CR3BPDifferentialCorrection.java

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package org.orekit.orbits;

import org.hipparchus.geometry.euclidean.threed.Rotation;
import org.hipparchus.geometry.euclidean.threed.Vector3D;
import org.hipparchus.linear.RealMatrix;
import org.hipparchus.ode.events.Action;
import org.hipparchus.ode.nonstiff.AdaptiveStepsizeIntegrator;
import org.hipparchus.ode.nonstiff.DormandPrince853Integrator;
import org.hipparchus.util.FastMath;
import org.orekit.attitudes.AttitudeProvider;
import org.orekit.attitudes.InertialProvider;
import org.orekit.bodies.CR3BPSystem;
import org.orekit.errors.OrekitException;
import org.orekit.errors.OrekitMessages;
import org.orekit.propagation.SpacecraftState;
import org.orekit.propagation.events.HaloXZPlaneCrossingDetector;
import org.orekit.propagation.numerical.NumericalPropagator;
import org.orekit.propagation.numerical.cr3bp.CR3BPForceModel;
import org.orekit.propagation.numerical.cr3bp.STMEquations;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.TimeScale;
import org.orekit.utils.AbsolutePVCoordinates;
import org.orekit.utils.PVCoordinates;


/**
 * Class implementing the differential correction method for Halo or Lyapunov
 * Orbits. It is not a simple differential correction, it uses higher order
 * terms to be more accurate and meet orbits requirements.
 * @see "Three-dimensional, periodic, Halo Orbits by Kathleen Connor Howell, Stanford University"
 * @author Vincent Mouraux
 * @since 10.2
 */
public class CR3BPDifferentialCorrection {

    /** Maximum number of iterations. */
    private static final int MAX_ITER = 30;

    /** Max check interval for crossing plane. */
    private static final double CROSSING_MAX_CHECK = 3600.0;

    /** Convergence tolerance for plane crossing time. */
    private static final double CROSSING_TOLERANCE = 1.0e-10;

    /** Arbitrary start date. */
    private static final AbsoluteDate START_DATE = AbsoluteDate.ARBITRARY_EPOCH;

    /** Boolean return true if the propagated trajectory crosses the plane. */
    private boolean cross;

    /** first guess PVCoordinates of the point to start differential correction. */
    private final PVCoordinates firstGuess;

    /** CR3BP System considered. */
    private final CR3BPSystem syst;

    /** orbitalPeriodApprox Orbital Period of the firstGuess. */
    private final double orbitalPeriodApprox;

    /** orbitalPeriod Orbital Period of the required orbit. */
    private double orbitalPeriod;

    /** Simple Constructor.
     * <p> Standard constructor using DormandPrince853 integrator for the differential correction </p>
     * @param firstguess first guess PVCoordinates of the point to start differential correction
     * @param syst CR3BP System considered
     * @param orbitalPeriod Orbital Period of the required orbit
     */
    public CR3BPDifferentialCorrection(final PVCoordinates firstguess,
                                       final CR3BPSystem syst, final double orbitalPeriod) {
        this.firstGuess = firstguess;
        this.syst = syst;
        this.orbitalPeriodApprox = orbitalPeriod;

    }

    /** Simple Constructor.
     * <p> Standard constructor using DormandPrince853 integrator for the differential correction </p>
     * @param firstguess first guess PVCoordinates of the point to start differential correction
     * @param syst CR3BP System considered
     * @param orbitalPeriod Orbital Period of the required orbit
     * @param attitudeProvider the attitude law for the numerical propagator
     * @param utc UTC time scale
     * @deprecated as of 11.1, replaced by {@link #CR3BPDifferentialCorrection(PVCoordinates, CR3BPSystem, double)}
     */
    @Deprecated
    public CR3BPDifferentialCorrection(final PVCoordinates firstguess,
                                       final CR3BPSystem syst,
                                       final double orbitalPeriod,
                                       final AttitudeProvider attitudeProvider,
                                       final TimeScale utc) {
        this(firstguess, syst, orbitalPeriod);
    }

    /** Build the propagator.
     * @return propagator
     * @since 11.1
     */
    private NumericalPropagator buildPropagator() {

        // Adaptive stepsize boundaries
        final double minStep = 1E-12;
        final double maxstep = 0.001;

