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Commercial Aircraft Range Maximization by Differential Inclusion

In this example we seek to maximize the range of a commercial aircraft flying at a constant Mach number with a fixed initial fuel load. The initial and final altitudes are constrained to 10000 ft (that is, in this simplified example we're ignoring the aircraft behavior near the ground).

This example is simplified in several ways. The Mach number is fixed at 0.8. When only considering fuel burn, the aircraft will tend to fly slower to conserve fuel, ignoring the running costs of being airborne.

For a more detailed optimization of commercial aircraft performance, see Betts1.

Differential Inclusion

In this case we also use the steady flight assumption to allow the problem to be parameterized with a different control set. Rather than providing throttle/thrust and angle of attack as control variables, we use a differential inclusion approach. Whereas altitude and velocity are often treated as state variables to be integrated, here we take a slightly different approach.

Rather than using the differential equations to compute rates for the flight path angle and true airspeed, we use a nonlinear solver to determine the alpha and thrust time-history which is needed to make the given altitude and airspeed time-history possible. This technique is known as differential inclusion. It was demonstrated by Seywald2. Since the collocation techniques in Dymos are based on polynomial approximations, rates of the control variables can be easily calculated, which can then be applied to the reordered dynamics equations to solve for angle of attack and thrust.

The use of collocation/psuedospectral techniques in solving problems via differential inclusion has been examined by Fahroo and Ross3 and Kumar and Seywald4. Since the differential inclusion approach demonstrated here relies on nonlinear solvers running within the ODE model, obtaining accurate derivatives is paramount. Computing derivatives with finite differences in the presence of nonlinear solvers can lead to inaccurate derivatives based on the properties of the solver. With OpenMDAO's unified derivatives framework, the sensitivy to solver tolerances is greatly reduced.

Pitfalls of Differential Inclusion

Differential inclusion works well in this case but it is highly dependent on the parameterization of the problem. For instance, it is possible for the optimizer to suggest a flight profile that requires thrust well beyond the capabilities of the vehicle. In our case, the throttle parameter \tau is path constrained within the optimizer, so that the optimizer can make the solution physically attainable by our model.

We have two options for how to tackle this problem. We could specify altitude as a control variable, and use it's approximate derivative (alt\_rate) to provide the altitude rate for the flight equilibrium conditions. In practice, however, this noisy derivative of altitude can cause numerical difficulties. Other times, the optimizer will shape the control to satisfy our equilibrium conditions at the collocation nodes but be wildly wrong in between these nodes. One simple way to get around this is to still integrate altitude, but to provide climb\_rate as the control variable. This makes it easy to constraint climb\_rate with bounds constraints, and the time-history of altitude will be smoother since it is the time integral of the rate of climb.

Solver Options

In general, openmdao.api.AnalysisError should be raised when the design variables provided by the optimizer result in nonconvergence of the solvers. This informs pyoptsparse to backtrack along its line search for a solution. This error can be raised by the compute method of a component. The nonlinear solver can also raise this error if it fails to converge by setting the following options:

self.nonlinear_solver.options['maxiter'] = 150
self.nonlinear_solver.options['err_on_maxiter'] = True

In the course of solving, an outer NewtonSolver won't necessarily force subsystems to be solved, instead relying on the derivative at the at the previous solution. In the context of OpenMDAO, even explicit components constitute subsystems. This can lead to poorly converged solutions.

Setting the solve_subystems option to True will force subsystems to be updated, making sure that all derivative information is up-to-date.

self.nonlinear_solver.options['solve_subsystems'] = True
self.nonlinear_solver.options['max_sub_solves'] = 10

The Impact of Choice of Transcription

The high-order Gauss-Lobatto method used by Dymos evaluates the ordinary differential equations in a two-step process. First, the ODEs are evaluated at the state discretization nodes. Using the state values and derivatives, values and rates at the collocation nodes are then interpolated. If a large rate is found at one of the state discretization nodes, the interpolation at the collocation node can be outside of the expected range, leading to nonconvergence of solvers within the ODEs.

There is also an overhead cost to invoking solvers. While differential inclusion reduces the number of design variables for the optimizer, it also slows down each evaluation of the ODE somewhat. Since evaluating the collocation constraints in the Gauss-Lobatto method requires two evaluations of the ODE, it typically suffers greater slowdown that the Radau Pseudospectral method, which evaluates the defects of the ODE with a single evaluation that encompasses all the nodes.

For these reasons the Radau Pseudospectral transcription is typically preferable when using a differential inclusion approach to problems.

Problem Formulation

State Variables

Name Description Fixed Initial Value Fixed Final Value
range distance flown along ground True (0 NM) False
mass_fuel mass of fuel aboard aircraft True (30000 lbm) True (0 lbm)
alt aircraft altitude True (10000 ft) True (10000 ft)

Dynamic Controls

Name Description Optimized Fixed Initial Value Fixed Final Value
climb_rate aircraft rate of climb True False False

Parameters

Name Description Optimized
mach mach number False (0.8)
S aerodynamic reference area False (427.8 m**2)
mass_empty aircraft empty mass False (330693.393 lbm)
mass_payload aircraft payload mass False (74100 lbm)

Objective

Name Description Location Minimized or Maximized
r range final Maximized

Nonlinear Path Constraints

Name Description Lower Upper
tau engine throttle parameter 0.01 1.0

Nonlinear Boundary Constraints

None

Models

Atmosphere

This problem uses an analytic fit to the 1976 standard atmosphere.

Name Description Input or Output
alt altitude (m) input
pres static pressure (Pa) output
temp temperature (K) output
sos speed of sound (m/s) output
rho density (kg/m**3) output

True Airspeed

TrueAirspeedComp uses the Mach number, provided as a control, and the speed of sound from the atmosphere model to compute the true airspeed of the aircraft.

\begin{align} TAS &= mach \cdot sos \end{align}
Name Description Input or Output
mach Mach number input
sos speed of sound (m/s) input
TAS true airspeed (m/s) output

Flight Path Angle

SteadyFlightPathAngleComp uses the true airspeed and the climb rate, obtained by differentiating the altitude time history at the nodes, to compute the flight path angle.

\begin{align} \gamma &= \arctan \frac{TAS}{\dot h} \end{align}
Name Description Input or Output
TAS true airspeed (m/s) input
alt_rate climb rate (m/s) input
gamma flight path angle (rad) output

Range Rate

RangeRateComp uses the true airspeed and the flight path angle to determine the velocity projected along the ground. This is the derivative of the state variable range.

\begin{align} \dot{range} &= TAS \cos \gamma \end{align}
Name Description Input or Output
TAS true airspeed (m/s) input
gamma flight path angle (rad) input
dXdt:range range rate (m/s) output

Mass

The component MassComp defined in mass_comp.py computes the aircraft total mass based on its empty mass, payload mass, and current fuel mass. It also computes total weight which simplifies some equations later on.

\begin{align} mass_{total} &= mass_{empty} + mass_{payload} + mass_{fuel} W_{total} = 9.80665 \, mass_{total} \end{align}
Name Description Input or Output
mass_empty aircraft empty mass (kg) input
mass_payload payload mass (kg) input
mass_fuel fuel mass (kg) input
mass_total total aircraft mass (kg) output
W_total total aircraft weight (N) output

Dynamic Pressure

The DynamicPressureComp computes the dynamic pressure from true airspeed and atmospheric density.

\begin{align} q &= \frac{1}{2} \rho TAS^2 \end{align}
Name Description Input or Output
TAS true airspeed (m/s) input
rho atmospheric density (kg/m**3) input
q dynamic pressure (Pa) output

Aerodynamics

The aerodynamics group computes the aerodynamic coefficients and forces on the vehicle. It consists of an interpolation component which outputs lift, drag, and moment coefficients as a function of Mach number, angle of attack, altitude, and tail rotation angle. A second component then uses these coefficients, along with dynamic pressure and aerodynamic reference area, to compute the lift and drag forces on the vehicle.

The aerodynamics group resides within the flight equilibrium group. As that group iterates to find the combination of thrust coefficient, angle of attack, and tail rotation angle, aerodynamics needs to update the values of the interpolated coefficients and resulting forces.

