Source code for scenarioLagrangePointOrbit

#
#  ISC License
#
#  Copyright (c) 2022, Autonomous Vehicle Systems Lab, University of Colorado at Boulder
#
#  Permission to use, copy, modify, and/or distribute this software for any
#  purpose with or without fee is hereby granted, provided that the above
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#  WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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#  ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
#  OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
#

r"""
Overview
--------

This script sets up a 3-DOF spacecraft which is operating at one of five Earth-Moon Lagrange points. The purpose
is to illustrate how to use multiple gravity bodies to create interesting 3-body orbit behavior.

The script is found in the folder ``basilisk/examples`` and executed by using::

    python3 scenarioLagrangePointOrbit.py

For this simulation, the Earth is assumed stationary, and the Moon's trajectory is generated using SPICE. Refer to
:ref:`scenarioOrbitMultiBody` to learn how to create multiple gravity bodies and read a SPICE trajectory.

The initial position of the spacecraft is specified using a Lagrange point index. The positioning of the Lagrange
points is illustrated `here <https://www.spaceacademy.net.au/library/notes/lagrangp.htm>`__.

For Lagrange points 1-3, the initial Earth-spacecraft distance is specified to lowest order
in :math:`\alpha = \mu_{M} / \mu_{E}`, where the subscript M is for the Moon and E is for the Earth.
These are unstable equilibrium points.

.. math::
    r_{L1} = a_{M} \left[ 1-\left(\frac{\alpha}{3}\right)^{1/3} \right]

.. math::
    r_{L2} = a_{M} \left[ 1+\left(\frac{\alpha}{3}\right)^{1/3} \right]

.. math::
    r_{L3} = a_{M} \left[ 1-\frac{7 \alpha}{12} \right]

For Lagrange points 4 and 5, the spacecraft is positioned at :math:`r_{L4} = r_{L5} = a_{M}` at +/- 60
degrees from the Earth-Moon vector. These are stable equilibrium points.

When the simulation completes, two plots are shown. The first plot shows the orbits of the Moon and spacecraft in
the Earth-centered inertial frame. The second plot shows the motion of the Moon and spacecraft in a frame rotating
with the Moon.

Illustration of Simulation Results
----------------------------------

The following images illustrate the simulation run results with the following settings:

::

    nOrbits=1, timestep=300, showPlots=True

When starting at L1, L2, or L3, the spacecraft moves away from the unstable equilibrium point.

::

    lagrangePoint=1

.. image:: /_images/Scenarios/scenarioLagrangePointOrbitL1Fig1.svg
    :align: center

.. image:: /_images/Scenarios/scenarioLagrangePointOrbitL1Fig2.svg
    :align: center

::

    lagrangePoint=2

.. image:: /_images/Scenarios/scenarioLagrangePointOrbitL2Fig1.svg
    :align: center

.. image:: /_images/Scenarios/scenarioLagrangePointOrbitL2Fig2.svg
    :align: center

::

    lagrangePoint=3

.. image:: /_images/Scenarios/scenarioLagrangePointOrbitL3Fig1.svg
    :align: center

.. image:: /_images/Scenarios/scenarioLagrangePointOrbitL3Fig2.svg
    :align: center

When starting at L4 or L5, the spacecraft remains near the stable equilibrium point.

::

    lagrangePoint=4

.. image:: /_images/Scenarios/scenarioLagrangePointOrbitL4Fig1.svg
    :align: center

.. image:: /_images/Scenarios/scenarioLagrangePointOrbitL4Fig2.svg
    :align: center


::

    lagrangePoint=5

.. image:: /_images/Scenarios/scenarioLagrangePointOrbitL5Fig1.svg
    :align: center

.. image:: /_images/Scenarios/scenarioLagrangePointOrbitL5Fig2.svg
    :align: center

"""

#
# Basilisk Scenario Script and Integrated Test
#
# Purpose:  This scenario illustrates the orbit of a spacecraft near the Earth-Moon Lagrange points.
# Author:   Scott McKinley
# Creation Date:  Aug. 31, 2022
#

import os
from datetime import datetime, timedelta

import matplotlib.pyplot as plt
import numpy as np
from Basilisk import __path__
from Basilisk.simulation import orbElemConvert
from Basilisk.simulation import spacecraft
from Basilisk.topLevelModules import pyswice
from Basilisk.utilities import (SimulationBaseClass, macros, orbitalMotion,
                                simIncludeGravBody, unitTestSupport, vizSupport)
from Basilisk.utilities.pyswice_spk_utilities import spkRead

bskPath = __path__[0]
fileName = os.path.basename(os.path.splitext(__file__)[0])

