Source code for scenarioHohmann

#
#  ISC License
#
#  Copyright (c) 2023, 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.
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r"""
Overview
--------

This Example simulates a single Hohmann transfer about earth. The spacecraft switches between a Hill frame
and an inertial frame aligned with the burn direction, although alignment with the burn is purely visual and the delta V
will be applied in te correct direction regardless of the attitude.

Compared to :ref:`scenarioOrbitManeuver` which also implements impulsive orbit maneuvers, here a set
of pointing modes are defined.  The Basilisk event system is used to then switch between the flight modes
by selectively turning on/off flight mode tasks.

The detail of the simulation script is as follows. This script sets up a basic spacecraft which starts on a circular
orbit around Earth aligned with a Hill reference frame. The spacecraft aligns with the orbit trajectory shortly before
delta V's are applied at the beginning and end of the transfer and returns to the Hill frame for the duration of the
simulation.

The required delta V is found by taking the difference between the velocity on the elliptical transfer orbit, found
using

.. math::
    V_{transfer} = \sqrt{\frac{2\mu}{r} - \frac{\mu}{a_{transfer}}}

and that of the circular orbit, defined as

.. math::
    V = \sqrt{\frac{\mu}{r}}

The delta V is then added to the current spacecraft velocity. This calculation is done at each transfer point using the
respective radius (inner or outer).

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

      python3 scenarioHohmann.py

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

::

    show_plots = True

Plots below illustrate

.. image:: /_images/Scenarios/scenarioHohmann1.svg
   :align: center

.. image:: /_images/Scenarios/scenarioHohmann2.svg
   :align: center

.. image:: /_images/Scenarios/scenarioHohmann3.svg
    :align: center

.. image:: /_images/Scenarios/scenarioHohmann4.svg
    :align: center

"""

#
# Basilisk Scenario Script and Integrated Test
#
# Purpose:  Basic simulation showing how to set up a Hohmann transfer and use reaction wheels to change the spacecraft's
#           reference attitude
# Author:   Peter Johnson
# Creation Date:  Sep. 6, 2023
#

import os

import matplotlib.pyplot as plt
from mpl_toolkits import mplot3d as plt3
import numpy as np
# The path to the location of Basilisk
# Used to get the location of supporting data.
from Basilisk import __path__
from Basilisk.architecture import messaging
from Basilisk.fswAlgorithms import mrpFeedback, attTrackingError, velocityPoint, hillPoint, mrpRotation, rwMotorTorque
from Basilisk.simulation import reactionWheelStateEffector, simpleNav, spacecraft, ephemerisConverter
from Basilisk.utilities import (SimulationBaseClass, fswSetupRW, macros, orbitalMotion, simIncludeGravBody,
                                simIncludeRW, unitTestSupport, vizSupport)

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


def plotOrbit(rFirst, rSecond, posData):
    # plot the earth
    ax = plt.axes(projection='3d')
    planetColor = '#008800'
    planetRadius = 6378.1
    u, v = np.mgrid[0:2 * np.pi:40j, 0:np.pi:40j]
    x = planetRadius * np.cos(u) * np.sin(v)
    y = planetRadius * np.sin(u) * np.sin(v)
    z = planetRadius * np.cos(v)
    if rSecond > rFirst:
        ax.set_xlim3d(-1.1 * rSecond / 1000, 1.1 * rSecond / 1000)
        ax.set_ylim3d(-1.1 * rSecond / 1000, 1.1 * rSecond / 1000)
        ax.set_zlim3d(-1.1 * rSecond / 1000, 1.1 * rSecond / 1000)
    else:
        ax.set_xlim3d(-1.1 * rFirst / 1000, 1.1 * rFirst / 1000)
        ax.set_ylim3d(-1.1 * rFirst / 1000, 1.1 * rFirst / 1000)
        ax.set_zlim3d(-1.1 * rFirst / 1000, 1.1 * rFirst / 1000)

    ax.plot_surface(x, y, z, color=planetColor)
    # plot the orbit
    ax.plot3D(posData[:, 0] / 1000, posData[:, 1] / 1000, posData[:, 2] / 1000,
              color='orangered', label='Simulated Flight')
    ax.set_xlabel('x [km]')
    ax.set_ylabel('y [km]')
    ax.set_zlabel('z [km]')
    ax.set_aspect('equal')


def plotAttitudeError(timeAxis, attErrorData):
    plt.figure(2)
    for idx in range(3):
        plt.plot(timeAxis * macros.NANO2MIN, attErrorData[:, idx],
                 color=unitTestSupport.getLineColor(idx, 3),
                 label=r'$\sigma_' + str(idx) + '$')
    plt.legend(loc='best')
    plt.xlabel('Time [min]')
    plt.ylabel(r'Attitude Error $\sigma_{B/R}$')


