0])
phase.set_state_val('vy', [1.0E-6, 0.0])
phase.set_state_val('m', 50000)
phase.set_control_val('tan_theta', [[0.5 * np.pi], [0.0]])
#
# Solve the problem.
#
dm.run_problem(p, simulate=True)
--- Constraint Report [traj] ---
--- phase0 ---
[final] 1.8500e+05 == y [m]
[final] 1.6270e+03 == vx [m/s]
[final] 0.0000e+00 == vy [m/s]
INFO: checking out_of_order
INFO: checking system
INFO: checking solvers
INFO: checking dup_inputs
INFO: checking missing_recorders
INFO: checking unserializable_options
INFO: checking comp_has_no_outputs
INFO: checking auto_ivc_warnings
Model viewer data has already been recorded for Driver.
INFO: checking out_of_order
INFO: checking system
INFO: checking solvers
INFO: checking dup_inputs
INFO: checking missing_recorders
INFO: checking unserializable_options
INFO: checking comp_has_no_outputs
INFO: checking auto_ivc_warnings
Full total jacobian for problem 'problem' was computed 3 times, taking 0.1250771679999616 seconds.
Total jacobian shape: (303, 398)
Jacobian shape: (303, 398) (1.63% nonzero)
FWD solves: 10 REV solves: 0
Total colors vs. total size: 10 vs 398 (97.49% improvement)
Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.1251 sec
Time to compute coloring: 0.2679 sec
Memory to compute coloring: 0.5000 MB
Coloring created on: 2024-11-18 20:35:15
Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
Objective Function: _objfunc
Solution:
--------------------------------------------------------------------------------
Total Time: 2.0118
User Objective Time : 0.0098
User Sensitivity Time : 1.0174
Interface Time : 0.0337
Opt Solver Time: 0.9509
Calls to Objective Function : 6
Calls to Sens Function : 5
Objectives
Index Name Value
0 traj.phase0.t 4.817168E+00
Variables (c - continuous, i - integer, d - discrete)
Index Name Type Lower Bound Value Upper Bound Status
0 traj.phase0.t_duration_0 c 1.000000E+01 4.817168E+02 1.000000E+03
1 traj.phase0.states:x_0 c 0.000000E+00 6.106930E+01 1.000000E+21
2 traj.phase0.states:x_1 c 0.000000E+00 3.496393E+02 1.000000E+21
3 traj.phase0.states:x_2 c 0.000000E+00 4.914075E+02 1.000000E+21
4 traj.phase0.states:x_3 c 0.000000E+00 4.914075E+02 1.000000E+21
5 traj.phase0.states:x_4 c 0.000000E+00 9.095034E+02 1.000000E+21
6 traj.phase0.states:x_5 c 0.000000E+00 1.704975E+03 1.000000E+21
7 traj.phase0.states:x_6 c 0.000000E+00 2.010769E+03 1.000000E+21
8 traj.phase0.states:x_7 c 0.000000E+00 2.010769E+03 1.000000E+21
9 traj.phase0.states:x_8 c 0.000000E+00 2.811263E+03 1.000000E+21
10 traj.phase0.states:x_9 c 0.000000E+00 4.150586E+03 1.000000E+21
11 traj.phase0.states:x_10 c 0.000000E+00 4.632596E+03 1.000000E+21
12 traj.phase0.states:x_11 c 0.000000E+00 4.632596E+03 1.000000E+21
13 traj.phase0.states:x_12 c 0.000000E+00 5.844355E+03 1.000000E+21
14 traj.phase0.states:x_13 c 0.000000E+00 7.769668E+03 1.000000E+21
15 traj.phase0.states:x_14 c 0.000000E+00 8.441819E+03 1.000000E+21
16 traj.phase0.states:x_15 c 0.000000E+00 8.441819E+03 1.000000E+21
17 traj.phase0.states:x_16 c 0.000000E+00 1.009787E+04 1.000000E+21
18 traj.phase0.states:x_17 c 0.000000E+00 1.265747E+04 1.000000E+21
19 traj.phase0.states:x_18 c 0.000000E+00 1.353576E+04 1.000000E+21
20 traj.phase0.states:x_19 c 0.000000E+00 1.353576E+04 1.000000E+21
21 traj.phase0.states:x_20 c 0.000000E+00 1.567405E+04 1.000000E+21
22 traj.phase0.states:x_21 c 0.000000E+00 1.892357E+04 1.000000E+21
23 traj.phase0.states:x_22 c 0.000000E+00 2.002641E+04 1.000000E+21
24 traj.phase0.states:x_23 c 0.000000E+00 2.002641E+04 1.000000E+21
25 traj.phase0.states:x_24 c 0.000000E+00 2.269073E+04 1.000000E+21
26 traj.phase0.states:x_25 c 0.000000E+00 2.669437E+04 1.000000E+21
27 traj.phase0.states:x_26 c 0.000000E+00 2.804305E+04 1.000000E+21
28 traj.phase0.states:x_27 c 0.000000E+00 2.804305E+04 1.000000E+21
29 traj.phase0.states:x_28 c 0.000000E+00 3.128395E+04 1.000000E+21
30 traj.phase0.states:x_29 c 0.000000E+00 3.611577E+04 1.000000E+21
31 traj.phase0.states:x_30 c 0.000000E+00 3.773482E+04 1.000000E+21
32 traj.phase0.states:x_31 c 0.000000E+00 3.773482E+04 1.000000E+21
33 traj.phase0.states:x_32 c 0.000000E+00 4.161043E+04 1.000000E+21
34 traj.phase0.states:x_33 c 0.000000E+00 4.735527E+04 1.000000E+21
35 traj.phase0.states:x_34 c 0.000000E+00 4.927265E+04 1.000000E+21
36 traj.phase0.states:x_35 c 0.000000E+00 4.927265E+04 1.000000E+21
37 traj.phase0.states:x_36 c 0.000000E+00 5.384901E+04 1.000000E+21