Organizationally speaking, we logically could have put the dynamic pressure component within the aerodynamics group. However, since that group doesn't need to be updated with changes in alpha and tail angle, it's more efficient to leave it outside of flight equilibrium group.

Name Description Input or Output
mach mach number input
alt altitude (m) input
alpha angle of attack (deg) input
eta tail rotation angle (deg) input
CL lift coefficient output
CD drag coefficient output
CM moment coefficient output
L lift force (N) output
D drag force (N) output

Note

This example uses openmdao.api.MetaModelStructuredComp to interpolate aerodynamic properties of the vehicle. This component is somewhat easier to use since it is distributed as part of OpenMDAO, but it can be significantly slower than alternatives such as MBI and SMT. The Aerodynamics group includes an implementation of the aerodynamics coefficients interpolant which uses MBI that is commented out. By switching to MBI for this component, this problem will solve roughly 20 times faster.

Flight Equilibrium

The steady flight equilibrium group uses balances to solve for the angle of attack and tail plane rotation angle such that the aircraft is in steady flight (the rates of change in flight path angle and true airspeed are zero) and the aerodynamic moment in the pitch axis is zero.

Of course, in reality the vehicle will accelerate, but the flight profile being modeled is so benign that assuming steady flight at discrete points (nodes) in the trajectory is not terribly inaccurate.

The thrust necessary for steady flight is computed by balancing the drag equation

\begin{align} C_T &= W_{total} \frac{sin \gamma}{q \cdot S \cdot \cos \alpha} + \frac{C_D}{\cos \alpha} \end{align}

The lift coefficient required for steady flight is found by balancing lift and weight:

\begin{align} \tilde{C_L} &= W_{total} \frac{cos \gamma}{q \cdot S} - C_T \sin \alpha \end{align}

Using coefficients in the balance equations is better scaled from a numerical standpoint.

Propulsion

Having determined the thrust, the propulsion group then computes the rate of fuel burn. In addition, by normalizing thrust at any point by the maximum possible thrust, we obtain the throttle parameter \tau. The propulsion group uses a number of components to perform these calculations.

\begin{align} T &= C_T \cdot q \cdot S \end{align}

Maximum thrust is computed by multiplying sea-level thrust by the ratio of pressure to sea-level atmospheric pressure.

\begin{align} T_{max} &= T_{max,sl} \frac{P}{P_{sl}} \end{align}

The throttle parameter is then the ratio current thrust to maximum possible thrust.

\begin{align} \tau &= \frac{T}{T_{max}} \end{align}

The thrust specific fuel consumption is computed as follows:

\begin{align} TSFC &= TSFC_{sl} - 1.5 E - 10 \cdot 9.80665 \cdot alt \end{align}

Finally, fuel burn rate is:

\begin{align} \dot{mass_{fuel}} &= -TSFC \frac{T}{9.80665} \end{align}

The ODE System: aircraft_ode.py

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class AircraftODE(om.Group):

    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(name='mass_comp',
                           subsys=MassComp(num_nodes=nn),
                           promotes_inputs=['mass_fuel'])

        self.connect('mass_comp.W_total', 'flight_equilibrium.W_total')

        self.add_subsystem(name='atmos',
                           subsys=USatm1976Comp(num_nodes=nn),
                           promotes_inputs=[('h', 'alt')])

        self.connect('atmos.pres', 'propulsion.pres')
        self.connect('atmos.sos', 'tas_comp.sos')
        self.connect('atmos.rho', 'q_comp.rho')

        self.add_subsystem(name='tas_comp',
                           subsys=TrueAirspeedComp(num_nodes=nn))

        self.connect('tas_comp.TAS',
                     ('gam_comp.TAS', 'q_comp.TAS', 'range_rate_comp.TAS'))

        self.add_subsystem(name='gam_comp',
                           subsys=SteadyFlightPathAngleComp(num_nodes=nn))

        self.connect('gam_comp.gam', ('flight_equilibrium.gam', 'range_rate_comp.gam'))

        self.add_subsystem(name='q_comp',
                           subsys=DynamicPressureComp(num_nodes=nn))

        self.connect('q_comp.q', ('aero.q', 'flight_equilibrium.q', 'propulsion.q'))

        self.add_subsystem(name='flight_equilibrium',
                           subsys=SteadyFlightEquilibriumGroup(num_nodes=nn),
                           promotes_inputs=['aero.*', 'alt'],
                           promotes_outputs=['aero.*'])

        self.connect('flight_equilibrium.CT', 'propulsion.CT')

        self.add_subsystem(name='propulsion', subsys=PropulsionGroup(num_nodes=nn),
                           promotes_inputs=['alt'])

        self.add_subsystem(name='range_rate_comp', subsys=RangeRateComp(num_nodes=nn))

        # We promoted multiple inputs to the group named 'alt'.
        # In order to automatically create a source variable for 'alt', we must specify their units
        # since they have different units in different components.
        self.set_input_defaults('alt', val=np.ones(nn,), units='m')

In this case the system has only two integrated states: range and mass_fuel. There are six parameters. Two of them (alt and climb_rate) will be varied dynamically in the phase The other four (mach, S, mass_empty, and mass_payload), will be set to fixed values as non-optimized parameters. More details on the various models involved can be found in the examples code.

Building and running the problem

In the following code we define and solve the optimal control problem. Note that we demonstrate the use of externally-connected design parameters in this case. The four parameters are connected to a source provided by the assumptions IndepVarComp.

import matplotlib.pyplot as plt

import openmdao.api as om
from openmdao.utils.assert_utils import assert_near_equal

import dymos as dm

from dymos.examples.aircraft_steady_flight.aircraft_ode import AircraftODE
from dymos.examples.plotting import plot_results
from dymos.utils.lgl import lgl

p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.driver.declare_coloring()

num_seg = 15
seg_ends, _ = lgl(num_seg + 1)

traj = p.model.add_subsystem('traj', dm.Trajectory())

phase = traj.add_phase('phase0',
                       dm.Phase(ode_class=AircraftODE,
                                transcription=dm.Radau(num_segments=num_seg,
                                                       segment_ends=seg_ends,
                                                       order=3, compressed=False)))

# Pass Reference Area from an external source
assumptions = p.model.add_subsystem('assumptions', om.IndepVarComp())
assumptions.add_output('S', val=427.8, units='m**2')
assumptions.add_output('mass_empty', val=1.0, units='kg')
assumptions.add_output('mass_payload', val=1.0, units='kg')

phase.set_time_options(fix_initial=True,
                       duration_bounds=(300, 10000),
                       duration_ref=5600)

phase.add_state('range', units='NM',
                rate_source='range_rate_comp.dXdt:range',
                fix_initial=True, fix_final=False, ref=1e-3,
                defect_ref=1e-3, lower=0, upper=2000)

phase.add_state('mass_fuel', units='lbm',
                rate_source='propulsion.dXdt:mass_fuel',
                fix_initial=True, fix_final=True,
                upper=1.5E5, lower=0.0, ref=1e2, defect_ref=1e2)

phase.add_state('alt', units='kft',
                rate_source='climb_rate',
                fix_initial=True, fix_final=True,
                lower=0.0, upper=60, ref=1e-3, defect_ref=1e-3)

phase.add_control('climb_rate', units='ft/min', opt=True, lower=-3000, upper=3000,
                  targets=['gam_comp.climb_rate'],
                  rate_continuity=True, rate2_continuity=False)

phase.add_control('mach', targets=['tas_comp.mach', 'aero.mach'], units=None, opt=False)

phase.add_parameter('S',
                    targets=['aero.S', 'flight_equilibrium.S', 'propulsion.S'],
                    units='m**2')

phase.add_parameter('mass_empty', targets=['mass_comp.mass_empty'], units='kg')
phase.add_parameter('mass_payload', targets=['mass_comp.mass_payload'], units='kg')

phase.add_path_constraint('propulsion.tau', lower=0.01, upper=2.0)

p.model.connect('assumptions.S', 'traj.phase0.parameters:S')
p.model.connect('assumptions.mass_empty', 'traj.phase0.parameters:mass_empty')
p.model.connect('assumptions.mass_payload', 'traj.phase0.parameters:mass_payload')