def plotAttitude(timeAxis, attData):
    plt.figure(3)
    for idx in range(3):
        plt.plot(timeAxis * macros.NANO2MIN, attData[:, idx],
                 color=unitTestSupport.getLineColor(idx, 3),
                 label=r'$\sigma_' + str(idx) + '$')
    plt.legend(loc='best')
    plt.xlabel('Time [min]')
    plt.ylabel(r'Attitude $\sigma_{B/N}$')


def plotReferenceAttitude(timeAxis, attRefData):
    plt.figure(4)
    for idx in range(3):
        plt.plot(timeAxis * macros.NANO2MIN, attRefData[:, idx],
                 color=unitTestSupport.getLineColor(idx, 3),
                 label=r'$\sigma_' + str(idx) + '$')
    plt.legend(loc='best')
    plt.xlabel('Time [min]')
    plt.ylabel(r'Reference Attitude $\sigma_{R/N}$')


[docs] def run(show_plots, rFirst, rSecond): """ The scenarios can be run with the followings setups parameters: Args: show_plots (bool): Determines if the script should display plots rFirst (double): radius of the initial circular orbit about Earth rSecond (double): radius of the final circular orbit about Earth """ # Create simulation variable names simTaskName = "simTask" simProcessName = "dynProcess" fwsProcessName = "fswProcess" # Create a sim module as an empty container scSim = SimulationBaseClass.SimBaseClass() # Create the simulation process scSim.dynProcess = scSim.CreateNewProcess(simProcessName, 0) scSim.fswProcess = scSim.CreateNewProcess(fwsProcessName, 0) # Create the dynamics task and specify the integration update time simulationTimeStep = macros.sec2nano(1) scSim.dynProcess.addTask(scSim.CreateNewTask(simTaskName, simulationTimeStep), 10) # Initialize spacecraft object and set properties scObject = spacecraft.Spacecraft() scObject.ModelTag = "bsk-Sat" I = [900., 0., 0., 0., 800., 0., 0., 0., 600.] scObject.hub.mHub = 750.0 # kg - spacecraft mass scObject.hub.r_BcB_B = [[0.0], [0.0], [0.0]] # m - position vector of body-fixed point B relative to CM scObject.hub.IHubPntBc_B = unitTestSupport.np2EigenMatrix3d(I) # Add spacecraft object to the simulation process scSim.AddModelToTask(simTaskName, scObject, None, 1) # Set up Earth Gravity Body gravFactory = simIncludeGravBody.gravBodyFactory() earth = gravFactory.createEarth() earth.isCentralBody = True # ensure this is the central gravitational body mu = earth.mu # Override information with SPICE timeInitString = "2021 MAY 04 07:47:48.965 (UTC)" gravFactory.createSpiceInterface(bskPath + '/supportData/EphemerisData/', timeInitString, epochInMsg=True) gravFactory.spiceObject.zeroBase = 'Earth' gravFactory.addBodiesTo(scObject) # Add ephemeris for Hill frame ephemObject = ephemerisConverter.EphemerisConverter() ephemObject.ModelTag = "ephem data" ephemObject.addSpiceInputMsg(gravFactory.spiceObject.planetStateOutMsgs[0]) scSim.AddModelToTask(simTaskName, ephemObject, None, 1) # Add RW devices rwFactory = simIncludeRW.rwFactory() RW1 = rwFactory.create('Honeywell_HR16', [1, 0, 0], maxMomentum=50., Omega=100.) RW2 = rwFactory.create('Honeywell_HR16', [0, 1, 0], maxMomentum=50., Omega=200.) RW3 = rwFactory.create('Honeywell_HR16', [0, 0, 1], maxMomentum=50., Omega=300.) rwStateEffector = reactionWheelStateEffector.ReactionWheelStateEffector() rwStateEffector.ModelTag = "RW_cluster" rwFactory.addToSpacecraft(rwStateEffector.ModelTag, rwStateEffector, scObject) scSim.AddModelToTask(simTaskName, rwStateEffector, None, 2) # Add the navigation sensor module. This sets the SC attitude, rate, position and velocity navigation message sNavObject = simpleNav.SimpleNav() sNavObject.ModelTag = "SimpleNavigation" scSim.AddModelToTask(simTaskName, sNavObject) # Create guidance message to connect 3 flight modes to attitude error attRefMsg = messaging.AttRefMsg_C() attRefMsg.write(messaging.AttRefMsgPayload()) # Set