38 traj.phase0.states:x_37 c 0.000000E+00 6.060228E+04 1.000000E+21
39 traj.phase0.states:x_38 c 0.000000E+00 6.284916E+04 1.000000E+21
40 traj.phase0.states:x_39 c 0.000000E+00 6.284916E+04 1.000000E+21
41 traj.phase0.states:x_40 c 0.000000E+00 6.819918E+04 1.000000E+21
42 traj.phase0.states:x_41 c 0.000000E+00 7.606414E+04 1.000000E+21
43 traj.phase0.states:x_42 c 0.000000E+00 7.867365E+04 1.000000E+21
44 traj.phase0.states:x_43 c 0.000000E+00 7.867365E+04 1.000000E+21
45 traj.phase0.states:x_44 c 0.000000E+00 8.487336E+04 1.000000E+21
46 traj.phase0.states:x_45 c 0.000000E+00 9.395375E+04 1.000000E+21
47 traj.phase0.states:x_46 c 0.000000E+00 9.695801E+04 1.000000E+21
48 traj.phase0.states:x_47 c 0.000000E+00 9.695801E+04 1.000000E+21
49 traj.phase0.states:x_48 c 0.000000E+00 1.040786E+05 1.000000E+21
50 traj.phase0.states:x_49 c 0.000000E+00 1.144647E+05 1.000000E+21
51 traj.phase0.states:x_50 c 0.000000E+00 1.178897E+05 1.000000E+21
52 traj.phase0.states:x_51 c 0.000000E+00 1.178897E+05 1.000000E+21
53 traj.phase0.states:x_52 c 0.000000E+00 1.259848E+05 1.000000E+21
54 traj.phase0.states:x_53 c 0.000000E+00 1.377346E+05 1.000000E+21
55 traj.phase0.states:x_54 c 0.000000E+00 1.415942E+05 1.000000E+21
56 traj.phase0.states:x_55 c 0.000000E+00 1.415942E+05 1.000000E+21
57 traj.phase0.states:x_56 c 0.000000E+00 1.506865E+05 1.000000E+21
58 traj.phase0.states:x_57 c 0.000000E+00 1.638094E+05 1.000000E+21
59 traj.phase0.states:x_58 c 0.000000E+00 1.681011E+05 1.000000E+21
60 traj.phase0.states:x_59 c 0.000000E+00 1.681011E+05 1.000000E+21
61 traj.phase0.states:x_60 c 0.000000E+00 1.781752E+05 1.000000E+21
62 traj.phase0.states:x_61 c 0.000000E+00 1.926292E+05 1.000000E+21
63 traj.phase0.states:x_62 c 0.000000E+00 1.973350E+05 1.000000E+21
64 traj.phase0.states:x_63 c 0.000000E+00 1.973350E+05 1.000000E+21
65 traj.phase0.states:x_64 c 0.000000E+00 2.083426E+05 1.000000E+21
66 traj.phase0.states:x_65 c 0.000000E+00 2.240467E+05 1.000000E+21
67 traj.phase0.states:x_66 c 0.000000E+00 2.291382E+05 1.000000E+21
68 traj.phase0.states:x_67 c 0.000000E+00 2.291382E+05 1.000000E+21
69 traj.phase0.states:x_68 c 0.000000E+00 2.410104E+05 1.000000E+21
70 traj.phase0.states:x_69 c 0.000000E+00 2.578637E+05 1.000000E+21
71 traj.phase0.states:x_70 c 0.000000E+00 2.633083E+05 1.000000E+21
72 traj.phase0.states:x_71 c 0.000000E+00 2.633083E+05 1.000000E+21
73 traj.phase0.states:x_72 c 0.000000E+00 2.759693E+05 1.000000E+21
74 traj.phase0.states:x_73 c 0.000000E+00 2.938674E+05 1.000000E+21
75 traj.phase0.states:x_74 c 0.000000E+00 2.996321E+05 1.000000E+21
76 traj.phase0.states:x_75 c 0.000000E+00 2.996321E+05 1.000000E+21
77 traj.phase0.states:x_76 c 0.000000E+00 3.130082E+05 1.000000E+21
78 traj.phase0.states:x_77 c 0.000000E+00 3.318524E+05 1.000000E+21
79 traj.phase0.states:x_78 c 0.000000E+00 3.379071E+05 1.000000E+21
80 traj.phase0.states:y_0 c 0.000000E+00 1.072874E+02 1.000000E+21
81 traj.phase0.states:y_1 c 0.000000E+00 6.062100E+02 1.000000E+21
82 traj.phase0.states:y_2 c 0.000000E+00 8.484836E+02 1.000000E+21
83 traj.phase0.states:y_3 c 0.000000E+00 8.484836E+02 1.000000E+21
84 traj.phase0.states:y_4 c 0.000000E+00 1.555240E+03 1.000000E+21
85 traj.phase0.states:y_5 c 0.000000E+00 2.875780E+03 1.000000E+21
86 traj.phase0.states:y_6 c 0.000000E+00 3.376666E+03 1.000000E+21
87 traj.phase0.states:y_7 c 0.000000E+00 3.376666E+03 1.000000E+21
88 traj.phase0.states:y_8 c 0.000000E+00 4.672843E+03 1.000000E+21
89 traj.phase0.states:y_9 c 0.000000E+00 6.799841E+03 1.000000E+21
90 traj.phase0.states:y_10 c 0.000000E+00 7.554202E+03 1.000000E+21
91 traj.phase0.states:y_11 c 0.000000E+00 7.554202E+03 1.000000E+21
92 traj.phase0.states:y_12 c 0.000000E+00 9.427357E+03 1.000000E+21
93 traj.phase0.states:y_13 c 0.000000E+00 1.234194E+04 1.000000E+21
94 traj.phase0.states:y_14 c 0.000000E+00 1.334336E+04 1.000000E+21
95 traj.phase0.states:y_15 c 0.000000E+00 1.334336E+04 1.000000E+21
96 traj.phase0.states:y_16 c 0.000000E+00 1.577789E+04 1.000000E+21
97 traj.phase0.states:y_17 c 0.000000E+00 1.945627E+04 1.000000E+21
98 traj.phase0.states:y_18 c 0.000000E+00 2.069660E+04 1.000000E+21
99 traj.phase0.states:y_19 c 0.000000E+00 2.069660E+04 1.000000E+21
100 traj.phase0.states:y_20 c 0.000000E+00 2.367267E+04 1.000000E+21
101 traj.phase0.states:y_21 c 0.000000E+00 2.808440E+04 1.000000E+21
102 traj.phase0.states:y_22 c 0.000000E+00 2.955320E+04 1.000000E+21