        // Integrator tolerances
        final double positionTolerance = 1E-5;
        final double velocityTolerance = 1E-5;
        final double massTolerance = 1.0e-6;
        final double[] vecAbsoluteTolerances = {positionTolerance, positionTolerance, positionTolerance, velocityTolerance, velocityTolerance, velocityTolerance, massTolerance};
        final double[] vecRelativeTolerances = new double[vecAbsoluteTolerances.length];

        // Integrator definition
        final AdaptiveStepsizeIntegrator integrator = new DormandPrince853Integrator(minStep, maxstep,
                                                                                     vecAbsoluteTolerances,
                                                                                     vecRelativeTolerances);

        // Propagator definition
        final NumericalPropagator propagator =
                        new NumericalPropagator(integrator, new InertialProvider(Rotation.IDENTITY, syst.getRotatingFrame()));

        // CR3BP has no defined orbit type
        propagator.setOrbitType(null);

        // CR3BP has central Attraction
        propagator.setIgnoreCentralAttraction(true);

        // Add CR3BP Force Model to the propagator
        propagator.addForceModel(new CR3BPForceModel(syst));

        // Add event detector for crossing plane
        propagator.addEventDetector(new HaloXZPlaneCrossingDetector(CROSSING_MAX_CHECK, CROSSING_TOLERANCE).
                                    withHandler((state, detector, increasing) -> {
                                        cross = true;
                                        return Action.STOP;
                                    }));

        return propagator;

    }

    /**
     * Return the real starting PVCoordinates on the Libration orbit type
     * after differential correction from a first guess.
     * @param type libration orbit type
     * @return pv Position-Velocity of the starting point on the Halo Orbit
     */
    public PVCoordinates compute(final LibrationOrbitType type) {
        return type == LibrationOrbitType.HALO ? computeHalo() : computeLyapunov();
    }

    /** Return the real starting PVCoordinates on the Halo orbit after differential correction from a first guess.
     * @return pv Position-Velocity of the starting point on the Halo Orbit
     */
    private PVCoordinates computeHalo() {

        // Initializing PVCoordinates with first guess
        PVCoordinates pvHalo = firstGuess;

        // Start a new differentially corrected propagation until it converges to a Halo Orbit
        // Converge within 1E-8 tolerance and under 5 iterations
        for (int iHalo = 0; iHalo < MAX_ITER; ++iHalo) {

            // SpacecraftState initialization
            final AbsolutePVCoordinates initialAbsPVHalo = new AbsolutePVCoordinates(syst.getRotatingFrame(), START_DATE, pvHalo);
            final SpacecraftState       initialStateHalo = new SpacecraftState(initialAbsPVHalo);

            // setup propagator
            final NumericalPropagator propagator = buildPropagator();
            final STMEquations        stm        = new STMEquations(syst);
            propagator.addAdditionalDerivativesProvider(stm);
            propagator.setInitialState(stm.setInitialPhi(initialStateHalo));

            // boolean changed to true by crossing XZ plane during propagation. Has to be true for the differential correction to converge
            cross = false;

            // Propagate until trajectory crosses XZ Plane
            final SpacecraftState finalStateHalo =
                propagator.propagate(START_DATE.shiftedBy(orbitalPeriodApprox));

            // Stops computation if trajectory did not cross XZ Plane after one full orbital period
            if (cross == false) {
                throw new OrekitException(OrekitMessages.TRAJECTORY_NOT_CROSSING_XZPLANE);
            }

            // Get State Transition Matrix phi
            final RealMatrix phiHalo = stm.getStateTransitionMatrix(finalStateHalo);

            // Gap from desired X and Z axis velocity value ()
            final double dvxf = -finalStateHalo.getPVCoordinates().getVelocity().getX();
            final double dvzf = -finalStateHalo.getPVCoordinates().getVelocity().getZ();

            orbitalPeriod = 2 * finalStateHalo.getDate().durationFrom(START_DATE);

            if (FastMath.abs(dvxf) <= 1E-8 && FastMath.abs(dvzf) <= 1E-8) {
                break;
            }

            // Y axis velocity
            final double vy = finalStateHalo.getPVCoordinates().getVelocity().getY();

            // Spacecraft acceleration
            final Vector3D acc  = finalStateHalo.getPVCoordinates().getAcceleration();
            final double   accx = acc.getX();
            final double   accz = acc.getZ();