up velocity-point guidance module for first burn firstBurn = velocityPoint.velocityPoint() firstBurn.ModelTag = "velocityPoint" firstBurn.mu = mu scSim.fswProcess.addTask(scSim.CreateNewTask("firstBurnTask", simulationTimeStep), 5) scSim.AddModelToTask("firstBurnTask", firstBurn) firstBurnMRPRotation = mrpRotation.mrpRotation() firstBurnMRPRotation.ModelTag = "mrpRotation" sigma_RR0 = np.array([np.tan(- np.pi / 8), 0, 0]) firstBurnMRPRotation.mrpSet = sigma_RR0 scSim.AddModelToTask("firstBurnTask", firstBurnMRPRotation) messaging.AttRefMsg_C_addAuthor(firstBurnMRPRotation.attRefOutMsg, attRefMsg) # setup velocity-point guidance module for second burn secondBurn = velocityPoint.velocityPoint() secondBurn.ModelTag = "velocityPoint" secondBurn.mu = mu scSim.fswProcess.addTask(scSim.CreateNewTask("secondBurnTask", simulationTimeStep), 5) scSim.AddModelToTask("secondBurnTask", secondBurn) # Need to get this reference attitude to rotate 180 secondBurnMRPRotation = mrpRotation.mrpRotation() secondBurnMRPRotation.ModelTag = "mrpRotation" sigma_RR0 = np.array([np.tan(np.pi / 8), 0, 0]) secondBurnMRPRotation.mrpSet = sigma_RR0 scSim.AddModelToTask("secondBurnTask", secondBurnMRPRotation) messaging.AttRefMsg_C_addAuthor(secondBurnMRPRotation.attRefOutMsg, attRefMsg) # Set up hill point guidance module attGuidanceHillPoint = hillPoint.hillPoint() attGuidanceHillPoint.ModelTag = "hillPoint" scSim.fswProcess.addTask(scSim.CreateNewTask("hillPointTask", simulationTimeStep), 5) scSim.AddModelToTask("hillPointTask", attGuidanceHillPoint) messaging.AttRefMsg_C_addAuthor(attGuidanceHillPoint.attRefOutMsg, attRefMsg) # Create flight software task to hold the remaining modules fswTaskName = "fswTask" scSim.fswProcess.addTask(scSim.CreateNewTask(fswTaskName, simulationTimeStep), 0) # Set up the attitude tracking error evaluation module attError = attTrackingError.attTrackingError() attError.ModelTag = "attError" scSim.AddModelToTask(fswTaskName, attError) # Set up the MRP Feedback control module mrpControl = mrpFeedback.mrpFeedback() mrpControl.ModelTag = "mrpFeedback" scSim.AddModelToTask(fswTaskName, mrpControl) mrpControl.K = 3.5 mrpControl.P = 30.0 mrpControl.Ki = -1 # make value negative to turn off integral feedback mrpControl.integralLimit = -1 # Add module that maps the Lr control torque into the RW motor torques rwMotorTorqueObj = rwMotorTorque.rwMotorTorque() rwMotorTorqueObj.ModelTag = "rwMotorTorque" controlAxes_B = [1, 0, 0, 0, 1, 0, 0, 0, 1] rwMotorTorqueObj.controlAxes_B = controlAxes_B scSim.AddModelToTask(fswTaskName, rwMotorTorqueObj) # Create the FSW vehicle configuration message vehicleConfigOut = messaging.VehicleConfigMsgPayload() vehicleConfigOut.ISCPntB_B = I # use the same inertia in the FSW algorithm as in the simulation vcMsg = messaging.VehicleConfigMsg().write(vehicleConfigOut) # Create the FSW reaction wheel configuration message fswSetupRW.clearSetup() fswRwParamMsg = rwFactory.getConfigMessage() # Set up the spacecraft's initial condition oe = orbitalMotion.ClassicElements() oe.a = rFirst oe.e = 0 oe.i = 30 * macros.D2R oe.Omega = 0 oe.omega = 0 oe.f = 0 rN, vN = orbitalMotion.elem2rv(mu, oe) scObject.hub.r_CN_NInit = rN # m - r_CN_N scObject.hub.v_CN_NInit = vN # m/s - v_CN_N scObject.hub.sigma_BNInit = [[0.1], [0.2], [-0.3]] # sigma_CN_B scObject.hub.omega_BN_BInit = [[0.001], [-0.01], [0.03]] # rad/s - omega_CN_B # Link and subscribe messages