103 traj.phase0.states:y_23 c 0.000000E+00 2.955320E+04 1.000000E+21
104 traj.phase0.states:y_24 c 0.000000E+00 3.304522E+04 1.000000E+21
105 traj.phase0.states:y_25 c 0.000000E+00 3.815080E+04 1.000000E+21
106 traj.phase0.states:y_26 c 0.000000E+00 3.983445E+04 1.000000E+21
107 traj.phase0.states:y_27 c 0.000000E+00 3.983445E+04 1.000000E+21
108 traj.phase0.states:y_28 c 0.000000E+00 4.380893E+04 1.000000E+21
109 traj.phase0.states:y_29 c 0.000000E+00 4.955634E+04 1.000000E+21
110 traj.phase0.states:y_30 c 0.000000E+00 5.143680E+04 1.000000E+21
111 traj.phase0.states:y_31 c 0.000000E+00 5.143680E+04 1.000000E+21
112 traj.phase0.states:y_32 c 0.000000E+00 5.584932E+04 1.000000E+21
113 traj.phase0.states:y_33 c 0.000000E+00 6.216918E+04 1.000000E+21
114 traj.phase0.states:y_34 c 0.000000E+00 6.422234E+04 1.000000E+21
115 traj.phase0.states:y_35 c 0.000000E+00 6.422234E+04 1.000000E+21
116 traj.phase0.states:y_36 c 0.000000E+00 6.901329E+04 1.000000E+21
117 traj.phase0.states:y_37 c 0.000000E+00 7.581228E+04 1.000000E+21
118 traj.phase0.states:y_38 c 0.000000E+00 7.800565E+04 1.000000E+21
119 traj.phase0.states:y_39 c 0.000000E+00 7.800565E+04 1.000000E+21
120 traj.phase0.states:y_40 c 0.000000E+00 8.309475E+04 1.000000E+21
121 traj.phase0.states:y_41 c 0.000000E+00 9.024734E+04 1.000000E+21
122 traj.phase0.states:y_42 c 0.000000E+00 9.253734E+04 1.000000E+21
123 traj.phase0.states:y_43 c 0.000000E+00 9.253734E+04 1.000000E+21
124 traj.phase0.states:y_44 c 0.000000E+00 9.781724E+04 1.000000E+21
125 traj.phase0.states:y_45 c 0.000000E+00 1.051572E+05 1.000000E+21
126 traj.phase0.states:y_46 c 0.000000E+00 1.074866E+05 1.000000E+21
127 traj.phase0.states:y_47 c 0.000000E+00 1.074866E+05 1.000000E+21
128 traj.phase0.states:y_48 c 0.000000E+00 1.128178E+05 1.000000E+21
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362 traj.phase0.states:m_45 c -1.000000E+21 4.995721E+04 1.000000E+21
363 traj.phase0.states:m_46 c -1.000000E+21 4.995665E+04 1.000000E+21
364 traj.phase0.states:m_47 c -1.000000E+21 4.995665E+04 1.000000E+21
365 traj.phase0.states:m_48 c -1.000000E+21 4.995536E+04 1.000000E+21
366 traj.phase0.states:m_49 c -1.000000E+21 4.995359E+04 1.000000E+21
367 traj.phase0.states:m_50 c -1.000000E+21 4.995303E+04 1.000000E+21
368 traj.phase0.states:m_51 c -1.000000E+21 4.995303E+04 1.000000E+21
369 traj.phase0.states:m_52 c -1.000000E+21 4.995175E+04 1.000000E+21
370 traj.phase0.states:m_53 c -1.000000E+21 4.994998E+04 1.000000E+21
371 traj.phase0.states:m_54 c -1.000000E+21 4.994942E+04 1.000000E+21
372 traj.phase0.states:m_55 c -1.000000E+21 4.994942E+04 1.000000E+21
373 traj.phase0.states:m_56 c -1.000000E+21 4.994814E+04 1.000000E+21
374 traj.phase0.states:m_57 c -1.000000E+21 4.994637E+04 1.000000E+21
375 traj.phase0.states:m_58 c -1.000000E+21 4.994581E+04 1.000000E+21
376 traj.phase0.states:m_59 c -1.000000E+21 4.994581E+04 1.000000E+21
377 traj.phase0.states:m_60 c -1.000000E+21 4.994452E+04 1.000000E+21
378 traj.phase0.states:m_61 c -1.000000E+21 4.994275E+04 1.000000E+21
379 traj.phase0.states:m_62 c -1.000000E+21 4.994219E+04 1.000000E+21
380 traj.phase0.states:m_63 c -1.000000E+21 4.994219E+04 1.000000E+21
381 traj.phase0.states:m_64 c -1.000000E+21 4.994091E+04 1.000000E+21
382 traj.phase0.states:m_65 c -1.000000E+21 4.993914E+04 1.000000E+21
383 traj.phase0.states:m_66 c -1.000000E+21 4.993858E+04 1.000000E+21
384 traj.phase0.states:m_67 c -1.000000E+21 4.993858E+04 1.000000E+21
385 traj.phase0.states:m_68 c -1.000000E+21 4.993730E+04 1.000000E+21
386 traj.phase0.states:m_69 c -1.000000E+21 4.993553E+04 1.000000E+21
387 traj.phase0.states:m_70 c -1.000000E+21 4.993497E+04 1.000000E+21
388 traj.phase0.states:m_71 c -1.000000E+21 4.993497E+04 1.000000E+21
389 traj.phase0.states:m_72 c -1.000000E+21 4.993369E+04 1.000000E+21
390 traj.phase0.states:m_73 c -1.000000E+21 4.993192E+04 1.000000E+21
391 traj.phase0.states:m_74 c -1.000000E+21 4.993136E+04 1.000000E+21
392 traj.phase0.states:m_75 c -1.000000E+21 4.993136E+04 1.000000E+21
393 traj.phase0.states:m_76 c -1.000000E+21 4.993007E+04 1.000000E+21
394 traj.phase0.states:m_77 c -1.000000E+21 4.992830E+04 1.000000E+21
395 traj.phase0.states:m_78 c -1.000000E+21 4.992774E+04 1.000000E+21
396 traj.phase0.controls:tan_theta_0 c -1.000000E+21 2.747399E+00 1.000000E+21
397 traj.phase0.controls:tan_theta_1 c -1.000000E+21 -1.241462E+00 1.000000E+21
Constraints (i - inequality, e - equality)
