NLPs Subpackage

Inheritance Diagram

Inheritance diagram of latom.nlp.nlp, latom.nlp.nlp_2d, latom.nlp.nlp_heo_2d

Modules List

latom.nlp.nlp

@authors: Alberto FOSSA’ Giuliana Elena MICELI

latom.nlp.nlp_2d

@authors: Alberto FOSSA’ Giuliana Elena MICELI

latom.nlp.nlp_heo_2d

@authors: Alberto FOSSA’ Giuliana Elena MICELI

Documentation

@authors: Alberto FOSSA’ Giuliana Elena MICELI

class latom.nlp.nlp.NLP(body, sc, method, nb_seg, order, solver, snopt_opts=None, rec_file=None)[source]

Bases: object

NLP class transcribes a continuous-time optimal control problem in trajectory optimization into a Non Linear Programming Problem (NLP) using the OpenMDAO and dymos libraries.

Parameters

  • body (Primary) – Instance of Primary class representing the central attracting body

  • sc (Spacecraft) – Instance of Spacecraft class representing the spacecraft

  • method (str) – Transcription method used to discretize the continuous time trajectory into a finite set of nodes, allowed gauss-lobatto, radau-ps and runge-kutta

  • nb_seg (int or tuple) – Number of segments in which each phase is discretized

  • order (int or tuple) – Transcription order within each phase, must be odd

  • solver (str) – NLP solver, must be supported by OpenMDAO

  • snopt_opts (dict or None, optional) – SNOPT optional settings expressed as key-value pairs. Refer to the SNOPT User Guide 1 for more details. Default is None

  • rec_file (str or None, optional) – Name of the file in which the computed solution is recorded or None. Default is None

Variables

  • body (Primary) – Instance of Primary class representing the central attracting body

  • sc (Spacecraft) – Instance of Spacecraft class representing the spacecraft

  • method (str) – Transcription method used to discretize the continuous time trajectory into a finite set of nodes, allowed gauss-lobatto, radau-ps and runge-kutta

  • nb_seg (int or tuple) – Number of segments in which each phase is discretized

  • order (int or tuple) – Transcription order within each phase, must be odd

  • solver (str) – NLP solver, must be supported by OpenMDAO

  • snopt_opts (dict or None) – SNOPT optional settings expressed as key-value pairs. Refer to the SNOPT User Guide 1 for more details.

  • rec_file (str or None) – Name of the file in which the computed solution is recorded or None

  • p (Problem) – OpenMDAO Problem class instance representing the NLP

  • trajectory (Trajectory) – Dymos Trajectory class instance representing the spacecraft trajectory

  • p_exp (Problem) – OpenMDAO Problem class instance representing the explicitly simulated trajectory

References

1(1,2,3,4)

Gill, Philip E., et al. User’s Guide for SNOPT Version 7.7: Software for Large-Scale Nonlinear Programming, Feb. 2019, p. 126.

setup()[source]

Set up the Jacobian type, linear solver and derivatives type.

exp_sim(rec_file=None)[source]

Explicitly simulate the implicitly obtained optimal solution using Scipy solve_ivp method.

cleanup()[source]

Clean up resources.

class latom.nlp.nlp.SinglePhaseNLP(body, sc, method, nb_seg, order, solver, ode_class, ode_kwargs, ph_name, snopt_opts=None, rec_file=None)[source]

Bases: latom.nlp.nlp.NLP

SinglePhaseNLP transcribes a continuous-time optimal control problem in trajectory optimization constituted by a single phase into a Non Linear Programming Problem (NLP) using the libraries OpenMDAO and dymos.

Parameters

  • body (Primary) – Instance of Primary class representing the central attracting body

  • sc (Spacecraft) – Instance of Spacecraft class representing the spacecraft

  • method (str) – Transcription method used to discretize the continuous time trajectory into a finite set of nodes, allowed gauss-lobatto, radau-ps and runge-kutta

  • nb_seg (int) – Number of segments in which each phase is discretized

  • order (int) – Transcription order within each phase, must be odd

  • solver (str) – NLP solver, must be supported by OpenMDAO

  • ode_class (ExplicitComponent) – Instance of OpenMDAO ExplicitComponent describing the Ordinary Differential Equations (ODEs) that drive the system dynamics

  • ode_kwargs (dict) – Keywords arguments to be passed to ode_class

  • ph_name (str) – Name of the phase within OpenMDAO

  • snopt_opts (dict or None, optional) – SNOPT optional settings expressed as key-value pairs. Refer to the SNOPT User Guide 1 for more details. Default is None

  • rec_file (str or None, optional) – Name of the file in which the computed solution is recorded or None. Default is None

Variables

  • phase (Phase) – Dymos Phase object representing the unique phase of the Trajectory class instance

  • phase_name (str) – Complete name of the Phase instance within OpenMDAO

  • state_nodes (ndarray) – Indexes corresponding to the state discretization nodes of the discretized phase

  • control_nodes (ndarray) – Indexes corresponding to the control discretization nodes of the discretized phase

  • t_all (ndarray) – Time instants corresponding to all discretization nodes [-]

  • t_state (ndarray) – Time instants corresponding to the state discretization nodes [-]

  • t_control (ndarray) – Time instants corresponding to the control discretization nodes [-]

  • idx_state_control (ndarray) – Indexes of the state discretization nodes among the control discretization nodes

  • tof (float) – Phase time of flight (TOF) [-]

set_objective()[source]

Set the NLP objective as the minimization of the opposite of the final spacecraft mass.

set_time_options(tof, t_bounds)[source]

Set the time options on the phase.

Parameters

  • tof (float) – Phase time of flight (TOF) [s]

  • t_bounds (tuple) – Time of flight lower and upper bounds expressed as a fraction of tof

set_time_guess(tof)[source]

Compute the time grid on the phase to retrieve the time instants corresponding to states, controls and all discretization nodes.

Parameters

tof (float) – Phase time of flight (TOF) [s]

cleanup()

Clean up resources.

exp_sim(rec_file=None)

Explicitly simulate the implicitly obtained optimal solution using Scipy solve_ivp method.

setup()

Set up the Jacobian type, linear solver and derivatives type.

class latom.nlp.nlp.MultiPhaseNLP(body, sc, method, nb_seg, order, solver, ode_class, ode_kwargs, ph_name, snopt_opts=None, rec_file=None)[source]

Bases: latom.nlp.nlp.NLP

MultiPhaseNLP transcribes a continuous-time optimal control problem in trajectory optimization constituted by multiple phases into a Non Linear Programming Problem (NLP) using the libraries OpenMDAO and dymos.

Parameters

  • body (Primary) – Instance of Primary class representing the central attracting body

  • sc (Spacecraft) – Instance of Spacecraft class representing the spacecraft

  • method (str) – Transcription method used to discretize the continuous time trajectory into a finite set of nodes, allowed gauss-lobatto, radau-ps and runge-kutta

  • nb_seg (int or tuple) – Number of segments in which each phase is discretized

  • order (int or tuple) – Transcription order within each phase, must be odd

  • solver (str) – NLP solver, must be supported by OpenMDAO

  • ode_class (tuple) – Instance of OpenMDAO ExplicitComponent describing the Ordinary Differential Equations (ODEs) that drive the system dynamics

  • ode_kwargs (tuple) – Keywords arguments to be passed to ode_class

  • ph_name (tuple) – Name of the phase within OpenMDAO

  • snopt_opts (dict or None, optional) – SNOPT optional settings expressed as key-value pairs. Refer to the SNOPT User Guide 1 for more details. Default is None

  • rec_file (str or None, optional) – Name of the file in which the computed solution is recorded or None. Default is None

Variables

  • transcription (list) – List of dymos transcription class instances representing the transcription method, order and segments within each phase

  • phase (list) – List of dymos Phase object representing the different phases of the Trajectory class instance

  • phase_name (list) – List of complete names of the Phase instance within OpenMDAO

set_time_phase(ti, tof, phase, phase_name)[source]

Compute the time grid within one phase to retrieve the time instants corresponding to the state, control and all discretization nodes.