phase.add_objective('range', loc='final', ref=-1.0e-4)

phase.add_timeseries_output('aero.CL')
phase.add_timeseries_output('aero.CD')

p.setup()

p['traj.phase0.t_initial'] = 0.0
p['traj.phase0.t_duration'] = 3600.0
p['traj.phase0.states:range'][:] = phase.interpolate(ys=(0, 724.0), nodes='state_input')
p['traj.phase0.states:mass_fuel'][:] = phase.interpolate(ys=(30000, 1e-3), nodes='state_input')
p['traj.phase0.states:alt'][:] = 10.0

p['traj.phase0.controls:mach'][:] = 0.8

p['assumptions.S'] = 427.8
p['assumptions.mass_empty'] = 0.15E6
p['assumptions.mass_payload'] = 84.02869 * 400

dm.run_problem(p)



exp_out = traj.simulate()





plot_results([('traj.phase0.timeseries.states:range', 'traj.phase0.timeseries.states:alt',
               'range (NM)', 'altitude (kft)'),
              ('traj.phase0.timeseries.time', 'traj.phase0.timeseries.states:mass_fuel',
               'time (s)', 'fuel mass (lbm)'),
              ('traj.phase0.timeseries.time', 'traj.phase0.timeseries.CL',
               'time (s)', 'lift coefficient'),
              ('traj.phase0.timeseries.time', 'traj.phase0.timeseries.CD',
               'time (s)', 'drag coefficient')],
             title='Commercial Aircraft Optimization',
             p_sol=p, p_sim=exp_out)

plt.show()
Full total jacobian was computed 3 times, taking 0.631199 seconds.
Total jacobian shape: (224, 221) 


Jacobian shape: (224, 221)  ( 2.65% nonzero)
FWD solves: 11   REV solves: 0
Total colors vs. total size: 11 vs 221  (95.0% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.631199 sec.
Time to compute coloring: 0.007026 sec.


Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
    Objective Function: _objfunc

    Solution: 
--------------------------------------------------------------------------------
    Total Time:                   22.3041
       User Objective Time :      14.1515
       User Sensitivity Time :     3.7681
       Interface Time :            1.0471
       Opt Solver Time:            3.3374
    Calls to Objective Function :      77
    Calls to Sens Function :           76


   Objectives
      Index  Name                                                    Value          Optimum
          0  traj.phases.phase0.indep_states.states:range    -7.253192E+06     0.000000E+00