Index Name Type Lower Value Upper Status Lagrange Multiplier (N/A)
0 traj.phases.phase0->final_boundary_constraint->y e 1.850000E+05 1.850000E+05 1.850000E+05 9.00000E+100
1 traj.phases.phase0->final_boundary_constraint->vx e 1.627000E+03 1.627000E+03 1.627000E+03 9.00000E+100
2 traj.phases.phase0->final_boundary_constraint->vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
3 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
4 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 4.278505E-14 0.000000E+00 9.00000E+100
5 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
6 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 3.422804E-13 0.000000E+00 9.00000E+100
7 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -2.567103E-13 0.000000E+00 9.00000E+100
8 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
9 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.711402E-13 0.000000E+00 9.00000E+100
10 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 1.026841E-12 0.000000E+00 9.00000E+100
11 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 1.540262E-12 0.000000E+00 9.00000E+100
12 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.711402E-12 0.000000E+00 9.00000E+100
13 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -2.053682E-12 0.000000E+00 9.00000E+100
14 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 4.449645E-12 0.000000E+00 9.00000E+100
15 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -7.872448E-12 0.000000E+00 9.00000E+100
16 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -2.738243E-12 0.000000E+00 9.00000E+100
17 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 3.765084E-12 0.000000E+00 9.00000E+100
18 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.163753E-11 0.000000E+00 9.00000E+100
19 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 2.053682E-12 0.000000E+00 9.00000E+100
20 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 1.369121E-12 0.000000E+00 9.00000E+100
21 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.848314E-11 0.000000E+00 9.00000E+100
22 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -6.161047E-12 0.000000E+00 9.00000E+100
23 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 1.300665E-11 0.000000E+00 9.00000E+100
24 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 1.369121E-12 0.000000E+00 9.00000E+100
25 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -2.053682E-12 0.000000E+00 9.00000E+100
26 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -4.791925E-12 0.000000E+00 9.00000E+100
27 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -2.190594E-11 0.000000E+00 9.00000E+100
28 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -6.845607E-13 0.000000E+00 9.00000E+100
29 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 1.369121E-12 0.000000E+00 9.00000E+100
30 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 1.369121E-11 0.000000E+00 9.00000E+100
31 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 4.107364E-12 0.000000E+00 9.00000E+100
32 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 6.845607E-12 0.000000E+00 9.00000E+100
33 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.232209E-11 0.000000E+00 9.00000E+100
34 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.916770E-11 0.000000E+00 9.00000E+100
35 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 5.476486E-12 0.000000E+00 9.00000E+100
36 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -8.214729E-12 0.000000E+00 9.00000E+100
37 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 1.779858E-11 0.000000E+00 9.00000E+100
38 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -3.285892E-11 0.000000E+00 9.00000E+100
39 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -5.887222E-11 0.000000E+00 9.00000E+100
40 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 1.369121E-12 0.000000E+00 9.00000E+100
41 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.369121E-12 0.000000E+00 9.00000E+100
42 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 8.214729E-12 0.000000E+00 9.00000E+100
43 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 5.887222E-11 0.000000E+00 9.00000E+100
44 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 7.119432E-11 0.000000E+00 9.00000E+100
45 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 3.012067E-11 0.000000E+00 9.00000E+100