            // Compute A coefficients
            final double a11 = phiHalo.getEntry(3, 0) - accx * phiHalo.getEntry(1, 0) / vy;
            final double a12 = phiHalo.getEntry(3, 4) - accx * phiHalo.getEntry(1, 4) / vy;
            final double a21 = phiHalo.getEntry(5, 0) - accz * phiHalo.getEntry(1, 0) / vy;
            final double a22 = phiHalo.getEntry(5, 4) - accz * phiHalo.getEntry(1, 4) / vy;

            // A determinant used for matrix inversion
            final double aDet = a11 * a22 - a21 * a12;

            // Correction to apply to initial conditions
            final double deltax0  = (a22 * dvxf - a12 * dvzf) / aDet;
            final double deltavy0 = (-a21 * dvxf + a11 * dvzf) / aDet;

            // Computation of the corrected initial PVCoordinates
            final double newx  = pvHalo.getPosition().getX() + deltax0;
            final double newvy = pvHalo.getVelocity().getY() + deltavy0;

            pvHalo = new PVCoordinates(new Vector3D(newx,
                                                    pvHalo.getPosition().getY(),
                                                    pvHalo.getPosition().getZ()),
                                       new Vector3D(pvHalo.getVelocity().getX(),
                                                    newvy,
                                                    pvHalo.getVelocity().getZ()));
        }

        // Return
        return pvHalo;
    }

    /** Return the real starting PVCoordinates on the Lyapunov orbit after differential correction from a first guess.
     * @return pv Position-Velocity of the starting point on the Lyapunov Orbit
     */
    public PVCoordinates computeLyapunov() {

        // Initializing PVCoordinates with first guess
        PVCoordinates pvLyapunov = firstGuess;

        // Start a new differentially corrected propagation until it converges to a Halo Orbit
        // Converge within 1E-8 tolerance and under 5 iterations
        for (int iLyapunov = 0; iLyapunov < MAX_ITER; ++iLyapunov) {

            // SpacecraftState initialization
            final AbsolutePVCoordinates initialAbsPVLyapunov = new AbsolutePVCoordinates(syst.getRotatingFrame(), START_DATE, pvLyapunov);
            final SpacecraftState       initialStateLyapunov = new SpacecraftState(initialAbsPVLyapunov);

            // setup propagator
            final NumericalPropagator propagator = buildPropagator();
            final STMEquations        stm        = new STMEquations(syst);
            propagator.addAdditionalDerivativesProvider(stm);
            propagator.setInitialState(stm.setInitialPhi(initialStateLyapunov));

            // boolean changed to true by crossing XZ plane during propagation. Has to be true for the differential correction to converge
            cross = false;

            // Propagate until trajectory crosses XZ Plane
            final SpacecraftState finalStateLyapunov =
                propagator.propagate(START_DATE.shiftedBy(orbitalPeriodApprox));

            // Stops computation if trajectory did not cross XZ Plane after one full orbital period
            if (cross == false) {
                throw new OrekitException(OrekitMessages.TRAJECTORY_NOT_CROSSING_XZPLANE);
            }

            // Get State Transition Matrix phi
            final RealMatrix phi = stm.getStateTransitionMatrix(finalStateLyapunov);

            // Gap from desired y position and x velocity value ()
            final double dvxf = -finalStateLyapunov.getPVCoordinates().getVelocity().getX();

            orbitalPeriod = 2 * finalStateLyapunov.getDate().durationFrom(START_DATE);

            if (FastMath.abs(dvxf) <= 1E-14) {
                break;
            }

            // Y axis velocity
            final double vy = finalStateLyapunov.getPVCoordinates().getVelocity().getY();

            // Spacecraft acceleration
            final double accy = finalStateLyapunov.getPVCoordinates().getAcceleration().getY();

            // Compute A coefficients
            final double deltavy0 = dvxf / (phi.getEntry(3, 4) - accy * phi.getEntry(1, 4) / vy);

            // Computation of the corrected initial PVCoordinates
            final double newvy = pvLyapunov.getVelocity().getY() + deltavy0;

            pvLyapunov = new PVCoordinates(new Vector3D(pvLyapunov.getPosition().getX(),
                                                        pvLyapunov.getPosition().getY(),
                                                        0),
                                           new Vector3D(pvLyapunov.getVelocity().getX(),
                                                        newvy,
                                                        0));

        }

        // Return
        return pvLyapunov;
    }

    /** Get the orbital period of the required orbit.
     * @return the orbitalPeriod
     */
    public double getOrbitalPeriod() {
        return orbitalPeriod;
    }

}