[docs] def run(lagrangePoint, nOrbits, timestep, showPlots=True): """ Args: lagrangePoint (int): Earth-Moon Lagrange point ID [1,2,3,4,5] nOrbits (float): Number of Earth orbits to simulate timestep (float): Simulation timestep in seconds showPlots (bool): Determines if the script should display plots """ # Create simulation variable names simTaskName = "dynTask" simProcessName = "dynProcess" # Create a sim module as an empty container scSim = SimulationBaseClass.SimBaseClass() scSim.SetProgressBar(True) # Create the simulation process (dynamics) dynProcess = scSim.CreateNewProcess(simProcessName) # Add the dynamics task to the dynamics process and specify the integration update time simulationTimeStep = macros.sec2nano(timestep) dynProcess.addTask(scSim.CreateNewTask(simTaskName, simulationTimeStep)) # Setup the spacecraft object scObject = spacecraft.Spacecraft() scObject.ModelTag = "lagrangeSat" # Setup the orbital element converter for planet position message output oeObject = orbElemConvert.OrbElemConvert() oeObject.ModelTag = "planetObj" # Add spacecraft object to the simulation process # Make this model a lower priority than the SPICE object task scSim.AddModelToTask(simTaskName, scObject, 0) # Setup gravity factory and gravity bodies # Include bodies as a list of SPICE names gravFactory = simIncludeGravBody.gravBodyFactory() gravBodies = gravFactory.createBodies('moon', 'earth') gravBodies['earth'].isCentralBody = True # Add gravity bodies to the spacecraft dynamics gravFactory.addBodiesTo(scObject) # Create default SPICE module, specify start date/time. timeInitString = "2022 August 31 15:00:00.0" spiceTimeStringFormat = '%Y %B %d %H:%M:%S.%f' timeInit = datetime.strptime(timeInitString, spiceTimeStringFormat) spiceObject = gravFactory.createSpiceInterface(time=timeInitString, epochInMsg=True) spiceObject.zeroBase = 'Earth' # Add SPICE object to the simulation task list scSim.AddModelToTask(simTaskName, spiceObject, 1) # Import SPICE ephemeris data into the python environment pyswice.furnsh_c(spiceObject.SPICEDataPath + 'de430.bsp') # solar system bodies pyswice.furnsh_c(spiceObject.SPICEDataPath + 'naif0012.tls') # leap second file pyswice.furnsh_c(spiceObject.SPICEDataPath + 'de-403-masses.tpc') # solar system masses pyswice.furnsh_c(spiceObject.SPICEDataPath + 'pck00010.tpc') # generic Planetary Constants Kernel # Set spacecraft ICs # Use Earth data moonSpiceName = 'moon' moonInitialState = 1000 * spkRead(moonSpiceName, timeInitString, 'J2000', 'earth') moon_rN_init = moonInitialState[0:3] moon_vN_init = moonInitialState[3:6] moon = gravBodies['moon'] earth = gravBodies['earth'] oe = orbitalMotion.rv2elem(earth.mu, moon_rN_init, moon_vN_init) moon_a = oe.a # Delay or advance the spacecraft by a few degrees to prevent strange spacecraft-moon interactions when the # spacecraft wanders from the unstable equilibrium points if lagrangePoint == 1: oe.a = oe.a * (1-np.power(moon.mu / (3*earth.mu), 1./3.)) oe.f = oe.f + macros.D2R*4 elif lagrangePoint == 2: oe.a = oe.a * (1+np.power(moon.mu / (3*earth.mu), 1./3.)) oe.f = oe.f - macros.D2R*4 elif lagrangePoint == 3: oe.a = oe.a * (1-(7*moon.mu/(12*earth.mu))) oe.f = oe.f + np.pi elif lagrangePoint == 4: oe.f = oe.f + np.pi/3 else: oe.f = oe.f - np.pi/3 oe.f = oe.f - macros.D2R*2 rN, vN = orbitalMotion.elem2rv(earth.mu, oe) scObject.hub.r_CN_NInit = rN scObject.hub.v_CN_NInit = vN # Set simulation time n = np.sqrt(earth.mu / np.power(moon_a, 3)) P = 2 * np.pi/n simulationTime = macros.sec2nano(nOrbits*P) # Setup data logging numDataPoints = 1000 samplingTime = unitTestSupport.samplingTime(simulationTime, simulationTimeStep, numDataPoints) # Setup spacecraft data recorder scDataRec = scObject.scStateOutMsg.recorder(samplingTime) scSim.AddModelToTask(simTaskName, scDataRec) viz = vizSupport.enableUnityVisualization(scSim, simTaskName, scObject, # saveFile=__file__ ) # Initialize simulation scSim.InitializeSimulation() # Execute simulation scSim.ConfigureStopTime(simulationTime) scSim.ExecuteSimulation() # Retrieve logged data posData = scDataRec.r_BN_N velData = scDataRec.v_BN_N timeData = scDataRec.times() # Plot