Parameters

  • ti (float) – Initial time [-]

  • tof (float) – Time of flight (TOF) [-]

  • phase (Phase) – Current phase

  • phase_name (str) – Current phase name

Returns

  • state_nodes (ndarray) – Indexes corresponding to the state discretization nodes

  • control_nodes (ndarray) – Indexes corresponding to the control discretization nodes

  • t_state (ndarray) – Time instants on the state discretization nodes [-]

  • t_control (ndarray) – Time instants on the control discretization nodes [-]

  • t_all (ndarray) – Time instants on all discretization nodes [-]

cleanup()

Clean up resources.

exp_sim(rec_file=None)

Explicitly simulate the implicitly obtained optimal solution using Scipy solve_ivp method.

setup()

Set up the Jacobian type, linear solver and derivatives type.

@authors: Alberto FOSSA’ Giuliana Elena MICELI

class latom.nlp.nlp_2d.TwoDimNLP(body, sc, alt, alpha_bounds, method, nb_seg, order, solver, ode_class, ode_kwargs, ph_name, snopt_opts=None, rec_file=None)[source]

Bases: latom.nlp.nlp.SinglePhaseNLP

TwoDimNLP class transcribes a two-dimensional, continuous-time optimal control problem in trajectory optimization into a Non Linear Programming Problem (NLP) using the OpenMDAO and dymos libraries.

The two-dimensional trajectory is described in polar coordinates centered at the center of the attracting body.

Parameters

  • body (Primary) – Instance of Primary class representing the central attracting body

  • sc (Spacecraft) – Instance of Spacecraft class representing the spacecraft

  • alt (float) – Orbit altitude [m]

  • alpha_bounds (iterable) – Lower and upper bounds on thrust vector direction [rad]

  • method (str) – Transcription method used to discretize the continuous time trajectory into a finite set of nodes, allowed gauss-lobatto, radau-ps and runge-kutta

  • nb_seg (int) – Number of segments in which each phase is discretized

  • order (int) – Transcription order within each phase, must be odd

  • solver (str) – NLP solver, must be supported by OpenMDAO

  • ode_class (ExplicitComponent) – Instance of OpenMDAO ExplicitComponent describing the Ordinary Differential Equations (ODEs) that drive the system dynamics

  • ode_kwargs (dict) – Keywords arguments to be passed to ode_class

  • ph_name (str) – Name of the phase within OpenMDAO

  • snopt_opts (dict or None, optional) – SNOPT optional settings expressed as key-value pairs. Refer to the SNOPT User Guide for more details. Default is None

  • rec_file (str or None, optional) – Name of the file in which the computed solution is recorded or None. Default is None

Variables

  • alt (float) – Orbit altitude [m]

  • alpha_bounds (ndarray) – Lower and upper bounds on thrust vector direction [rad]

  • r_circ (float) – Orbit radius [m]

  • v_circ (float) – Orbital velocity [m/s]

  • guess (TwoDimGuess) – Initial guess to be provided before solving the NLP

set_states_options(theta, u_bound=None)[source]

Set options on the state variables of the NLP.

Parameters

  • theta (float) – Reference value for spawn angle [rad]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_controls_options(throttle=True)[source]

Set options on control variables.

Parameters

throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess(check_partials=False, fix_final=False, throttle=True)[source]

Set the initial guess for the iterative solution of the NLP.

Parameters

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess_interpolation(bcs=array([[1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.]]), check_partials=False, throttle=True)[source]

Set the initial guess for the solution of the NLP interpolating the Boundary Conditions (BCs) imposed on the state and control variables.

Parameters

  • bcs (ndarray, optional) – Boundary Conditions on state and control variables. Default is all ones

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

cleanup()

Clean up resources.

exp_sim(rec_file=None)

Explicitly simulate the implicitly obtained optimal solution using Scipy solve_ivp method.

set_objective()

Set the NLP objective as the minimization of the opposite of the final spacecraft mass.

set_time_guess(tof)

Compute the time grid on the phase to retrieve the time instants corresponding to states, controls and all discretization nodes.

Parameters

tof (float) – Phase time of flight (TOF) [s]

set_time_options(tof, t_bounds)

Set the time options on the phase.

Parameters

  • tof (float) – Phase time of flight (TOF) [s]

  • t_bounds (tuple) – Time of flight lower and upper bounds expressed as a fraction of tof

setup()

Set up the Jacobian type, linear solver and derivatives type.

class latom.nlp.nlp_2d.TwoDimConstNLP(body, sc, alt, theta, alpha_bounds, tof, t_bounds, method, nb_seg, order, solver, ph_name, snopt_opts=None, rec_file=None, u_bound=None)[source]

Bases: latom.nlp.nlp_2d.TwoDimNLP

TwoDimConstNLP class transcribes a two-dimensional, continuous-time optimal control problem in trajectory optimization into a Non Linear Programming Problem (NLP) using the OpenMDAO and dymos libraries.

The two-dimensional trajectory is described in polar coordinates centered at the center of the attracting body. The thrust delivered by the spacecraft engines is supposed to have a constant magnitude throughout the whole phase.

Parameters

  • body (Primary) – Instance of Primary class representing the central attracting body

  • sc (Spacecraft) – Instance of Spacecraft class representing the spacecraft

  • alt (float) – Orbit altitude [m]

  • theta (float) – Guessed spawn angle [rad]

  • alpha_bounds (tuple) – Lower and upper bounds on thrust vector direction [rad]

  • tof (float) – Guessed time of flight [s]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of TOF [-]

  • method (str) – Transcription method used to discretize the continuous time trajectory into a finite set of nodes, allowed gauss-lobatto, radau-ps and runge-kutta

  • nb_seg (int) – Number of segments in which each phase is discretized

  • order (int) – Transcription order within each phase, must be odd

  • solver (str) – NLP solver, must be supported by OpenMDAO

  • ph_name (str) – Name of the phase within OpenMDAO

  • snopt_opts (dict or None, optional) – SNOPT optional settings expressed as key-value pairs. Refer to the SNOPT User Guide for more details. Default is None

  • rec_file (str or None, optional) – Name of the file in which the computed solution is recorded or None. Default is None

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_options(theta, tof, t_bounds, u_bound=None)[source]

Set options on state and control variables, time and objective function.

Parameters

  • theta (float) – Guessed spawn angle [rad]

  • tof (float) – Guessed time of flight [s]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of TOF [-]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

cleanup()

Clean up resources.

exp_sim(rec_file=None)

Explicitly simulate the implicitly obtained optimal solution using Scipy solve_ivp method.

set_controls_options(throttle=True)

Set options on control variables.

Parameters

throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess(check_partials=False, fix_final=False, throttle=True)

Set the initial guess for the iterative solution of the NLP.

Parameters

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess_interpolation(bcs=array([[1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.]]), check_partials=False, throttle=True)

Set the initial guess for the solution of the NLP interpolating the Boundary Conditions (BCs) imposed on the state and control variables.