46 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 8.214729E-12 0.000000E+00 9.00000E+100
47 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 1.095297E-11 0.000000E+00 9.00000E+100
48 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 4.381189E-11 0.000000E+00 9.00000E+100
49 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -3.833540E-11 0.000000E+00 9.00000E+100
50 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.095297E-11 0.000000E+00 9.00000E+100
51 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 1.177444E-10 0.000000E+00 9.00000E+100
52 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -8.214729E-12 0.000000E+00 9.00000E+100
53 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.369121E-11 0.000000E+00 9.00000E+100
54 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -4.655013E-11 0.000000E+00 9.00000E+100
55 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 1.916770E-11 0.000000E+00 9.00000E+100
56 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -6.024134E-11 0.000000E+00 9.00000E+100
57 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 1.807240E-10 0.000000E+00 9.00000E+100
58 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.369121E-11 0.000000E+00 9.00000E+100
59 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 8.214729E-12 0.000000E+00 9.00000E+100
60 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.588181E-10 0.000000E+00 9.00000E+100
61 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -5.476486E-12 0.000000E+00 9.00000E+100
62 traj.phase0.collocation_constraint.defects:x e 0.000000E+00 -5.476486E-12 0.000000E+00 9.00000E+100
63 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 9.176232E-14 0.000000E+00 9.00000E+100
64 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -1.283551E-13 0.000000E+00 9.00000E+100
65 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -8.557009E-14 0.000000E+00 9.00000E+100
66 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 3.422804E-13 0.000000E+00 9.00000E+100
67 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -1.711402E-13 0.000000E+00 9.00000E+100
68 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 6.845607E-13 0.000000E+00 9.00000E+100
69 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 2.395963E-12 0.000000E+00 9.00000E+100
70 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 1.369121E-12 0.000000E+00 9.00000E+100
71 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -3.422804E-13 0.000000E+00 9.00000E+100
72 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 1.369121E-12 0.000000E+00 9.00000E+100
73 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
74 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 4.107364E-12 0.000000E+00 9.00000E+100
75 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -1.163753E-11 0.000000E+00 9.00000E+100
76 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 3.422804E-12 0.000000E+00 9.00000E+100
77 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -1.369121E-12 0.000000E+00 9.00000E+100
78 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -1.026841E-11 0.000000E+00 9.00000E+100
79 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -1.369121E-12 0.000000E+00 9.00000E+100
80 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 6.845607E-13 0.000000E+00 9.00000E+100
81 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -8.899290E-12 0.000000E+00 9.00000E+100
82 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 3.422804E-12 0.000000E+00 9.00000E+100
83 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -2.053682E-11 0.000000E+00 9.00000E+100
84 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 4.791925E-11 0.000000E+00 9.00000E+100
85 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -4.107364E-12 0.000000E+00 9.00000E+100
86 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 2.053682E-12 0.000000E+00 9.00000E+100
87 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -1.642946E-11 0.000000E+00 9.00000E+100
88 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -1.369121E-12 0.000000E+00 9.00000E+100
89 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 6.845607E-12 0.000000E+00 9.00000E+100
90 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -3.148979E-11 0.000000E+00 9.00000E+100
91 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -2.601331E-11 0.000000E+00 9.00000E+100
92 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