   Variables (c - continuous, i - integer, d - discrete)
      Index  Name                                                                     Type      Lower Bound            Value      Upper Bound     Status
          0  traj.phases.phase0.time_extents.t_duration_0                                c     5.357143E-02     1.005745E+00     1.785714E+00           
          1  traj.phases.phase0.indep_states.states:range_0                              c     0.000000E+00     4.296678E+03     2.000000E+06           
          2  traj.phases.phase0.indep_states.states:range_1                              c     0.000000E+00     1.018510E+04     2.000000E+06           
          3  traj.phases.phase0.indep_states.states:range_2                              c     0.000000E+00     1.203902E+04     2.000000E+06           
          4  traj.phases.phase0.indep_states.states:range_3                              c     0.000000E+00     1.203902E+04     2.000000E+06           
          5  traj.phases.phase0.indep_states.states:range_4                              c     0.000000E+00     2.177664E+04     2.000000E+06           
          6  traj.phases.phase0.indep_states.states:range_5                              c     0.000000E+00     3.499256E+04     2.000000E+06           
          7  traj.phases.phase0.indep_states.states:range_6                              c     0.000000E+00     3.912151E+04     2.000000E+06           
          8  traj.phases.phase0.indep_states.states:range_7                              c     0.000000E+00     3.912151E+04     2.000000E+06           
          9  traj.phases.phase0.indep_states.states:range_8                              c     0.000000E+00     5.331891E+04     2.000000E+06           
         10  traj.phases.phase0.indep_states.states:range_9                              c     0.000000E+00     7.243469E+04     2.000000E+06           
         11  traj.phases.phase0.indep_states.states:range_10                             c     0.000000E+00     7.838492E+04     2.000000E+06           
         12  traj.phases.phase0.indep_states.states:range_11                             c     0.000000E+00     7.838492E+04     2.000000E+06           
         13  traj.phases.phase0.indep_states.states:range_12                             c     0.000000E+00     9.617161E+04     2.000000E+06           
         14  traj.phases.phase0.indep_states.states:range_13                             c     0.000000E+00     1.207224E+05     2.000000E+06           
         15  traj.phases.phase0.indep_states.states:range_14                             c     0.000000E+00     1.284922E+05     2.000000E+06           
         16  traj.phases.phase0.indep_states.states:range_15                             c     0.000000E+00     1.284922E+05     2.000000E+06           
         17  traj.phases.phase0.indep_states.states:range_16                             c     0.000000E+00     1.496890E+05     2.000000E+06           
         18  traj.phases.phase0.indep_states.states:range_17                             c     0.000000E+00     1.789362E+05     2.000000E+06           
         19  traj.phases.phase0.indep_states.states:range_18                             c     0.000000E+00     1.881928E+05     2.000000E+06           
         20  traj.phases.phase0.indep_states.states:range_19                             c     0.000000E+00     1.881928E+05     2.000000E+06           
         21  traj.phases.phase0.indep_states.states:range_20                             c     0.000000E+00     2.119256E+05     2.000000E+06           
         22  traj.phases.phase0.indep_states.states:range_21                             c     0.000000E+00     2.446719E+05     2.000000E+06           
         23  traj.phases.phase0.indep_states.states:range_22                             c     0.000000E+00     2.550361E+05     2.000000E+06           
         24  traj.phases.phase0.indep_states.states:range_23                             c     0.000000E+00     2.550361E+05     2.000000E+06           
         25  traj.phases.phase0.indep_states.states:range_24                             c     0.000000E+00     2.803331E+05     2.000000E+06           
         26  traj.phases.phase0.indep_states.states:range_25                             c     0.000000E+00     3.152380E+05     2.000000E+06           
         27  traj.phases.phase0.indep_states.states:range_26                             c     0.000000E+00     3.262852E+05     2.000000E+06           
         28  traj.phases.phase0.indep_states.states:range_27                             c     0.000000E+00     3.262852E+05     2.000000E+06           
         29  traj.phases.phase0.indep_states.states:range_28                             c     0.000000E+00     3.521110E+05     2.000000E+06           
         30  traj.phases.phase0.indep_states.states:range_29                             c     0.000000E+00     3.877453E+05     2.000000E+06           
         31  traj.phases.phase0.indep_states.states:range_30                             c     0.000000E+00     3.990234E+05     2.000000E+06           
         32  traj.phases.phase0.indep_states.states:range_31                             c     0.000000E+00     3.990234E+05     2.000000E+06           
         33  traj.phases.phase0.indep_states.states:range_32                             c     0.000000E+00     4.243205E+05     2.000000E+06           
         34  traj.phases.phase0.indep_states.states:range_33                             c     0.000000E+00     4.592253E+05     2.000000E+06           
         35  traj.phases.phase0.indep_states.states:range_34                             c     0.000000E+00     4.702726E+05     2.000000E+06           
         36  traj.phases.phase0.indep_states.states:range_35                             c     0.000000E+00     4.702726E+05     2.000000E+06           
         37  traj.phases.phase0.indep_states.states:range_36                             c     0.000000E+00     4.940054E+05     2.000000E+06           
         38  traj.phases.phase0.indep_states.states:range_37                             c     0.000000E+00     5.267517E+05     2.000000E+06           
         39  traj.phases.phase0.indep_states.states:range_38                             c     0.000000E+00     5.371158E+05     2.000000E+06           
         40  traj.phases.phase0.indep_states.states:range_39                             c     0.000000E+00     5.371158E+05     2.000000E+06           
         41  traj.phases.phase0.indep_states.states:range_40                             c     0.000000E+00     5.583125E+05     2.000000E+06           
         42  traj.phases.phase0.indep_states.states:range_41                             c     0.000000E+00     5.875596E+05     2.000000E+06           
         43  traj.phases.phase0.indep_states.states:range_42                             c     0.000000E+00     5.968163E+05     2.000000E+06           
         44  traj.phases.phase0.indep_states.states:range_43                             c     0.000000E+00     5.968163E+05     2.000000E+06           
         45  traj.phases.phase0.indep_states.states:range_44                             c     0.000000E+00     6.146093E+05     2.000000E+06           
         46  traj.phases.phase0.indep_states.states:range_45                             c     0.000000E+00     6.391551E+05     2.000000E+06           
         47  traj.phases.phase0.indep_states.states:range_46                             c     0.000000E+00     6.469212E+05     2.000000E+06           
         48  traj.phases.phase0.indep_states.states:range_47                             c     0.000000E+00     6.469212E+05     2.000000E+06           
         49  traj.phases.phase0.indep_states.states:range_48                             c     0.000000E+00     6.606407E+05     2.000000E+06           
         50  traj.phases.phase0.indep_states.states:range_49                             c     0.000000E+00     6.799508E+05     2.000000E+06           
         51  traj.phases.phase0.indep_states.states:range_50                             c     0.000000E+00     6.861976E+05     2.000000E+06           
         52  traj.phases.phase0.indep_states.states:range_51                             c     0.000000E+00     6.861976E+05     2.000000E+06           
         53  traj.phases.phase0.indep_states.states:range_52                             c     0.000000E+00     6.956909E+05     2.000000E+06           
         54  traj.phases.phase0.indep_states.states:range_53                             c     0.000000E+00     7.090114E+05     2.000000E+06           
         55  traj.phases.phase0.indep_states.states:range_54                             c     0.000000E+00     7.132801E+05     2.000000E+06           
         56  traj.phases.phase0.indep_states.states:range_55                             c     0.000000E+00     7.132801E+05     2.000000E+06           
         57  traj.phases.phase0.indep_states.states:range_56                             c     0.000000E+00     7.175324E+05     2.000000E+06           
         58  traj.phases.phase0.indep_states.states:range_57                             c     0.000000E+00     7.234398E+05     2.000000E+06           
         59  traj.phases.phase0.indep_states.states:range_58                             c     0.000000E+00     7.253192E+05     2.000000E+06           
         60  traj.phases.phase0.indep_states.states:mass_fuel_0                          c     0.000000E+00     2.957288E+02     1.500000E+03           
         61  traj.phases.phase0.indep_states.states:mass_fuel_1                          c     0.000000E+00     2.900532E+02     1.500000E+03           
         62  traj.phases.phase0.indep_states.states:mass_fuel_2                          c     0.000000E+00     2.883071E+02     1.500000E+03           
         63  traj.phases.phase0.indep_states.states:mass_fuel_3                          c     0.000000E+00     2.883071E+02     1.500000E+03           
         64  traj.phases.phase0.indep_states.states:mass_fuel_4                          c     0.000000E+00     2.794375E+02     1.500000E+03           
         65  traj.phases.phase0.indep_states.states:mass_fuel_5                          c     0.000000E+00     2.681251E+02     1.500000E+03           
         66  traj.phases.phase0.indep_states.states:mass_fuel_6                          c     0.000000E+00     2.647390E+02     1.500000E+03           
         67  traj.phases.phase0.indep_states.states:mass_fuel_7                          c     0.000000E+00     2.647390E+02     1.500000E+03           
         68  traj.phases.phase0.indep_states.states:mass_fuel_8                          c     0.000000E+00     2.536039E+02     1.500000E+03           
         69  traj.phases.phase0.indep_states.states:mass_fuel_9                          c     0.000000E+00     2.402198E+02     1.500000E+03           
         70  traj.phases.phase0.indep_states.states:mass_fuel_10                         c     0.000000E+00     2.365303E+02     1.500000E+03           