Parameters

  • bcs (ndarray, optional) – Boundary Conditions on state and control variables. Default is all ones

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_objective()

Set the NLP objective as the minimization of the opposite of the final spacecraft mass.

set_states_options(theta, u_bound=None)

Set options on the state variables of the NLP.

Parameters

  • theta (float) – Reference value for spawn angle [rad]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_time_guess(tof)

Compute the time grid on the phase to retrieve the time instants corresponding to states, controls and all discretization nodes.

Parameters

tof (float) – Phase time of flight (TOF) [s]

set_time_options(tof, t_bounds)

Set the time options on the phase.

Parameters

  • tof (float) – Phase time of flight (TOF) [s]

  • t_bounds (tuple) – Time of flight lower and upper bounds expressed as a fraction of tof

setup()

Set up the Jacobian type, linear solver and derivatives type.

class latom.nlp.nlp_2d.TwoDimAscConstNLP(body, sc, alt, theta, alpha_bounds, tof, t_bounds, method, nb_seg, order, solver, ph_name, snopt_opts=None, rec_file=None, check_partials=False, u_bound='lower')[source]

Bases: latom.nlp.nlp_2d.TwoDimConstNLP

TwoDimAscConstNLP class transcribes a two-dimensional, continuous-time optimal control problem in trajectory optimization into a Non Linear Programming Problem (NLP) using the OpenMDAO and dymos libraries.

The two-dimensional ascent trajectory is described in polar coordinates centered at the center of the attracting body. The thrust delivered by the spacecraft engines is supposed to have a constant magnitude throughout the whole phase.

Parameters

  • body (Primary) – Instance of Primary class representing the central attracting body

  • sc (Spacecraft) – Instance of Spacecraft class representing the spacecraft

  • alt (float) – Orbit altitude [m]

  • theta (float) – Guessed spawn angle [rad]

  • alpha_bounds (tuple) – Lower and upper bounds on thrust vector direction [rad]

  • tof (float) – Guessed time of flight [s]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • method (str) – Transcription method used to discretize the continuous time trajectory into a finite set of nodes, allowed gauss-lobatto, radau-ps and runge-kutta

  • nb_seg (int) – Number of segments in which each phase is discretized

  • order (int) – Transcription order within each phase, must be odd

  • solver (str) – NLP solver, must be supported by OpenMDAO

  • ph_name (str) – Name of the phase within OpenMDAO

  • snopt_opts (dict or None, optional) – SNOPT optional settings expressed as key-value pairs. Refer to the SNOPT User Guide for more details. Default is None

  • rec_file (str or None, optional) – Name of the file in which the computed solution is recorded or None. Default is None

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is lower

cleanup()

Clean up resources.

exp_sim(rec_file=None)

Explicitly simulate the implicitly obtained optimal solution using Scipy solve_ivp method.

set_controls_options(throttle=True)

Set options on control variables.

Parameters

throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess(check_partials=False, fix_final=False, throttle=True)

Set the initial guess for the iterative solution of the NLP.

Parameters

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess_interpolation(bcs=array([[1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.]]), check_partials=False, throttle=True)

Set the initial guess for the solution of the NLP interpolating the Boundary Conditions (BCs) imposed on the state and control variables.

Parameters

  • bcs (ndarray, optional) – Boundary Conditions on state and control variables. Default is all ones

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_objective()

Set the NLP objective as the minimization of the opposite of the final spacecraft mass.

set_options(theta, tof, t_bounds, u_bound=None)

Set options on state and control variables, time and objective function.

Parameters

  • theta (float) – Guessed spawn angle [rad]

  • tof (float) – Guessed time of flight [s]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of TOF [-]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_states_options(theta, u_bound=None)

Set options on the state variables of the NLP.

Parameters

  • theta (float) – Reference value for spawn angle [rad]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_time_guess(tof)

Compute the time grid on the phase to retrieve the time instants corresponding to states, controls and all discretization nodes.

Parameters

tof (float) – Phase time of flight (TOF) [s]

set_time_options(tof, t_bounds)

Set the time options on the phase.

Parameters

  • tof (float) – Phase time of flight (TOF) [s]

  • t_bounds (tuple) – Time of flight lower and upper bounds expressed as a fraction of tof

setup()

Set up the Jacobian type, linear solver and derivatives type.

class latom.nlp.nlp_2d.TwoDimDescConstNLP(body, sc, alt, vp, theta, alpha_bounds, tof, t_bounds, method, nb_seg, order, solver, ph_name, snopt_opts=None, rec_file=None, check_partials=False, u_bound='upper')[source]

Bases: latom.nlp.nlp_2d.TwoDimConstNLP

TwoDimDescConstNLP class transcribes a two-dimensional, continuous-time optimal control problem in trajectory optimization into a Non Linear Programming Problem (NLP) using the OpenMDAO and dymos libraries.

The two-dimensional descent trajectory is described in polar coordinates centered at the center of the attracting body. The thrust delivered by the spacecraft engines is supposed to have a constant magnitude throughout the whole phase.

Parameters

  • body (Primary) – Instance of Primary class representing the central attracting body

  • sc (Spacecraft) – Instance of Spacecraft class representing the spacecraft

  • alt (float) – Orbit altitude [m]

  • theta (float) – Guessed spawn angle [rad]

  • alpha_bounds (tuple) – Lower and upper bounds on thrust vector direction [rad]

  • tof (float) – Guessed time of flight [s]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • method (str) – Transcription method used to discretize the continuous time trajectory into a finite set of nodes, allowed gauss-lobatto, radau-ps and runge-kutta

  • nb_seg (int) – Number of segments in which each phase is discretized

  • order (int) – Transcription order within each phase, must be odd

  • solver (str) – NLP solver, must be supported by OpenMDAO

  • ph_name (str) – Name of the phase within OpenMDAO

  • snopt_opts (dict or None, optional) – SNOPT optional settings expressed as key-value pairs. Refer to the SNOPT User Guide for more details. Default is None

  • rec_file (str or None, optional) – Name of the file in which the computed solution is recorded or None. Default is None

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is upper

Variables

vp (float) – Velocity at the periapsis of the Hohmann transfer where the final powered descent is initiated [m/s]

cleanup()

Clean up resources.

exp_sim(rec_file=None)

Explicitly simulate the implicitly obtained optimal solution using Scipy solve_ivp method.

set_controls_options(throttle=True)

Set options on control variables.

Parameters

throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess(check_partials=False, fix_final=False, throttle=True)

Set the initial guess for the iterative solution of the NLP.

Parameters

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess_interpolation(bcs=array([[1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.]]), check_partials=False, throttle=True)

Set the initial guess for the solution of the NLP interpolating the Boundary Conditions (BCs) imposed on the state and control variables.

Parameters

  • bcs (ndarray, optional) – Boundary Conditions on state and control variables. Default is all ones

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_objective()

Set the NLP objective as the minimization of the opposite of the final spacecraft mass.

set_options(theta, tof, t_bounds, u_bound=None)

Set options on state and control variables, time and objective function.

Parameters

  • theta (float) – Guessed spawn angle [rad]

  • tof (float) – Guessed time of flight [s]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of TOF [-]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_states_options(theta, u_bound=None)

Set options on the state variables of the NLP.

Parameters

  • theta (float) – Reference value for spawn angle [rad]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_time_guess(tof)

Compute the time grid on the phase to retrieve the time instants corresponding to states, controls and all discretization nodes.

Parameters

tof (float) – Phase time of flight (TOF) [s]

set_time_options(tof, t_bounds)

Set the time options on the phase.