93 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 1.369121E-12 0.000000E+00 9.00000E+100
94 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -1.095297E-11 0.000000E+00 9.00000E+100
95 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 1.506034E-11 0.000000E+00 9.00000E+100
96 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 1.369121E-12 0.000000E+00 9.00000E+100
97 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 1.095297E-11 0.000000E+00 9.00000E+100
98 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 1.369121E-11 0.000000E+00 9.00000E+100
99 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -1.506034E-11 0.000000E+00 9.00000E+100
100 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 9.583850E-12 0.000000E+00 9.00000E+100
101 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -1.095297E-11 0.000000E+00 9.00000E+100
102 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -1.054224E-10 0.000000E+00 9.00000E+100
103 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 2.053682E-11 0.000000E+00 9.00000E+100
104 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -5.476486E-11 0.000000E+00 9.00000E+100
105 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -7.119432E-11 0.000000E+00 9.00000E+100
106 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 1.916770E-11 0.000000E+00 9.00000E+100
107 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -1.013150E-10 0.000000E+00 9.00000E+100
108 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -6.161047E-11 0.000000E+00 9.00000E+100
109 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 4.723469E-11 0.000000E+00 9.00000E+100
110 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 8.420097E-11 0.000000E+00 9.00000E+100
111 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -1.622409E-10 0.000000E+00 9.00000E+100
112 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 3.217435E-11 0.000000E+00 9.00000E+100
113 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -6.366415E-11 0.000000E+00 9.00000E+100
114 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 7.530168E-12 0.000000E+00 9.00000E+100
115 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 2.806699E-11 0.000000E+00 9.00000E+100
116 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -3.559716E-11 0.000000E+00 9.00000E+100
117 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -2.567103E-11 0.000000E+00 9.00000E+100
118 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 3.046295E-11 0.000000E+00 9.00000E+100
119 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -5.099977E-11 0.000000E+00 9.00000E+100
120 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 3.936224E-12 0.000000E+00 9.00000E+100
121 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 2.139252E-11 0.000000E+00 9.00000E+100
122 traj.phase0.collocation_constraint.defects:y e 0.000000E+00 -4.000402E-11 0.000000E+00 9.00000E+100
123 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 1.337033E-14 0.000000E+00 9.00000E+100
124 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 -8.022196E-15 0.000000E+00 9.00000E+100
125 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 1.069626E-14 0.000000E+00 9.00000E+100
126 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 -2.674065E-15 0.000000E+00 9.00000E+100
127 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 -3.743692E-14 0.000000E+00 9.00000E+100
128 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 3.208878E-14 0.000000E+00 9.00000E+100
129 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 -2.674065E-15 0.000000E+00 9.00000E+100
130 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 -1.871846E-14 0.000000E+00 9.00000E+100
131 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 2.674065E-14 0.000000E+00 9.00000E+100
132 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 2.674065E-14 0.000000E+00 9.00000E+100
133 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 -1.069626E-14 0.000000E+00 9.00000E+100
134 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 3.743692E-14 0.000000E+00 9.00000E+100
135 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 -1.069626E-13 0.000000E+00 9.00000E+100
136 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 1.604439E-14 0.000000E+00 9.00000E+100
137 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 -5.348131E-15 0.000000E+00 9.00000E+100