         71  traj.phases.phase0.indep_states.states:mass_fuel_11                         c     0.000000E+00     2.365303E+02     1.500000E+03           
         72  traj.phases.phase0.indep_states.states:mass_fuel_12                         c     0.000000E+00     2.271569E+02     1.500000E+03           
         73  traj.phases.phase0.indep_states.states:mass_fuel_13                         c     0.000000E+00     2.167718E+02     1.500000E+03           
         74  traj.phases.phase0.indep_states.states:mass_fuel_14                         c     0.000000E+00     2.137406E+02     1.500000E+03           
         75  traj.phases.phase0.indep_states.states:mass_fuel_15                         c     0.000000E+00     2.137406E+02     1.500000E+03           
         76  traj.phases.phase0.indep_states.states:mass_fuel_16                         c     0.000000E+00     2.055505E+02     1.500000E+03           
         77  traj.phases.phase0.indep_states.states:mass_fuel_17                         c     0.000000E+00     1.942440E+02     1.500000E+03           
         78  traj.phases.phase0.indep_states.states:mass_fuel_18                         c     0.000000E+00     1.906474E+02     1.500000E+03           
         79  traj.phases.phase0.indep_states.states:mass_fuel_19                         c     0.000000E+00     1.906474E+02     1.500000E+03           
         80  traj.phases.phase0.indep_states.states:mass_fuel_20                         c     0.000000E+00     1.813684E+02     1.500000E+03           
         81  traj.phases.phase0.indep_states.states:mass_fuel_21                         c     0.000000E+00     1.685055E+02     1.500000E+03           
         82  traj.phases.phase0.indep_states.states:mass_fuel_22                         c     0.000000E+00     1.644405E+02     1.500000E+03           
         83  traj.phases.phase0.indep_states.states:mass_fuel_23                         c     0.000000E+00     1.644405E+02     1.500000E+03           
         84  traj.phases.phase0.indep_states.states:mass_fuel_24                         c     0.000000E+00     1.545595E+02     1.500000E+03           
         85  traj.phases.phase0.indep_states.states:mass_fuel_25                         c     0.000000E+00     1.410109E+02     1.500000E+03           
         86  traj.phases.phase0.indep_states.states:mass_fuel_26                         c     0.000000E+00     1.367395E+02     1.500000E+03           
         87  traj.phases.phase0.indep_states.states:mass_fuel_27                         c     0.000000E+00     1.367395E+02     1.500000E+03           
         88  traj.phases.phase0.indep_states.states:mass_fuel_28                         c     0.000000E+00     1.267741E+02     1.500000E+03           
         89  traj.phases.phase0.indep_states.states:mass_fuel_29                         c     0.000000E+00     1.130167E+02     1.500000E+03           
         90  traj.phases.phase0.indep_states.states:mass_fuel_30                         c     0.000000E+00     1.086476E+02     1.500000E+03           
         91  traj.phases.phase0.indep_states.states:mass_fuel_31                         c     0.000000E+00     1.086476E+02     1.500000E+03           
         92  traj.phases.phase0.indep_states.states:mass_fuel_32                         c     0.000000E+00     9.882068E+01     1.500000E+03           
         93  traj.phases.phase0.indep_states.states:mass_fuel_33                         c     0.000000E+00     8.533850E+01     1.500000E+03           
         94  traj.phases.phase0.indep_states.states:mass_fuel_34                         c     0.000000E+00     8.112566E+01     1.500000E+03           
         95  traj.phases.phase0.indep_states.states:mass_fuel_35                         c     0.000000E+00     8.112566E+01     1.500000E+03           
         96  traj.phases.phase0.indep_states.states:mass_fuel_36                         c     0.000000E+00     7.217445E+01     1.500000E+03           
         97  traj.phases.phase0.indep_states.states:mass_fuel_37                         c     0.000000E+00     5.977096E+01     1.500000E+03           
         98  traj.phases.phase0.indep_states.states:mass_fuel_38                         c     0.000000E+00     5.576169E+01     1.500000E+03           
         99  traj.phases.phase0.indep_states.states:mass_fuel_39                         c     0.000000E+00     5.576169E+01     1.500000E+03           
        100  traj.phases.phase0.indep_states.states:mass_fuel_40                         c     0.000000E+00     4.740508E+01     1.500000E+03           
        101  traj.phases.phase0.indep_states.states:mass_fuel_41                         c     0.000000E+00     3.591060E+01     1.500000E+03           
        102  traj.phases.phase0.indep_states.states:mass_fuel_42                         c     0.000000E+00     3.238019E+01     1.500000E+03           
        103  traj.phases.phase0.indep_states.states:mass_fuel_43                         c     0.000000E+00     3.238019E+01     1.500000E+03           
        104  traj.phases.phase0.indep_states.states:mass_fuel_44                         c     0.000000E+00     2.594932E+01     1.500000E+03           
        105  traj.phases.phase0.indep_states.states:mass_fuel_45                         c     0.000000E+00     1.877792E+01     1.500000E+03           
        106  traj.phases.phase0.indep_states.states:mass_fuel_46                         c     0.000000E+00     1.714725E+01     1.500000E+03           
        107  traj.phases.phase0.indep_states.states:mass_fuel_47                         c     0.000000E+00     1.714725E+01     1.500000E+03           
        108  traj.phases.phase0.indep_states.states:mass_fuel_48                         c     0.000000E+00     1.500528E+01     1.500000E+03           
        109  traj.phases.phase0.indep_states.states:mass_fuel_49                         c     0.000000E+00     1.242885E+01     1.500000E+03           
        110  traj.phases.phase0.indep_states.states:mass_fuel_50                         c     0.000000E+00     1.140878E+01     1.500000E+03           
        111  traj.phases.phase0.indep_states.states:mass_fuel_51                         c     0.000000E+00     1.140878E+01     1.500000E+03           
        112  traj.phases.phase0.indep_states.states:mass_fuel_52                         c     0.000000E+00     9.488592E+00     1.500000E+03           
        113  traj.phases.phase0.indep_states.states:mass_fuel_53                         c     0.000000E+00     5.926274E+00     1.500000E+03           
        114  traj.phases.phase0.indep_states.states:mass_fuel_54                         c     0.000000E+00     4.549629E+00     1.500000E+03           
        115  traj.phases.phase0.indep_states.states:mass_fuel_55                         c     0.000000E+00     4.549629E+00     1.500000E+03           
        116  traj.phases.phase0.indep_states.states:mass_fuel_56                         c     0.000000E+00     3.057672E+00     1.500000E+03           
        117  traj.phases.phase0.indep_states.states:mass_fuel_57                         c     0.000000E+00     7.774804E-01     1.500000E+03           
        118  traj.phases.phase0.indep_states.states:alt_0                                c     0.000000E+00     1.152138E+04     6.000000E+04           
        119  traj.phases.phase0.indep_states.states:alt_1                                c     0.000000E+00     1.362057E+04     6.000000E+04           
        120  traj.phases.phase0.indep_states.states:alt_2                                c     0.000000E+00     1.428495E+04     6.000000E+04           
        121  traj.phases.phase0.indep_states.states:alt_3                                c     0.000000E+00     1.428495E+04     6.000000E+04           
        122  traj.phases.phase0.indep_states.states:alt_4                                c     0.000000E+00     1.780282E+04     6.000000E+04           
        123  traj.phases.phase0.indep_states.states:alt_5                                c     0.000000E+00     2.265675E+04     6.000000E+04           
        124  traj.phases.phase0.indep_states.states:alt_6                                c     0.000000E+00     2.419300E+04     6.000000E+04           
        125  traj.phases.phase0.indep_states.states:alt_7                                c     0.000000E+00     2.419300E+04     6.000000E+04           
        126  traj.phases.phase0.indep_states.states:alt_8                                c     0.000000E+00     2.945322E+04     6.000000E+04           
        127  traj.phases.phase0.indep_states.states:alt_9                                c     0.000000E+00     3.561675E+04     6.000000E+04           
        128  traj.phases.phase0.indep_states.states:alt_10                               c     0.000000E+00     3.708274E+04     6.000000E+04           
        129  traj.phases.phase0.indep_states.states:alt_11                               c     0.000000E+00     3.708274E+04     6.000000E+04           
        130  traj.phases.phase0.indep_states.states:alt_12                               c     0.000000E+00     3.975775E+04     6.000000E+04           
        131  traj.phases.phase0.indep_states.states:alt_13                               c     0.000000E+00     4.064557E+04     6.000000E+04           
        132  traj.phases.phase0.indep_states.states:alt_14                               c     0.000000E+00     4.061959E+04     6.000000E+04           
        133  traj.phases.phase0.indep_states.states:alt_15                               c     0.000000E+00     4.061959E+04     6.000000E+04           
        134  traj.phases.phase0.indep_states.states:alt_16                               c     0.000000E+00     4.049324E+04     6.000000E+04           
        135  traj.phases.phase0.indep_states.states:alt_17                               c     0.000000E+00     4.035069E+04     6.000000E+04           
        136  traj.phases.phase0.indep_states.states:alt_18                               c     0.000000E+00     4.033242E+04     6.000000E+04           
        137  traj.phases.phase0.indep_states.states:alt_19                               c     0.000000E+00     4.033242E+04     6.000000E+04           
        138  traj.phases.phase0.indep_states.states:alt_20                               c     0.000000E+00     4.036582E+04     6.000000E+04           
        139  traj.phases.phase0.indep_states.states:alt_21                               c     0.000000E+00     4.051293E+04     6.000000E+04           
        140  traj.phases.phase0.indep_states.states:alt_22                               c     0.000000E+00     4.056016E+04     6.000000E+04           
        141  traj.phases.phase0.indep_states.states:alt_23                               c     0.000000E+00     4.056016E+04     6.000000E+04           
        142  traj.phases.phase0.indep_states.states:alt_24                               c     0.000000E+00     4.064259E+04     6.000000E+04           
        143  traj.phases.phase0.indep_states.states:alt_25                               c     0.000000E+00     4.069208E+04     6.000000E+04           