Parameters

  • tof (float) – Phase time of flight (TOF) [s]

  • t_bounds (tuple) – Time of flight lower and upper bounds expressed as a fraction of tof

setup()

Set up the Jacobian type, linear solver and derivatives type.

class latom.nlp.nlp_2d.TwoDimVarNLP(body, sc, alt, alpha_bounds, t_bounds, method, nb_seg, order, solver, ph_name, guess, snopt_opts=None, rec_file=None, check_partials=False, u_bound=None, fix_final=False)[source]

Bases: latom.nlp.nlp_2d.TwoDimNLP

TwoDimVarNLP class transcribes a two-dimensional, continuous-time optimal control problem in trajectory optimization into a Non Linear Programming Problem (NLP) using the OpenMDAO and dymos libraries.

The two-dimensional trajectory is described in polar coordinates centered at the center of the attracting body. The thrust delivered by the spacecraft engines varies in magnitude during the phase.

Parameters

  • body (Primary) – Instance of Primary class representing the central attracting body

  • sc (Spacecraft) – Instance of Spacecraft class representing the spacecraft

  • alt (float) – Orbit altitude [m]

  • alpha_bounds (tuple) – Lower and upper bounds on thrust vector direction [rad]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • method (str) – Transcription method used to discretize the continuous time trajectory into a finite set of nodes, allowed gauss-lobatto, radau-ps and runge-kutta

  • nb_seg (int) – Number of segments in which each phase is discretized

  • order (int) – Transcription order within each phase, must be odd

  • solver (str) – NLP solver, must be supported by OpenMDAO

  • ph_name (str) – Name of the phase within OpenMDAO

  • guess (TwoDimGuess) – Initial guess for the NLP solution

  • snopt_opts (dict or None, optional) – SNOPT optional settings expressed as key-value pairs. Refer to the SNOPT User Guide for more details. Default is None

  • rec_file (str or None, optional) – Name of the file in which the computed solution is recorded or None. Default is None

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is False

Variables

guess (TwoDimGuess) – Initial guess for the NLP solution

set_options(theta, t_bounds, u_bound=None)[source]

Set options on state and control variables, time and objective function.

Parameters

  • theta (float) – Guessed spawn angle [rad]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

cleanup()

Clean up resources.

exp_sim(rec_file=None)

Explicitly simulate the implicitly obtained optimal solution using Scipy solve_ivp method.

set_controls_options(throttle=True)

Set options on control variables.

Parameters

throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess(check_partials=False, fix_final=False, throttle=True)

Set the initial guess for the iterative solution of the NLP.

Parameters

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess_interpolation(bcs=array([[1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.]]), check_partials=False, throttle=True)

Set the initial guess for the solution of the NLP interpolating the Boundary Conditions (BCs) imposed on the state and control variables.

Parameters

  • bcs (ndarray, optional) – Boundary Conditions on state and control variables. Default is all ones

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_objective()

Set the NLP objective as the minimization of the opposite of the final spacecraft mass.

set_states_options(theta, u_bound=None)

Set options on the state variables of the NLP.

Parameters

  • theta (float) – Reference value for spawn angle [rad]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_time_guess(tof)

Compute the time grid on the phase to retrieve the time instants corresponding to states, controls and all discretization nodes.

Parameters

tof (float) – Phase time of flight (TOF) [s]

set_time_options(tof, t_bounds)

Set the time options on the phase.

Parameters

  • tof (float) – Phase time of flight (TOF) [s]

  • t_bounds (tuple) – Time of flight lower and upper bounds expressed as a fraction of tof

setup()

Set up the Jacobian type, linear solver and derivatives type.

class latom.nlp.nlp_2d.TwoDimAscVarNLP(body, sc, alt, alpha_bounds, t_bounds, method, nb_seg, order, solver, ph_name, snopt_opts=None, rec_file=None, check_partials=False, u_bound='lower', fix_final=False)[source]

Bases: latom.nlp.nlp_2d.TwoDimVarNLP

TwoDimAscVarNLP class transcribes a two-dimensional, continuous-time optimal control problem in trajectory optimization into a Non Linear Programming Problem (NLP) using the OpenMDAO and dymos libraries.

The two-dimensional ascent trajectory is described in polar coordinates centered at the center of the attracting body. The thrust delivered by the spacecraft engines varies in magnitude during the phase.

Parameters

  • body (Primary) – Instance of Primary class representing the central attracting body

  • sc (Spacecraft) – Instance of Spacecraft class representing the spacecraft

  • alt (float) – Orbit altitude [-]

  • alpha_bounds (tuple) – Lower and upper bounds on thrust vector direction [rad]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • method (str) – Transcription method used to discretize the continuous time trajectory into a finite set of nodes, allowed gauss-lobatto, radau-ps and runge-kutta

  • nb_seg (int) – Number of segments in which each phase is discretized

  • order (int) – Transcription order within each phase, must be odd

  • solver (str) – NLP solver, must be supported by OpenMDAO

  • ph_name (str) – Name of the phase within OpenMDAO

  • snopt_opts (dict or None, optional) – SNOPT optional settings expressed as key-value pairs. Refer to the SNOPT User Guide for more details. Default is None

  • rec_file (str or None, optional) – Name of the file in which the computed solution is recorded or None. Default is None

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is lower

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is False

cleanup()

Clean up resources.

exp_sim(rec_file=None)

Explicitly simulate the implicitly obtained optimal solution using Scipy solve_ivp method.

set_controls_options(throttle=True)

Set options on control variables.

Parameters

throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess(check_partials=False, fix_final=False, throttle=True)

Set the initial guess for the iterative solution of the NLP.

Parameters

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess_interpolation(bcs=array([[1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.]]), check_partials=False, throttle=True)

Set the initial guess for the solution of the NLP interpolating the Boundary Conditions (BCs) imposed on the state and control variables.

Parameters

  • bcs (ndarray, optional) – Boundary Conditions on state and control variables. Default is all ones

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_objective()

Set the NLP objective as the minimization of the opposite of the final spacecraft mass.

set_options(theta, t_bounds, u_bound=None)

Set options on state and control variables, time and objective function.

Parameters

  • theta (float) – Guessed spawn angle [rad]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_states_options(theta, u_bound=None)

Set options on the state variables of the NLP.

Parameters

  • theta (float) – Reference value for spawn angle [rad]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_time_guess(tof)

Compute the time grid on the phase to retrieve the time instants corresponding to states, controls and all discretization nodes.

Parameters

tof (float) – Phase time of flight (TOF) [s]

set_time_options(tof, t_bounds)

Set the time options on the phase.

Parameters

  • tof (float) – Phase time of flight (TOF) [s]

  • t_bounds (tuple) – Time of flight lower and upper bounds expressed as a fraction of tof

setup()

Set up the Jacobian type, linear solver and derivatives type.

class latom.nlp.nlp_2d.TwoDimDescVarNLP(body, sc, alt, alpha_bounds, t_bounds, method, nb_seg, order, solver, ph_name, snopt_opts=None, rec_file=None, check_partials=False, u_bound='upper', fix_final=False)[source]

Bases: latom.nlp.nlp_2d.TwoDimVarNLP

TwoDimDescVarNLP class transcribes a two-dimensional, continuous-time optimal control problem in trajectory optimization into a Non Linear Programming Problem (NLP) using the OpenMDAO and dymos libraries.

The two-dimensional descent trajectory is described in polar coordinates centered at the center of the attracting body. The thrust delivered by the spacecraft engines varies in magnitude during the phase.