138 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 1.390514E-13 0.000000E+00 9.00000E+100
139 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 2.139252E-14 0.000000E+00 9.00000E+100
140 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 3.743692E-14 0.000000E+00 9.00000E+100
141 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 1.176589E-13 0.000000E+00 9.00000E+100
142 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 -1.443995E-13 0.000000E+00 9.00000E+100
143 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 1.390514E-13 0.000000E+00 9.00000E+100
144 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 9.626635E-14 0.000000E+00 9.00000E+100
145 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 -6.417757E-14 0.000000E+00 9.00000E+100
146 traj.phase0.collocation_constraint.defects:vx e 0.000000E+00 1.123107E-13 0.000000E+00 9.00000E+100
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323 traj.phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
324 traj.phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
325 traj.phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
326 traj.phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
327 traj.phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
328 traj.phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
329 traj.phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
330 traj.phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
331 traj.phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
332 traj.phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
333 traj.phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
334 traj.phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
335 traj.phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
336 traj.phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
337 traj.phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
338 traj.phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
339 traj.phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
340 traj.phase0.continuity_comp.defect_states:y e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
341 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
342 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
343 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
344 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
345 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
346 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
347 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
348 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
349 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
350 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
351 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
352 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
353 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
354 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
355 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
356 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
357 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
358 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
359 traj.phase0.continuity_comp.defect_states:vx e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
360 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
361 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
362 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
363 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
364 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
365 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
366 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
367 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
368 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
369 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
370 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
371 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
372 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
373 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
374 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
375 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
376 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
377 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
378 traj.phase0.continuity_comp.defect_states:vy e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