        144  traj.phases.phase0.indep_states.states:alt_26                               c     0.000000E+00     4.069663E+04     6.000000E+04           
        145  traj.phases.phase0.indep_states.states:alt_27                               c     0.000000E+00     4.069663E+04     6.000000E+04           
        146  traj.phases.phase0.indep_states.states:alt_28                               c     0.000000E+00     4.069966E+04     6.000000E+04           
        147  traj.phases.phase0.indep_states.states:alt_29                               c     0.000000E+00     4.074913E+04     6.000000E+04           
        148  traj.phases.phase0.indep_states.states:alt_30                               c     0.000000E+00     4.079143E+04     6.000000E+04           
        149  traj.phases.phase0.indep_states.states:alt_31                               c     0.000000E+00     4.079143E+04     6.000000E+04           
        150  traj.phases.phase0.indep_states.states:alt_32                               c     0.000000E+00     4.093453E+04     6.000000E+04           
        151  traj.phases.phase0.indep_states.states:alt_33                               c     0.000000E+00     4.107631E+04     6.000000E+04           
        152  traj.phases.phase0.indep_states.states:alt_34                               c     0.000000E+00     4.106519E+04     6.000000E+04           
        153  traj.phases.phase0.indep_states.states:alt_35                               c     0.000000E+00     4.106519E+04     6.000000E+04           
        154  traj.phases.phase0.indep_states.states:alt_36                               c     0.000000E+00     4.093627E+04     6.000000E+04           
        155  traj.phases.phase0.indep_states.states:alt_37                               c     0.000000E+00     4.085195E+04     6.000000E+04           
        156  traj.phases.phase0.indep_states.states:alt_38                               c     0.000000E+00     4.093274E+04     6.000000E+04           
        157  traj.phases.phase0.indep_states.states:alt_39                               c     0.000000E+00     4.093274E+04     6.000000E+04           
        158  traj.phases.phase0.indep_states.states:alt_40                               c     0.000000E+00     4.130027E+04     6.000000E+04           
        159  traj.phases.phase0.indep_states.states:alt_41                               c     0.000000E+00     4.178899E+04     6.000000E+04           
        160  traj.phases.phase0.indep_states.states:alt_42                               c     0.000000E+00     4.181894E+04     6.000000E+04           
        161  traj.phases.phase0.indep_states.states:alt_43                               c     0.000000E+00     4.181894E+04     6.000000E+04           
        162  traj.phases.phase0.indep_states.states:alt_44                               c     0.000000E+00     4.145803E+04     6.000000E+04           
        163  traj.phases.phase0.indep_states.states:alt_45                               c     0.000000E+00     3.888731E+04     6.000000E+04           
        164  traj.phases.phase0.indep_states.states:alt_46                               c     0.000000E+00     3.728542E+04     6.000000E+04           
        165  traj.phases.phase0.indep_states.states:alt_47                               c     0.000000E+00     3.728542E+04     6.000000E+04           
        166  traj.phases.phase0.indep_states.states:alt_48                               c     0.000000E+00     3.339057E+04     6.000000E+04           
        167  traj.phases.phase0.indep_states.states:alt_49                               c     0.000000E+00     2.652575E+04     6.000000E+04           
        168  traj.phases.phase0.indep_states.states:alt_50                               c     0.000000E+00     2.419300E+04     6.000000E+04           
        169  traj.phases.phase0.indep_states.states:alt_51                               c     0.000000E+00     2.419300E+04     6.000000E+04           
        170  traj.phases.phase0.indep_states.states:alt_52                               c     0.000000E+00     2.067514E+04     6.000000E+04           
        171  traj.phases.phase0.indep_states.states:alt_53                               c     0.000000E+00     1.582121E+04     6.000000E+04           
        172  traj.phases.phase0.indep_states.states:alt_54                               c     0.000000E+00     1.428495E+04     6.000000E+04           
        173  traj.phases.phase0.indep_states.states:alt_55                               c     0.000000E+00     1.428495E+04     6.000000E+04           
        174  traj.phases.phase0.indep_states.states:alt_56                               c     0.000000E+00     1.276358E+04     6.000000E+04           
        175  traj.phases.phase0.indep_states.states:alt_57                               c     0.000000E+00     1.066439E+04     6.000000E+04           
        176  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_0       c    -3.000000E+03     3.000000E+03     3.000000E+03          u
        177  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_1       c    -3.000000E+03     3.000000E+03     3.000000E+03          u
        178  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_2       c    -3.000000E+03     3.000000E+03     3.000000E+03          u
        179  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_3       c    -3.000000E+03     3.000000E+03     3.000000E+03          u
        180  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_4       c    -3.000000E+03     3.000000E+03     3.000000E+03          u
        181  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_5       c    -3.000000E+03     3.000000E+03     3.000000E+03          u
        182  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_6       c    -3.000000E+03     3.000000E+03     3.000000E+03          u
        183  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_7       c    -3.000000E+03     2.834371E+03     3.000000E+03           
        184  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_8       c    -3.000000E+03     2.061971E+03     3.000000E+03           
        185  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_9       c    -3.000000E+03     1.686121E+03     3.000000E+03           
        186  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_10      c    -3.000000E+03     6.845453E+02     3.000000E+03           
        187  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_11      c    -3.000000E+03     4.147195E+00     3.000000E+03           
        188  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_12      c    -3.000000E+03    -4.170977E+01     3.000000E+03           
        189  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_13      c    -3.000000E+03    -4.636420E+01     3.000000E+03           
        190  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_14      c    -3.000000E+03    -2.228770E+01     3.000000E+03           
        191  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_15      c    -3.000000E+03    -7.299650E+00     3.000000E+03           
        192  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_16      c    -3.000000E+03     2.539918E+01     3.000000E+03           
        193  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_17      c    -3.000000E+03     3.679450E+01     3.000000E+03           
        194  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_18      c    -3.000000E+03     3.225436E+01     3.000000E+03           
        195  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_19      c    -3.000000E+03     1.818121E+01     3.000000E+03           
        196  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_20      c    -3.000000E+03     4.637643E+00     3.000000E+03           
        197  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_21      c    -3.000000E+03     1.770328E+00     3.000000E+03           
        198  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_22      c    -3.000000E+03     2.110102E+00     3.000000E+03           
        199  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_23      c    -3.000000E+03     2.308602E+01     3.000000E+03           
        200  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_24      c    -3.000000E+03     3.467896E+01     3.000000E+03           
        201  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_25      c    -3.000000E+03     4.607942E+01     3.000000E+03           
        202  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_26      c    -3.000000E+03     5.087413E+00     3.000000E+03           
        203  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_27      c    -3.000000E+03    -2.158948E+01     3.000000E+03           
        204  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_28      c    -3.000000E+03    -4.925130E+01     3.000000E+03           
        205  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_29      c    -3.000000E+03     3.317302E+01     3.000000E+03           
        206  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_30      c    -3.000000E+03     8.839285E+01     3.000000E+03           
        207  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_31      c    -3.000000E+03     1.573793E+02     3.000000E+03           
        208  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_32      c    -3.000000E+03     6.121676E+01     3.000000E+03           
        209  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_33      c    -3.000000E+03    -1.544493E+01     3.000000E+03           
        210  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_34      c    -3.000000E+03    -3.501028E+02     3.000000E+03           
        211  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_35      c    -3.000000E+03    -1.356744E+03     3.000000E+03           
        212  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_36      c    -3.000000E+03    -1.806976E+03     3.000000E+03           
        213  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_37      c    -3.000000E+03    -2.503751E+03     3.000000E+03           
        214  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_38      c    -3.000000E+03    -2.971319E+03     3.000000E+03           
        215  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_39      c    -3.000000E+03    -3.000000E+03     3.000000E+03          l
        216  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_40      c    -3.000000E+03    -3.000000E+03     3.000000E+03          l
        217  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_41      c    -3.000000E+03    -3.000000E+03     3.000000E+03          l
        218  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_42      c    -3.000000E+03    -3.000000E+03     3.000000E+03          l
        219  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_43      c    -3.000000E+03    -3.000000E+03     3.000000E+03          l
        220  traj.phases.phase0.control_group.indep_controls.controls:climb_rate_44      c    -3.000000E+03    -3.000000E+03     3.000000E+03          l