Parameters

  • body (Primary) – Instance of Primary class representing the central attracting body

  • sc (Spacecraft) – Instance of Spacecraft class representing the spacecraft

  • alt (float) – Orbit altitude [m]

  • alpha_bounds (tuple) – Lower and upper bounds on thrust vector direction [rad]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • method (str) – Transcription method used to discretize the continuous time trajectory into a finite set of nodes, allowed gauss-lobatto, radau-ps and runge-kutta

  • nb_seg (int) – Number of segments in which each phase is discretized

  • order (int) – Transcription order within each phase, must be odd

  • solver (str) – NLP solver, must be supported by OpenMDAO

  • ph_name (str) – Name of the phase within OpenMDAO

  • snopt_opts (dict or None, optional) – SNOPT optional settings expressed as key-value pairs. Refer to the SNOPT User Guide for more details. Default is None

  • rec_file (str or None, optional) – Name of the file in which the computed solution is recorded or None. Default is None

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is upper

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is False

cleanup()

Clean up resources.

exp_sim(rec_file=None)

Explicitly simulate the implicitly obtained optimal solution using Scipy solve_ivp method.

set_controls_options(throttle=True)

Set options on control variables.

Parameters

throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess(check_partials=False, fix_final=False, throttle=True)

Set the initial guess for the iterative solution of the NLP.

Parameters

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess_interpolation(bcs=array([[1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.]]), check_partials=False, throttle=True)

Set the initial guess for the solution of the NLP interpolating the Boundary Conditions (BCs) imposed on the state and control variables.

Parameters

  • bcs (ndarray, optional) – Boundary Conditions on state and control variables. Default is all ones

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_objective()

Set the NLP objective as the minimization of the opposite of the final spacecraft mass.

set_options(theta, t_bounds, u_bound=None)

Set options on state and control variables, time and objective function.

Parameters

  • theta (float) – Guessed spawn angle [rad]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_states_options(theta, u_bound=None)

Set options on the state variables of the NLP.

Parameters

  • theta (float) – Reference value for spawn angle [rad]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_time_guess(tof)

Compute the time grid on the phase to retrieve the time instants corresponding to states, controls and all discretization nodes.

Parameters

tof (float) – Phase time of flight (TOF) [s]

set_time_options(tof, t_bounds)

Set the time options on the phase.

Parameters

  • tof (float) – Phase time of flight (TOF) [s]

  • t_bounds (tuple) – Time of flight lower and upper bounds expressed as a fraction of tof

setup()

Set up the Jacobian type, linear solver and derivatives type.

class latom.nlp.nlp_2d.TwoDimVToffNLP(body, sc, alt, alt_safe, slope, alpha_bounds, t_bounds, method, nb_seg, order, solver, ph_name, guess, snopt_opts=None, rec_file=None, check_partials=False, u_bound=None, fix_final=False)[source]

Bases: latom.nlp.nlp_2d.TwoDimVarNLP

TwoDimVToffNLP class transcribes a two-dimensional, continuous-time optimal control problem in trajectory optimization into a Non Linear Programming Problem (NLP) using the OpenMDAO and dymos libraries.

The two-dimensional ascent/descent trajectory is described in polar coordinates centered at the center of the attracting body. The thrust delivered by the spacecraft engines varies in magnitude during the phase. An appropriate path constraint is imposed on the spacecraft state to guarantee a vertical take-off or landing.

Parameters

  • body (Primary) – Instance of Primary class representing the central attracting body

  • sc (Spacecraft) – Instance of Spacecraft class representing the spacecraft

  • alt (float) – Orbit altitude [m]

  • alt_safe (float) – Minimum altitude above the Moon surface to be maintained by the spacecraft far from the launch site [m]

  • slope (float) – Slope of the path constraint on the spacecraft radius and angle close to the launch site. Higher the value, steeper the ascent/descent [-]

  • alpha_bounds (tuple) – Lower and upper bounds on thrust vector direction [rad]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • method (str) – Transcription method used to discretize the continuous time trajectory into a finite set of nodes, allowed gauss-lobatto, radau-ps and runge-kutta

  • nb_seg (int) – Number of segments in which each phase is discretized

  • order (int) – Transcription order within each phase, must be odd

  • solver (str) – NLP solver, must be supported by OpenMDAO

  • ph_name (str) – Name of the phase within OpenMDAO

  • guess (TwoDimGuess) – Initial guess for the NLP solution

  • snopt_opts (dict or None, optional) – SNOPT optional settings expressed as key-value pairs. Refer to the SNOPT User Guide for more details. Default is None

  • rec_file (str or None, optional) – Name of the file in which the computed solution is recorded or None. Default is None

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is False

Variables

  • alt_safe (float) – Minimum altitude above the Moon surface to be maintained by the spacecraft far from the launch site [m]

  • slope (float) – Slope of the path constraint on the spacecraft radius and angle close to the launch site. Higher the value, steeper the ascent [-]

  • guess (TwoDimGuess) – Initial guess for the NLP solution

set_options(theta, t_bounds, u_bound=None)[source]

Set the states and controls options and the path constraint.

Parameters

  • theta (float) – Guessed spawn angle [rad]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

cleanup()

Clean up resources.

exp_sim(rec_file=None)

Explicitly simulate the implicitly obtained optimal solution using Scipy solve_ivp method.

set_controls_options(throttle=True)

Set options on control variables.

Parameters

throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess(check_partials=False, fix_final=False, throttle=True)

Set the initial guess for the iterative solution of the NLP.

Parameters

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess_interpolation(bcs=array([[1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.]]), check_partials=False, throttle=True)

Set the initial guess for the solution of the NLP interpolating the Boundary Conditions (BCs) imposed on the state and control variables.

Parameters

  • bcs (ndarray, optional) – Boundary Conditions on state and control variables. Default is all ones

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_objective()

Set the NLP objective as the minimization of the opposite of the final spacecraft mass.

set_states_options(theta, u_bound=None)

Set options on the state variables of the NLP.

Parameters

  • theta (float) – Reference value for spawn angle [rad]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_time_guess(tof)

Compute the time grid on the phase to retrieve the time instants corresponding to states, controls and all discretization nodes.

Parameters

tof (float) – Phase time of flight (TOF) [s]

set_time_options(tof, t_bounds)

Set the time options on the phase.

Parameters

  • tof (float) – Phase time of flight (TOF) [s]

  • t_bounds (tuple) – Time of flight lower and upper bounds expressed as a fraction of tof

setup()

Set up the Jacobian type, linear solver and derivatives type.

class latom.nlp.nlp_2d.TwoDimAscVToffNLP(body, sc, alt, alt_safe, slope, alpha_bounds, t_bounds, method, nb_seg, order, solver, ph_name, snopt_opts=None, rec_file=None, check_partials=False, u_bound='lower', fix_final=False)[source]

Bases: latom.nlp.nlp_2d.TwoDimVToffNLP

TwoDimAscVToffNLP class transcribes a two-dimensional, continuous-time optimal control problem in trajectory optimization into a Non Linear Programming Problem (NLP) using the OpenMDAO and dymos libraries.

The two-dimensional ascent trajectory is described in polar coordinates centered at the center of the attracting body. The thrust delivered by the spacecraft engines varies in magnitude during the phase. An appropriate path constraint is imposed on the spacecraft state to guarantee a vertical take-off.