results np.set_printoptions(precision=16) plt.close("all") figureList = {} b = oe.a * np.sqrt(1 - oe.e * oe.e) # First plot: Draw orbit in inertial frame fig = plt.figure(1, figsize=np.array((1.0, b / oe.a)) * 4.75, dpi=100) plt.axis(np.array([-oe.rApoap, oe.rPeriap, -b, b]) / 1000 * 1.25) ax = fig.gca() ax.ticklabel_format(style='scientific', scilimits=[-5, 3]) # Draw 'cartoon' Earth ax.add_artist(plt.Circle((0, 0), 0.2e5, color='b')) # Plot spacecraft orbit data rDataSpacecraft = [] fDataSpacecraft = [] for ii in range(len(posData)): oeDataSpacecraft = orbitalMotion.rv2elem(earth.mu, posData[ii], velData[ii]) rDataSpacecraft.append(oeDataSpacecraft.rmag) fDataSpacecraft.append(oeDataSpacecraft.f + oeDataSpacecraft.omega - oe.omega) # Why the add/subtract of omegas? plt.plot(rDataSpacecraft * np.cos(fDataSpacecraft) / 1000, rDataSpacecraft * np.sin(fDataSpacecraft) / 1000, color='g', linewidth=3.0, label='Spacecraft') # Plot moon orbit data rDataMoon = [] fDataMoon = [] for ii in range(len(timeData)): simTime = timeData[ii] * macros.NANO2SEC sec = int(simTime) usec = (simTime - sec) * 1e6 time = timeInit + timedelta(seconds=sec, microseconds=usec) timeString = time.strftime(spiceTimeStringFormat) moonState = 1000 * spkRead(moonSpiceName, timeString, 'J2000', 'earth') moon_rN = moonState[0:3] moon_vN = moonState[3:6] oeDataMoon = orbitalMotion.rv2elem(earth.mu, moon_rN, moon_vN) rDataMoon.append(oeDataMoon.rmag) fDataMoon.append(oeDataMoon.f + oeDataMoon.omega - oe.omega) plt.plot(rDataMoon * np.cos(fDataMoon) / 1000, rDataMoon * np.sin(fDataMoon) / 1000, color='0.5', linewidth=3.0, label='Moon') plt.xlabel('$i_e$ Coord. [km]') plt.ylabel('$i_p$ Coord. [km]') plt.grid() plt.legend() pltName = fileName + "L" + str(lagrangePoint) + "Fig1" figureList[pltName] = plt.figure(1) # Second plot: Draw orbit in frame rotating with the Moon fig = plt.figure(2, figsize=np.array((1.0, b / oe.a)) * 4.75, dpi=100) plt.axis(np.array([-oe.rApoap, oe.rPeriap, -b, b]) / 1000 * 1.25) ax = fig.gca() ax.ticklabel_format(style='scientific', scilimits=[-5, 3]) # Draw 'cartoon' Earth ax.add_artist(plt.Circle((0, 0), 0.2e5, color='b')) # Plot spacecraft and Moon orbit data rDataSpacecraft = [] fDataSpacecraft = [] rDataMoon = [] fDataMoon = [] for ii in range(len(posData)): # Get Moon f simTime = timeData[ii] * macros.NANO2SEC sec = int(simTime) usec = (simTime - sec) * 1e6 time = timeInit + timedelta(seconds=sec, microseconds=usec) timeString = time.strftime(spiceTimeStringFormat) moonState = 1000 * spkRead(moonSpiceName, timeString, 'J2000', 'earth') moon_rN = moonState[0:3] moon_vN = moonState[3:6] oeDataMoon = orbitalMotion.rv2elem(earth.mu, moon_rN, moon_vN) moon_f = oeDataMoon.f # Get spacecraft data, with spacecraft f = oe data f - moon f oeDataSpacecraft = orbitalMotion.rv2elem(earth.mu, posData[ii], velData[ii]) rDataSpacecraft.append(oeDataSpacecraft.rmag) fDataSpacecraft.append(oeDataSpacecraft.f - moon_f + oeDataSpacecraft.omega - oe.omega) # Get Moon data rDataMoon.append(oeDataMoon.rmag) fDataMoon.append(0) plt.plot(rDataSpacecraft * np.cos(fDataSpacecraft) / 1000, rDataSpacecraft * np.sin(fDataSpacecraft) / 1000, color='g', linewidth=3.0, label='Spacecraft') plt.plot(rDataMoon * np.cos(fDataMoon) / 1000, rDataMoon * np.sin(fDataMoon) / 1000, color='0.5', linewidth=3.0, label='Moon') plt.xlabel('Earth-Moon axis [km]') plt.ylabel('Earth-Moon perpendicular axis [km]') plt.grid() plt.legend() pltName = fileName + "L" + str(lagrangePoint) + "Fig2" figureList[pltName] = plt.figure(2) if showPlots: plt.show() plt.close("all") # Unload spice libraries gravFactory.unloadSpiceKernels() pyswice.unload_c(spiceObject.SPICEDataPath + 'de430.bsp') # solar system bodies pyswice.unload_c(spiceObject.SPICEDataPath + 'naif0012.tls') # leap second file pyswice.unload_c(spiceObject.SPICEDataPath + 'de-403-masses.tpc') # solar system masses pyswice.unload_c(spiceObject.SPICEDataPath + 'pck00010.tpc') # generic Planetary Constants Kernel return figureList
if __name__ == "__main__": run( 5, # Lagrange point 1, # Number of Moon orbits 300, # Timestep (seconds) True # Show plots )