   Constraints (i - inequality, e - equality)
      Index  Name                                                                    Type          Lower           Value           Upper    Status  Lagrange Multiplier (N/A)
          0  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    1.189313E-12    0.000000E+00              9.00000E+100
          1  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -3.567939E-12    0.000000E+00              9.00000E+100
          2  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -1.189313E-12    0.000000E+00              9.00000E+100
          3  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -2.750037E-12    0.000000E+00              9.00000E+100
          4  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
          5  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
          6  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    4.189187E-11    0.000000E+00              9.00000E+100
          7  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -3.351349E-11    0.000000E+00              9.00000E+100
          8  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    4.189187E-11    0.000000E+00              9.00000E+100
          9  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -3.273889E-11    0.000000E+00              9.00000E+100
         10  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    5.456482E-12    0.000000E+00              9.00000E+100
         11  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    2.728241E-11    0.000000E+00              9.00000E+100
         12  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    5.200260E-11    0.000000E+00              9.00000E+100
         13  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -6.500325E-12    0.000000E+00              9.00000E+100
         14  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    6.500325E-12    0.000000E+00              9.00000E+100
         15  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -7.278025E-12    0.000000E+00              9.00000E+100
         16  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    3.639013E-11    0.000000E+00              9.00000E+100
         17  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -1.091704E-10    0.000000E+00              9.00000E+100
         18  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    1.551551E-11    0.000000E+00              9.00000E+100
         19  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -4.654653E-11    0.000000E+00              9.00000E+100
         20  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -3.878877E-11    0.000000E+00              9.00000E+100
         21  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    1.583975E-11    0.000000E+00              9.00000E+100
         22  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -3.167951E-11    0.000000E+00              9.00000E+100
         23  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    3.959938E-11    0.000000E+00              9.00000E+100
         24  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -2.637637E-10    0.000000E+00              9.00000E+100
         25  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    2.482481E-10    0.000000E+00              9.00000E+100
         26  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -2.172171E-10    0.000000E+00              9.00000E+100
         27  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -2.183408E-10    0.000000E+00              9.00000E+100
         28  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    2.183408E-11    0.000000E+00              9.00000E+100
         29  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    7.278025E-11    0.000000E+00              9.00000E+100
         30  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -7.215361E-10    0.000000E+00              9.00000E+100
         31  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    1.560078E-10    0.000000E+00              9.00000E+100
         32  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -1.235062E-10    0.000000E+00              9.00000E+100
         33  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -3.110195E-10    0.000000E+00              9.00000E+100
         34  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    3.437583E-10    0.000000E+00              9.00000E+100
         35  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -6.002130E-11    0.000000E+00              9.00000E+100
         36  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    3.309457E-10    0.000000E+00              9.00000E+100
         37  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    2.262161E-10    0.000000E+00              9.00000E+100
         38  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -2.178377E-10    0.000000E+00              9.00000E+100
         39  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -1.870025E-10    0.000000E+00              9.00000E+100
         40  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    2.200030E-10    0.000000E+00              9.00000E+100
         41  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -1.705023E-10    0.000000E+00              9.00000E+100
         42  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    5.601664E-10    0.000000E+00              9.00000E+100
         43  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00   -4.162596E-10    0.000000E+00              9.00000E+100
         44  traj.phases.phase0.collocation_constraint.defects:range                    e   0.000000E+00    4.816718E-10    0.000000E+00              9.00000E+100
         45  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -2.123637E-13    0.000000E+00              9.00000E+100
         46  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    6.850443E-14    0.000000E+00              9.00000E+100
         47  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -7.535487E-14    0.000000E+00              9.00000E+100
         48  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -3.872052E-14    0.000000E+00              9.00000E+100
         49  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    4.928066E-14    0.000000E+00              9.00000E+100
         50  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -5.632076E-14    0.000000E+00              9.00000E+100
         51  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    1.689080E-13    0.000000E+00              9.00000E+100
         52  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    1.608648E-14    0.000000E+00              9.00000E+100
         53  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -5.094051E-14    0.000000E+00              9.00000E+100
         54  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -1.746074E-14    0.000000E+00              9.00000E+100
         55  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -2.968326E-14    0.000000E+00              9.00000E+100
         56  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    7.508119E-14    0.000000E+00              9.00000E+100
         57  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -3.307365E-13    0.000000E+00              9.00000E+100
         58  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -8.320416E-15    0.000000E+00              9.00000E+100
         59  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    1.705685E-13    0.000000E+00              9.00000E+100
         60  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -3.493452E-14    0.000000E+00              9.00000E+100
         61  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -4.657936E-15    0.000000E+00              9.00000E+100
         62  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -3.493452E-14    0.000000E+00              9.00000E+100
         63  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    3.971970E-14    0.000000E+00              9.00000E+100
         64  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    5.213211E-14    0.000000E+00              9.00000E+100
         65  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -8.936933E-14    0.000000E+00              9.00000E+100
         66  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    5.068721E-14    0.000000E+00              9.00000E+100
         67  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    1.267180E-14    0.000000E+00              9.00000E+100
         68  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -1.267180E-14    0.000000E+00              9.00000E+100
         69  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    1.117117E-13    0.000000E+00              9.00000E+100
         70  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -1.985985E-14    0.000000E+00              9.00000E+100
         71  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -9.929926E-15    0.000000E+00              9.00000E+100
         72  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -6.986904E-14    0.000000E+00              9.00000E+100
         73  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -1.863174E-14    0.000000E+00              9.00000E+100
         74  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    3.726349E-14    0.000000E+00              9.00000E+100
         75  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    3.328166E-14    0.000000E+00              9.00000E+100
         76  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    1.872094E-14    0.000000E+00              9.00000E+100
         77  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    1.040052E-14    0.000000E+00              9.00000E+100
         78  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -3.492148E-15    0.000000E+00              9.00000E+100
         79  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    2.269896E-14    0.000000E+00              9.00000E+100
         80  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -3.492148E-15    0.000000E+00              9.00000E+100
         81  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    2.211890E-14    0.000000E+00              9.00000E+100
         82  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    1.709188E-14    0.000000E+00              9.00000E+100
         83  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -2.681079E-15    0.000000E+00              9.00000E+100
         84  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -2.640036E-15    0.000000E+00              9.00000E+100
         85  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -1.760024E-15    0.000000E+00              9.00000E+100
         86  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -7.040095E-15    0.000000E+00              9.00000E+100
         87  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    1.141741E-15    0.000000E+00              9.00000E+100
         88  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00   -1.902901E-15    0.000000E+00              9.00000E+100
         89  traj.phases.phase0.collocation_constraint.defects:mass_fuel                e   0.000000E+00    3.805802E-16    0.000000E+00              9.00000E+100
         90  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -2.973283E-13    0.000000E+00              9.00000E+100
         91  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -2.378626E-12    0.000000E+00              9.00000E+100
         92  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    8.919848E-13    0.000000E+00              9.00000E+100
         93  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -1.375019E-11    0.000000E+00              9.00000E+100
         94  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -7.562602E-12    0.000000E+00              9.00000E+100
         95  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    4.812565E-12    0.000000E+00              9.00000E+100
         96  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    1.885134E-11    0.000000E+00              9.00000E+100
         97  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -1.361486E-11    0.000000E+00              9.00000E+100
         98  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -4.189187E-12    0.000000E+00              9.00000E+100
         99  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -1.841563E-11    0.000000E+00              9.00000E+100
        100  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    8.525753E-12    0.000000E+00              9.00000E+100
        101  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    2.228419E-11    0.000000E+00              9.00000E+100
        102  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    8.074622E-12    0.000000E+00              9.00000E+100
        103  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    3.173987E-12    0.000000E+00              9.00000E+100
        104  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -1.859956E-11    0.000000E+00              9.00000E+100
        105  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    1.464134E-11    0.000000E+00              9.00000E+100
        106  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -1.620498E-11    0.000000E+00              9.00000E+100
        107  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -1.222481E-12    0.000000E+00              9.00000E+100
        108  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    3.897060E-11    0.000000E+00              9.00000E+100
        109  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    6.530454E-12    0.000000E+00              9.00000E+100
        110  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    2.507634E-12    0.000000E+00              9.00000E+100
        111  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -5.962917E-11    0.000000E+00              9.00000E+100
        112  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    1.574501E-11    0.000000E+00              9.00000E+100
        113  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    1.203450E-11    0.000000E+00              9.00000E+100
        114  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    1.412154E-11    0.000000E+00              9.00000E+100
        115  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -1.024266E-11    0.000000E+00              9.00000E+100
        116  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -1.234877E-12    0.000000E+00              9.00000E+100
        117  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    1.519572E-11    0.000000E+00              9.00000E+100
        118  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -6.055544E-12    0.000000E+00              9.00000E+100
        119  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    1.120134E-11    0.000000E+00              9.00000E+100
        120  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -2.204016E-11    0.000000E+00              9.00000E+100
        121  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -3.250162E-12    0.000000E+00              9.00000E+100
        122  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -1.640316E-11    0.000000E+00              9.00000E+100
        123  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    2.795381E-11    0.000000E+00              9.00000E+100
        124  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -1.193605E-11    0.000000E+00              9.00000E+100
        125  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        126  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    1.728039E-11    0.000000E+00              9.00000E+100
        127  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    5.236483E-12    0.000000E+00              9.00000E+100
        128  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    2.094593E-12    0.000000E+00              9.00000E+100