Parameters

  • body (Primary) – Instance of Primary class representing the central attracting body

  • sc (Spacecraft) – Instance of Spacecraft class representing the spacecraft

  • alt (float) – Orbit altitude [m]

  • alt_safe (float) – Minimum altitude above the Moon surface to be maintained by the spacecraft far from the launch site [m]

  • slope (float) – Slope of the path constraint on the spacecraft radius and angle close to the launch site. Higher the value, steeper the ascent [-]

  • alpha_bounds (tuple) – Lower and upper bounds on thrust vector direction [rad]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • method (str) – Transcription method used to discretize the continuous time trajectory into a finite set of nodes, allowed gauss-lobatto, radau-ps and runge-kutta

  • nb_seg (int) – Number of segments in which each phase is discretized

  • order (int) – Transcription order within each phase, must be odd

  • solver (str) – NLP solver, must be supported by OpenMDAO

  • ph_name (str) – Name of the phase within OpenMDAO

  • snopt_opts (dict or None, optional) – SNOPT optional settings expressed as key-value pairs. Refer to the SNOPT User Guide for more details. Default is None

  • rec_file (str or None, optional) – Name of the file in which the computed solution is recorded or None. Default is None

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is lower

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is False

cleanup()

Clean up resources.

exp_sim(rec_file=None)

Explicitly simulate the implicitly obtained optimal solution using Scipy solve_ivp method.

set_controls_options(throttle=True)

Set options on control variables.

Parameters

throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess(check_partials=False, fix_final=False, throttle=True)

Set the initial guess for the iterative solution of the NLP.

Parameters

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess_interpolation(bcs=array([[1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.]]), check_partials=False, throttle=True)

Set the initial guess for the solution of the NLP interpolating the Boundary Conditions (BCs) imposed on the state and control variables.

Parameters

  • bcs (ndarray, optional) – Boundary Conditions on state and control variables. Default is all ones

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_objective()

Set the NLP objective as the minimization of the opposite of the final spacecraft mass.

set_options(theta, t_bounds, u_bound=None)

Set the states and controls options and the path constraint.

Parameters

  • theta (float) – Guessed spawn angle [rad]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_states_options(theta, u_bound=None)

Set options on the state variables of the NLP.

Parameters

  • theta (float) – Reference value for spawn angle [rad]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_time_guess(tof)

Compute the time grid on the phase to retrieve the time instants corresponding to states, controls and all discretization nodes.

Parameters

tof (float) – Phase time of flight (TOF) [s]

set_time_options(tof, t_bounds)

Set the time options on the phase.

Parameters

  • tof (float) – Phase time of flight (TOF) [s]

  • t_bounds (tuple) – Time of flight lower and upper bounds expressed as a fraction of tof

setup()

Set up the Jacobian type, linear solver and derivatives type.

class latom.nlp.nlp_2d.TwoDimDescVLandNLP(body, sc, alt, alt_safe, slope, alpha_bounds, t_bounds, method, nb_seg, order, solver, ph_name, snopt_opts=None, rec_file=None, check_partials=False, u_bound='upper', fix_final=True)[source]

Bases: latom.nlp.nlp_2d.TwoDimVToffNLP

TwoDimAscVToffNLP class transcribes a two-dimensional, continuous-time optimal control problem in trajectory optimization into a Non Linear Programming Problem (NLP) using the OpenMDAO and dymos libraries.

The two-dimensional descent trajectory is described in polar coordinates centered at the center of the attracting body. The thrust delivered by the spacecraft engines varies in magnitude during the phase. An appropriate path constraint is imposed on the spacecraft state to guarantee a vertical landing.

Parameters

  • body (Primary) – Instance of Primary class representing the central attracting body

  • sc (Spacecraft) – Instance of Spacecraft class representing the spacecraft

  • alt (float) – Orbit altitude [m]

  • alt_safe (float) – Minimum altitude above the Moon surface to be maintained by the spacecraft far from the launch site [m]

  • slope (float) – Slope of the path constraint on the spacecraft radius and angle close to the launch site. Higher the value, steeper the descent [-]

  • alpha_bounds (tuple) – Lower and upper bounds on thrust vector direction [rad]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • method (str) – Transcription method used to discretize the continuous time trajectory into a finite set of nodes, allowed gauss-lobatto, radau-ps and runge-kutta

  • nb_seg (int) – Number of segments in which each phase is discretized

  • order (int) – Transcription order within each phase, must be odd

  • solver (str) – NLP solver, must be supported by OpenMDAO

  • ph_name (str) – Name of the phase within OpenMDAO

  • snopt_opts (dict or None, optional) – SNOPT optional settings expressed as key-value pairs. Refer to the SNOPT User Guide for more details. Default is None

  • rec_file (str or None, optional) – Name of the file in which the computed solution is recorded or None. Default is None

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is upper

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is False

cleanup()

Clean up resources.

exp_sim(rec_file=None)

Explicitly simulate the implicitly obtained optimal solution using Scipy solve_ivp method.

set_controls_options(throttle=True)

Set options on control variables.

Parameters

throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess(check_partials=False, fix_final=False, throttle=True)

Set the initial guess for the iterative solution of the NLP.

Parameters

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess_interpolation(bcs=array([[1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.]]), check_partials=False, throttle=True)

Set the initial guess for the solution of the NLP interpolating the Boundary Conditions (BCs) imposed on the state and control variables.

Parameters

  • bcs (ndarray, optional) – Boundary Conditions on state and control variables. Default is all ones

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_objective()

Set the NLP objective as the minimization of the opposite of the final spacecraft mass.

set_options(theta, t_bounds, u_bound=None)

Set the states and controls options and the path constraint.

Parameters

  • theta (float) – Guessed spawn angle [rad]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_states_options(theta, u_bound=None)

Set options on the state variables of the NLP.

Parameters

  • theta (float) – Reference value for spawn angle [rad]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_time_guess(tof)

Compute the time grid on the phase to retrieve the time instants corresponding to states, controls and all discretization nodes.

Parameters

tof (float) – Phase time of flight (TOF) [s]

set_time_options(tof, t_bounds)

Set the time options on the phase.

Parameters

  • tof (float) – Phase time of flight (TOF) [s]

  • t_bounds (tuple) – Time of flight lower and upper bounds expressed as a fraction of tof

setup()

Set up the Jacobian type, linear solver and derivatives type.

class latom.nlp.nlp_2d.TwoDimDescTwoPhasesNLP(body, sc, alt, alt_switch, vp, theta, alpha_bounds, tof, t_bounds, method, nb_seg, order, solver, ph_name, snopt_opts=None, rec_file=None, check_partials=False, fix='alt')[source]

Bases: latom.nlp.nlp.MultiPhaseNLP

TwoDimDescTwoPhasesNLP transcribes a continuous-time optimal control problem for a two-dimensional descent trajectory into a Non Linear Programming Problem (NLP) using the OpenMDAO and dymos libraries.

The two-phases transfer is constituted by an initial deorbit burn to lower the periapsis of the departure orbit, an Hohmann transfer, a first powered phase from its periapsis to a predetermined altitude or time to go and a final vertical descent at full thrust.