379 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
380 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
381 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
382 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
383 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
384 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
385 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
386 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
387 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
388 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
389 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
390 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
391 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
392 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
393 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
394 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
395 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
396 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
397 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
Exit Status
Inform Description
0 Optimization terminated successfully.
--------------------------------------------------------------------------------
/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/visualization/opt_report/opt_report.py:625: UserWarning: Attempting to set identical low and high ylims makes transformation singular; automatically expanding.
ax.set_ylim([ymin_plot, ymax_plot])
/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/group.py:1137: DerivativesWarning:Constraints or objectives [ode_eval.control_interp.control_rates:tan_theta_rate, ode_eval.control_interp.control_rates:tan_theta_rate2, ode_eval.control_interp.control_values:tan_theta] cannot be impacted by the design variables of the problem because no partials were defined for them in their parent component(s).
Simulating trajectory traj
Model viewer data has already been recorded for Driver.
Done simulating trajectory traj
Problem: problem
Driver: pyOptSparseDriver
success : True
iterations : 8
runtime : 2.4969E+00 s
model_evals : 8
model_time : 8.5201E-03 s
deriv_evals : 6
deriv_time : 7.8792E-02 s
exit_status : SUCCESS
sol = om.CaseReader(p.get_outputs_dir() / 'dymos_solution.db').get_case('final')
sim = om.CaseReader(traj.sim_prob.get_outputs_dir() / 'dymos_simulation.db').get_case('final')
fig, [traj_ax, control_ax, param_ax] = plt.subplots(nrows=3, ncols=1, figsize=(10, 8))
traj_ax.plot(sol.get_val('traj.phase0.timeseries.x'),
sol.get_val('traj.phase0.timeseries.y'),
marker='o',
ms=4,
linestyle='None',
label='solution')
traj_ax.plot(sim.get_val('traj.phase0.timeseries.x'),
sim.get_val('traj.phase0.timeseries.y'),
marker=None,
linestyle='-',
label='simulation')
traj_ax.set_xlabel('range (m)')
traj_ax.set_ylabel('altitude (m)')
traj_ax.set_aspect('equal')
traj_ax.grid(True)
control_ax.plot(sol.get_val('traj.phase0.timeseries.time'),
sol.get_val('traj.phase0.timeseries.theta'),
marker='o',
ms=4,
linestyle='None')
control_ax.plot(sim.get_val('traj.phase0.timeseries.time'),
sim.get_val('traj.phase0.timeseries.theta'),
linestyle='-',
marker=None)
control_ax.set_ylabel(r'$\theta$ (deg)')
control_ax.grid(True)
tan_theta_sol = sol.get_val('traj.phase0.timeseries.tan_theta')
tan_theta_sim = sim.get_val('traj.phase0.timeseries.tan_theta')
param_ax.plot(sol.get_val('traj.phase0.timeseries.time'),
tan_theta_sol,
marker='o',
ms=4,
linestyle='None')
param_ax.plot(sim.get_val('traj.phase0.timeseries.time'),
tan_theta_sim,
linestyle='-',
marker=None)
param_ax.set_xlabel('time (s)')
param_ax.set_ylabel(r'$tan(\theta)$')
param_ax.grid(True)
plt.suptitle('Single Stage to Orbit Solution Using a Polynomial Control')
fig.legend(loc='lower center', ncol=2)
plt.show()