        129  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    2.062528E-12    0.000000E+00              9.00000E+100
        130  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -4.125056E-12    0.000000E+00              9.00000E+100
        131  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    2.062528E-12    0.000000E+00              9.00000E+100
        132  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    6.243893E-12    0.000000E+00              9.00000E+100
        133  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00   -1.189313E-12    0.000000E+00              9.00000E+100
        134  traj.phases.phase0.collocation_constraint.defects:alt                      e   0.000000E+00    4.162596E-12    0.000000E+00              9.00000E+100
        135  traj.phases.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        136  traj.phases.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        137  traj.phases.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        138  traj.phases.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        139  traj.phases.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        140  traj.phases.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        141  traj.phases.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        142  traj.phases.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        143  traj.phases.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        144  traj.phases.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        145  traj.phases.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        146  traj.phases.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        147  traj.phases.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        148  traj.phases.phase0.continuity_comp.defect_states:range                     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        149  traj.phases.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        150  traj.phases.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        151  traj.phases.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        152  traj.phases.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        153  traj.phases.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        154  traj.phases.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        155  traj.phases.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        156  traj.phases.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        157  traj.phases.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        158  traj.phases.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        159  traj.phases.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        160  traj.phases.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        161  traj.phases.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        162  traj.phases.phase0.continuity_comp.defect_states:mass_fuel                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        163  traj.phases.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        164  traj.phases.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        165  traj.phases.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        166  traj.phases.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        167  traj.phases.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        168  traj.phases.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        169  traj.phases.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        170  traj.phases.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        171  traj.phases.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        172  traj.phases.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        173  traj.phases.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        174  traj.phases.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        175  traj.phases.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        176  traj.phases.phase0.continuity_comp.defect_states:alt                       e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        177  traj.phases.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        178  traj.phases.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00    4.547474E-13    0.000000E+00              9.00000E+100
        179  traj.phases.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00    6.821210E-13    0.000000E+00              9.00000E+100
        180  traj.phases.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00   -1.492140E-13    0.000000E+00              9.00000E+100
        181  traj.phases.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00    7.105427E-15    0.000000E+00              9.00000E+100
        182  traj.phases.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        183  traj.phases.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00   -6.661338E-16    0.000000E+00              9.00000E+100
        184  traj.phases.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        185  traj.phases.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00    3.552714E-15    0.000000E+00              9.00000E+100
        186  traj.phases.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        187  traj.phases.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00   -1.421085E-14    0.000000E+00              9.00000E+100
        188  traj.phases.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00   -2.273737E-13    0.000000E+00              9.00000E+100
        189  traj.phases.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        190  traj.phases.phase0.continuity_comp.defect_controls:climb_rate              e   0.000000E+00   -4.547474E-13    0.000000E+00              9.00000E+100
        191  traj.phases.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00   -5.301588E-11    0.000000E+00              9.00000E+100
        192  traj.phases.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00    1.055363E-11    0.000000E+00              9.00000E+100
        193  traj.phases.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00    5.002376E-12    0.000000E+00              9.00000E+100
        194  traj.phases.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00   -1.367837E-12    0.000000E+00              9.00000E+100
        195  traj.phases.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00    1.563242E-13    0.000000E+00              9.00000E+100
        196  traj.phases.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00    1.563242E-13    0.000000E+00              9.00000E+100
        197  traj.phases.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00   -8.793239E-14    0.000000E+00              9.00000E+100
        198  traj.phases.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        199  traj.phases.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00    1.563242E-13    0.000000E+00              9.00000E+100
        200  traj.phases.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00   -3.126485E-13    0.000000E+00              9.00000E+100
        201  traj.phases.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00   -1.875891E-12    0.000000E+00              9.00000E+100
        202  traj.phases.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        203  traj.phases.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00   -3.878389E-12    0.000000E+00              9.00000E+100
        204  traj.phases.phase0.continuity_comp.defect_control_rates:climb_rate_rate    e   0.000000E+00   -3.292872E-11    0.000000E+00              9.00000E+100
        205  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    5.287165E-01    2.000000E+00              9.00000E+100
        206  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    5.455790E-01    2.000000E+00              9.00000E+100
        207  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    5.708413E-01    2.000000E+00              9.00000E+100
        208  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    5.793714E-01    2.000000E+00              9.00000E+100
        209  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    5.793714E-01    2.000000E+00              9.00000E+100
        210  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    6.295869E-01    2.000000E+00              9.00000E+100
        211  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.166454E-01    2.000000E+00              9.00000E+100
        212  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.497986E-01    2.000000E+00              9.00000E+100
        213  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.497986E-01    2.000000E+00              9.00000E+100
        214  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    8.705334E-01    2.000000E+00              9.00000E+100
        215  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    9.784255E-01    2.000000E+00              9.00000E+100
        216  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    9.722337E-01    2.000000E+00              9.00000E+100
        217  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    9.722337E-01    2.000000E+00              9.00000E+100
        218  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    8.858042E-01    2.000000E+00              9.00000E+100
        219  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.729146E-01    2.000000E+00              9.00000E+100
        220  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.612330E-01    2.000000E+00              9.00000E+100
        221  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.612330E-01    2.000000E+00              9.00000E+100
        222  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.540830E-01    2.000000E+00              9.00000E+100
        223  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.522796E-01    2.000000E+00              9.00000E+100
        224  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.543455E-01    2.000000E+00              9.00000E+100
        225  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.543455E-01    2.000000E+00              9.00000E+100
        226  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.614380E-01    2.000000E+00              9.00000E+100
        227  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.677779E-01    2.000000E+00              9.00000E+100
        228  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.680366E-01    2.000000E+00              9.00000E+100
        229  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.680366E-01    2.000000E+00              9.00000E+100
        230  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.667308E-01    2.000000E+00              9.00000E+100
        231  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.637120E-01    2.000000E+00              9.00000E+100
        232  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.626380E-01    2.000000E+00              9.00000E+100
        233  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.626380E-01    2.000000E+00              9.00000E+100
        234  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.613815E-01    2.000000E+00              9.00000E+100
        235  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.658748E-01    2.000000E+00              9.00000E+100
        236  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.694120E-01    2.000000E+00              9.00000E+100
        237  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.694120E-01    2.000000E+00              9.00000E+100
        238  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.760668E-01    2.000000E+00              9.00000E+100
        239  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.706216E-01    2.000000E+00              9.00000E+100
        240  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.636822E-01    2.000000E+00              9.00000E+100
        241  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.636822E-01    2.000000E+00              9.00000E+100
        242  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.513433E-01    2.000000E+00              9.00000E+100
        243  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.642405E-01    2.000000E+00              9.00000E+100
        244  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.787588E-01    2.000000E+00              9.00000E+100
        245  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.787588E-01    2.000000E+00              9.00000E+100
        246  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    8.073426E-01    2.000000E+00              9.00000E+100
        247  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    8.044014E-01    2.000000E+00              9.00000E+100
        248  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.878013E-01    2.000000E+00              9.00000E+100
        249  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    7.878013E-01    2.000000E+00              9.00000E+100
        250  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    6.981312E-01    2.000000E+00              9.00000E+100
        251  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    4.196413E-01    2.000000E+00              9.00000E+100
        252  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    3.125440E-01    2.000000E+00              9.00000E+100
        253  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    3.125440E-01    2.000000E+00              9.00000E+100
        254  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    1.839862E-01    2.000000E+00              9.00000E+100
        255  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    1.535443E-01    2.000000E+00              9.00000E+100
        256  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    1.637752E-01    2.000000E+00              9.00000E+100
        257  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    1.637752E-01    2.000000E+00              9.00000E+100
        258  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    1.819536E-01    2.000000E+00              9.00000E+100
        259  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    2.026946E-01    2.000000E+00              9.00000E+100
        260  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    2.081639E-01    2.000000E+00              9.00000E+100
        261  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    2.081639E-01    2.000000E+00              9.00000E+100
        262  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    2.130709E-01    2.000000E+00              9.00000E+100
        263  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    2.190292E-01    2.000000E+00              9.00000E+100
        264  traj.phases.phase0.path_constraints.path:tau                               i   1.000000E-02    2.207246E-01    2.000000E+00              9.00000E+100

--------------------------------------------------------------------------------


Simulating trajectory traj
Done simulating trajectory traj

References


  1. John T Betts and Evin J Cramer. Application of direct transcription to commercial aircraft trajectory optimization. Journal of Guidance, Control, and Dynamics, 181:151–159, 1995. 

  2. Hans Seywald. Trajectory optimization based on differential inclusion Revised. Journal of Guidance, Control, and Dynamics, 173:480–487, may 1994. URL: https://doi.org/10.2514/3.21224, doi:10.2514/3.21224

  3. Fariba Fahroo and I Michael Ross. Second look at approximating differential inclusions. Journal of Guidance, Control, and Dynamics, 241:131–133, 2001. 

  4. Renjith R Kumar and Hans Seywald. Should controls be eliminated while solving optimal control problems via direct methods? Journal of Guidance, Control, and Dynamics, 192:418–423, mar 1996. URL: https://doi.org/10.2514/3.21634, doi:10.2514/3.21634