Parameters

  • body (Primary) – Instance of Primary class representing the central attracting body

  • sc (Spacecraft) – Instance of Spacecraft class representing the spacecraft

  • alt (float) – Periselene altitude at which the powered descent is initiated [m]

  • alt_switch (float) – Altitude at which the vertical descent is triggered [m]

  • vp (float) – Periselene velocity at which the powered descent is initiated [m/s]

  • theta (float) – Guessed spawn angle [rad]

  • alpha_bounds (iterable) – Lower and upper bounds on thrust vector direction [rad]

  • tof (iterable) – Guessed time of flight for the two phases [s]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • method (str) – Transcription method used to discretize the continuous time trajectory into a finite set of nodes, allowed gauss-lobatto, radau-ps and runge-kutta

  • nb_seg (int or tuple) – Number of segments in which each phase is discretized

  • order (int or tuple) – Transcription order within each phase, must be odd

  • solver (str) – NLP solver, must be supported by OpenMDAO

  • ph_name (tuple) – Name of the phase within OpenMDAO

  • snopt_opts (dict or None, optional) – SNOPT optional settings expressed as key-value pairs. Refer to the SNOPT User Guide for more details. Default is None

  • rec_file (str or None, optional) – Name of the file in which the computed solution is recorded or None. Default is None

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • fix (str, optional) – alt to trigger the vertical phase at fixed altitude equal to alt_switch, time to trigger the vertical phase at fixed time to go equal to the second component of tof. Default is alt

Variables

  • alt (float) – Periselene altitude at which the powered descent is initiated [m]

  • alt_switch (float) – Altitude at which the vertical descent is triggered [m]

  • rp (float) – Periselene radius at which the powered descent is initiated [m]

  • r_switch (float) – Radius at which the vertical descent is triggered [m]

  • vp (float) – Periselene velocity at which the powered descent is initiated [m/s]

  • alpha_bounds (iterable) – Lower and upper bounds on thrust vector direction [rad]

  • tof (iterable) – Guessed time of flight for the two phases [s]

  • fix (str, optional) – alt to trigger the vertical phase at fixed altitude equal to alt_switch, time to trigger the vertical phase at fixed time to go equal to the second component of tof. Default is alt

set_options(theta, t_bounds)[source]

Set the time, states and control options for both phases and add the NLP objective.

Parameters

  • theta (float) – Guessed spawn angle [rad]

  • t_bounds (iterable) – Time of flight bounds expressed as fraction of tof [-]

set_initial_guess(theta, check_partials=False)[source]

Set the initial guess for the NLP solution as simple linear interpolation of the Boundary Conditions.

Parameters

  • theta (float) – Guessed spawn angle [rad]

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

cleanup()

Clean up resources.

exp_sim(rec_file=None)

Explicitly simulate the implicitly obtained optimal solution using Scipy solve_ivp method.

set_time_phase(ti, tof, phase, phase_name)

Compute the time grid within one phase to retrieve the time instants corresponding to the state, control and all discretization nodes.

Parameters

  • ti (float) – Initial time [-]

  • tof (float) – Time of flight (TOF) [-]

  • phase (Phase) – Current phase

  • phase_name (str) – Current phase name

Returns

  • state_nodes (ndarray) – Indexes corresponding to the state discretization nodes

  • control_nodes (ndarray) – Indexes corresponding to the control discretization nodes

  • t_state (ndarray) – Time instants on the state discretization nodes [-]

  • t_control (ndarray) – Time instants on the control discretization nodes [-]

  • t_all (ndarray) – Time instants on all discretization nodes [-]

setup()

Set up the Jacobian type, linear solver and derivatives type.

@authors: Alberto FOSSA’ Giuliana Elena MICELI

class latom.nlp.nlp_heo_2d.TwoDimLLO2HEONLP(body, sc, alt, rp, t, alpha_bounds, t_bounds, method, nb_seg, order, solver, ph_name, snopt_opts=None, rec_file=None, check_partials=False, u_bound='lower', fix_final=True)[source]

Bases: latom.nlp.nlp_2d.TwoDimVarNLP

TwoDimLLO2HEONLP transcribes a continuous-time optimal control problem for a two-dimensional transfer trajectory from a Low Lunar Orbit (LLO) to an Highly Elliptical Orbit (HEO) into a Non Linear Programming Problem (NLP) using the OpenMDAO and dymos libraries.

The transfer is modeled as a single phase ascent trajectory from the departure LLO to the apoapsis of the arrival HEO. The thrust magnitude is allowed to vary over time.

Parameters

  • body (Primary) – Instance of Primary class representing the central attracting body

  • sc (Spacecraft) – Instance of Spacecraft class representing the spacecraft

  • alt (float) – LLO altitude [m]

  • rp (float) – HEO periapsis radius [m]

  • t (float) – HEO period [s]

  • alpha_bounds (tuple) – Lower and upper bounds on thrust vector direction [rad]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • method (str) – Transcription method used to discretize the continuous time trajectory into a finite set of nodes, allowed gauss-lobatto, radau-ps and runge-kutta

  • nb_seg (int) – Number of segments in which each phase is discretized

  • order (int) – Transcription order within each phase, must be odd

  • solver (str) – NLP solver, must be supported by OpenMDAO

  • ph_name (str) – Name of the phase within OpenMDAO

  • snopt_opts (dict or None, optional) – SNOPT optional settings expressed as key-value pairs. Refer to the SNOPT User Guide for more details. Default is None

  • rec_file (str or None, optional) – Name of the file in which the computed solution is recorded or None. Default is None

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is lower

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is True

set_states_options(theta, u_bound=None)[source]

Set the states variables options.

Parameters

  • theta (float) – Unit reference value for spawn angle [rad]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is lower

cleanup()

Clean up resources.

exp_sim(rec_file=None)

Explicitly simulate the implicitly obtained optimal solution using Scipy solve_ivp method.

set_controls_options(throttle=True)

Set options on control variables.

Parameters

throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess(check_partials=False, fix_final=False, throttle=True)

Set the initial guess for the iterative solution of the NLP.

Parameters

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess_interpolation(bcs=array([[1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.]]), check_partials=False, throttle=True)

Set the initial guess for the solution of the NLP interpolating the Boundary Conditions (BCs) imposed on the state and control variables.

Parameters

  • bcs (ndarray, optional) – Boundary Conditions on state and control variables. Default is all ones

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_objective()

Set the NLP objective as the minimization of the opposite of the final spacecraft mass.

set_options(theta, t_bounds, u_bound=None)

Set options on state and control variables, time and objective function.

Parameters

  • theta (float) – Guessed spawn angle [rad]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_time_guess(tof)

Compute the time grid on the phase to retrieve the time instants corresponding to states, controls and all discretization nodes.

Parameters

tof (float) – Phase time of flight (TOF) [s]

set_time_options(tof, t_bounds)

Set the time options on the phase.

Parameters

  • tof (float) – Phase time of flight (TOF) [s]

  • t_bounds (tuple) – Time of flight lower and upper bounds expressed as a fraction of tof

setup()

Set up the Jacobian type, linear solver and derivatives type.

class latom.nlp.nlp_heo_2d.TwoDimLLO2ApoNLP(body, sc, alt, rp, t, alpha_bounds, t_bounds, method, nb_seg, order, solver, ph_name, snopt_opts=None, rec_file=None, check_partials=False, params=None)[source]

Bases: latom.nlp.nlp_2d.TwoDimNLP

TwoDimLLO2HEONLP transcribes a continuous-time optimal control problem for a two-dimensional transfer trajectory from a Low Lunar Orbit (LLO) to an Highly Elliptical Orbit (HEO) into a Non Linear Programming Problem (NLP) using the OpenMDAO and dymos libraries.

The transfer is modeled as a single phase ascent trajectory from the departure LLO to the apoapsis of the arrival HEO. The thrust magnitude is allowed to vary over time.

