latom.nlp.nlp_heo_2d

@authors: Alberto FOSSA’ Giuliana Elena MICELI

Classes

MultiPhaseNLP(body, sc, method, nb_seg, …)

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.

ODE2dLLO2Apo(**kwargs)

ODE2dLLO2Apo class defines the equations of motion for a two dim.

ODE2dLLO2HEO(**kwargs)

ODE2dLLO2HEO class defines the equations of motion for a two dim.

TwoDim3PhasesLLO2HEOGuess(gm, r, alt, rp, t, sc)

TwoDim3PhasesLLO2HEOGuess provides an initial guess for a LLO to HEO transfer trajectory subdivided into two powered phases and an intermediate coasting phase.

TwoDim3PhasesLLO2HEONLP(body, sc, alt, rp, …)

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.

TwoDimLLO2ApoNLP(body, sc, alt, rp, t, …)

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.

TwoDimLLO2HEOGuess(gm, r, alt, rp, t, sc)

TwoDimLLO2HEOGuess provides an initial guess for an LLO to HEO transfer.

TwoDimLLO2HEONLP(body, sc, alt, rp, t, …)

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.

TwoDimNLP(body, sc, alt, alpha_bounds, …)

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.

TwoDimVarNLP(body, sc, alt, alpha_bounds, …)

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.
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.