Parameters

  • body (Primary) – Instance of Primary class representing the central attracting body

  • sc (Spacecraft) – Instance of Spacecraft class representing the spacecraft

  • alt (float) – LLO altitude [m]

  • rp (float) – HEO periapsis radius [m]

  • t (float) – HEO period [s]

  • alpha_bounds (tuple) – Lower and upper bounds on thrust vector direction [rad]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • method (str) – Transcription method used to discretize the continuous time trajectory into a finite set of nodes, allowed gauss-lobatto, radau-ps and runge-kutta

  • nb_seg (int) – Number of segments in which each phase is discretized

  • order (int) – Transcription order within each phase, must be odd

  • solver (str) – NLP solver, must be supported by OpenMDAO

  • ph_name (str) – Name of the phase within OpenMDAO

  • snopt_opts (dict or None, optional) – SNOPT optional settings expressed as key-value pairs. Refer to the SNOPT User Guide for more details. Default is None

  • rec_file (str or None, optional) – Name of the file in which the computed solution is recorded or None. Default is None

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • params (dict or None, optional) – Optional parameters to be passed when a continuation method is employed and the NLP guess is not defined or None. Default is None

Variables

guess (TwoDimLLO2HEOGuess or None) – Initial guess or None if continuation is used

add_timeseries_output(names=('a', 'eps', 'h'))[source]

Adds the semi-major axis, specific energy and specific angular momentum magnitude to the time series outputs of the phase.

Parameters

names (iterable) – List of strings corresponding to the names of the variables to be added to the outputs

set_options(rp, vp, thetaf, tof, t_bounds=None)[source]

Set the states, controls and time options, add the design parameters and boundary constraints, define the objective of the optimization.

Parameters

  • rp (float) – Unit reference value for lengths [m]

  • vp (float) – Unit reference value for velocities [m/s]

  • thetaf (float) – Unit reference value for spawn angle [rad]

  • tof (float) – Guessed time of flight [s]

  • t_bounds (iterable or None, optional) – Time of flight lower and upper bounds expressed as fraction of tof [-]

set_initial_guess(check_partials=False, fix_final=False, throttle=False)[source]

Set the initial guess for a single solution or the first solution of a continuation procedure.

Parameters

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • fix_final (bool, optional) – True if the final time is fixed, False otherwise. Default is False

  • throttle (bool, optional) – True of variable thrust, False otherwise

set_continuation_guess(tof, states, controls, check_partials=False)[source]

Set the initial guess for the solution k+1 as the optimal transfer found for the solution k during a continuation procedure.

Parameters

  • tof (float) – Time of flight for the previous optimal solution [s]

  • states (ndarray) – States on the states discretization nodes for the previous optimal solution

  • controls (ndarray) – Controls on the controls discretization nodes for the previous optimal solution

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

cleanup()

Clean up resources.

exp_sim(rec_file=None)

Explicitly simulate the implicitly obtained optimal solution using Scipy solve_ivp method.

set_controls_options(throttle=True)

Set options on control variables.

Parameters

throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_initial_guess_interpolation(bcs=array([[1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.], [1., 1.]]), check_partials=False, throttle=True)

Set the initial guess for the solution of the NLP interpolating the Boundary Conditions (BCs) imposed on the state and control variables.

Parameters

  • bcs (ndarray, optional) – Boundary Conditions on state and control variables. Default is all ones

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

  • throttle (bool, optional) – True for variable thrust magnitude, False otherwise. Default is ‘True`

set_objective()

Set the NLP objective as the minimization of the opposite of the final spacecraft mass.

set_states_options(theta, u_bound=None)

Set options on the state variables of the NLP.

Parameters

  • theta (float) – Reference value for spawn angle [rad]

  • u_bound (str or None, optional) – Bounds on spacecraft radial velocity between lower and upper or None. Default is None

set_time_guess(tof)

Compute the time grid on the phase to retrieve the time instants corresponding to states, controls and all discretization nodes.

Parameters

tof (float) – Phase time of flight (TOF) [s]

set_time_options(tof, t_bounds)

Set the time options on the phase.

Parameters

  • tof (float) – Phase time of flight (TOF) [s]

  • t_bounds (tuple) – Time of flight lower and upper bounds expressed as a fraction of tof

setup()

Set up the Jacobian type, linear solver and derivatives type.

class latom.nlp.nlp_heo_2d.TwoDim3PhasesLLO2HEONLP(body, sc, alt, rp, t, alpha_bounds, t_bounds, method, nb_seg, order, solver, ph_name, snopt_opts=None, rec_file=None, check_partials=False)[source]

Bases: latom.nlp.nlp.MultiPhaseNLP

TwoDim3PhasesLLO2HEONLP transcribes an optimal control problem for a three-phases ascent trajectory from a circular Low Lunar Orbit (LLO) to an Highly Elliptical Orbit (HEO) into a Non Linear Programming Problem (NLP) using the OpenMDAO and dymos libraries.

The transfer is modeled with a first powered phase at maximum thrust to leave the initial LLO, and intermediate coasting phase and a second powered phase to inject in the target HEO.

Parameters

  • body (Primary) – Instance of Primary class representing the central attracting body

  • sc (Spacecraft) – Instance of Spacecraft class representing the spacecraft

  • alt (float) – Periselene altitude at which the powered descent is initiated [m]

  • rp (float) – HEO periapsis radius [m]

  • t (float) – HEO period [s]

  • alpha_bounds (iterable) – Lower and upper bounds on thrust vector direction [rad]

  • t_bounds (tuple) – Time of flight bounds expressed as fraction of tof [-]

  • method (str) – Transcription method used to discretize the continuous time trajectory into a finite set of nodes, allowed gauss-lobatto, radau-ps and runge-kutta

  • nb_seg (int or tuple) – Number of segments in which each phase is discretized

  • order (int or tuple) – Transcription order within each phase, must be odd

  • solver (str) – NLP solver, must be supported by OpenMDAO

  • ph_name (tuple) – Name of the phase within OpenMDAO

  • snopt_opts (dict or None, optional) – SNOPT optional settings expressed as key-value pairs. Refer to the SNOPT User Guide for more details. Default is None

  • rec_file (str or None, optional) – Name of the file in which the computed solution is recorded or None. Default is None

  • check_partials (bool, optional) – Check the partial derivatives computed analytically against complex step method. Default is False

Variables

  • guess (TwoDim3PhasesLLO2HEOGuess) – Initial guess for the iterative NLP solution

  • tof_adim (ndarray) – Time of flight in non-dimensional units [-]

set_initial_guess_phase(state_nodes, control_nodes, phase_name)[source]

Set the initial guess for a given Phase.

Parameters

  • state_nodes (ndarray) – Indexes corresponding to the states discretization nodes within the specified transcription

  • control_nodes (ndarray) – Indexes corresponding to the controls discretization nodes within the specified transcription

  • phase_name (str) – Name of the current Phase object

cleanup()

Clean up resources.

exp_sim(rec_file=None)

Explicitly simulate the implicitly obtained optimal solution using Scipy solve_ivp method.

set_time_phase(ti, tof, phase, phase_name)

Compute the time grid within one phase to retrieve the time instants corresponding to the state, control and all discretization nodes.

Parameters

  • ti (float) – Initial time [-]

  • tof (float) – Time of flight (TOF) [-]

  • phase (Phase) – Current phase

  • phase_name (str) – Current phase name

Returns

  • state_nodes (ndarray) – Indexes corresponding to the state discretization nodes

  • control_nodes (ndarray) – Indexes corresponding to the control discretization nodes

  • t_state (ndarray) – Time instants on the state discretization nodes [-]

  • t_control (ndarray) – Time instants on the control discretization nodes [-]

  • t_all (ndarray) – Time instants on all discretization nodes [-]

setup()

Set up the Jacobian type, linear solver and derivatives type.