sNavObject.scStateInMsg.subscribeTo(scObject.scStateOutMsg) firstBurn.transNavInMsg.subscribeTo(sNavObject.transOutMsg) firstBurn.celBodyInMsg.subscribeTo(ephemObject.ephemOutMsgs[0]) firstBurnMRPRotation.attRefInMsg.subscribeTo(firstBurn.attRefOutMsg) secondBurn.transNavInMsg.subscribeTo(sNavObject.transOutMsg) secondBurn.celBodyInMsg.subscribeTo(ephemObject.ephemOutMsgs[0]) secondBurnMRPRotation.attRefInMsg.subscribeTo(secondBurn.attRefOutMsg) attGuidanceHillPoint.transNavInMsg.subscribeTo(sNavObject.transOutMsg) attGuidanceHillPoint.celBodyInMsg.subscribeTo(ephemObject.ephemOutMsgs[0]) attError.attNavInMsg.subscribeTo(sNavObject.attOutMsg) attError.attRefInMsg.subscribeTo(attRefMsg) mrpControl.guidInMsg.subscribeTo(attError.attGuidOutMsg) mrpControl.vehConfigInMsg.subscribeTo(vcMsg) mrpControl.rwParamsInMsg.subscribeTo(fswRwParamMsg) mrpControl.rwSpeedsInMsg.subscribeTo(rwStateEffector.rwSpeedOutMsg) rwMotorTorqueObj.rwParamsInMsg.subscribeTo(fswRwParamMsg) rwMotorTorqueObj.vehControlInMsg.subscribeTo(mrpControl.cmdTorqueOutMsg) rwStateEffector.rwMotorCmdInMsg.subscribeTo(rwMotorTorqueObj.rwMotorTorqueOutMsg) # Set up data logging before the simulation is initialized samplingTime = macros.sec2nano(0.5) scRec = scObject.scStateOutMsg.recorder(samplingTime) attLog = sNavObject.attOutMsg.recorder(samplingTime) attErrorLog = attError.attGuidOutMsg.recorder(samplingTime) attRefLog = attRefMsg.recorder(samplingTime) scSim.AddModelToTask(fswTaskName, scRec) scSim.AddModelToTask(fswTaskName, attLog) scSim.AddModelToTask(fswTaskName, attErrorLog) scSim.AddModelToTask(fswTaskName, attRefLog) # Create tje attitude events (three different reference attitudes are required for the sim) scSim.createNewEvent("firstBurnEvent", simulationTimeStep, True, ["self.modeRequest == 'firstBurn'"], ["self.fswProcess.disableAllTasks()", "self.enableTask('firstBurnTask')", "self.enableTask('fswTask')", "self.setAllButCurrentEventActivity('firstBurnEvent', True, useIndex=True)"]) scSim.createNewEvent("secondBurnEvent", simulationTimeStep, True, ["self.modeRequest == 'secondBurn'"], ["self.fswProcess.disableAllTasks()", "self.enableTask('secondBurnTask')", "self.enableTask('fswTask')", "self.setAllButCurrentEventActivity('secondBurnEvent', True, useIndex=True)"]) scSim.createNewEvent("hillPointEvent", simulationTimeStep, True, ["self.modeRequest == 'hillPoint'"], ["self.fswProcess.disableAllTasks()", "self.enableTask('hillPointTask')", "self.enableTask('fswTask')", "self.setAllButCurrentEventActivity('hillPointEvent', True, useIndex=True)"]) # Set the simulation time variable and the period of the first orbit simulationTime = 0 P1 = 2 * np.pi * np.sqrt(oe.a ** 3 / mu) # if this scenario is to interface with the BSK Viz, uncomment the following line vizSupport.enableUnityVisualization(scSim, simTaskName, scObject # , saveFile=fileName ) scSim.InitializeSimulation() scSim.ShowExecutionOrder() scSim.SetProgressBar(True) # Start in Hill Point and run 40% of a period on the initial circular orbit scSim.modeRequest = 'hillPoint' simulationTime += macros.sec2nano(0.4 * P1) scSim.ConfigureStopTime(simulationTime) scSim.ExecuteSimulation() # Change to first burn orientation in preparation for burn scSim.modeRequest = 'firstBurn' simulationTime += macros.sec2nano(0.1 * P1) scSim.ConfigureStopTime(simulationTime) scSim.ExecuteSimulation() # Get access to translational states velRef = scObject.dynManager.getStateObject(scObject.hub.nameOfHubVelocity) rN = scRec.r_BN_N[-1] vN = scRec.v_BN_N[-1] # Conduct the first burn of a Hohmann transfer from rFirst to rSecond rData = np.linalg.norm(rN) vData = np.linalg.norm(vN) at = (rData + rSecond) * .5 vt1 = np.sqrt((2 * mu / rData) - (mu / at)) Delta_V_1 = vt1 - vData vHat = vN / np.linalg.norm(vN) new_v = vN + Delta_V_1 * vHat velRef.setState(new_v) # Define the transfer time time_Transfer = np.pi * np.sqrt(at ** 3 / mu) # Continue the simulation with new delta v simulationTime += macros.sec2nano(0.2 * time_Transfer) scSim.ConfigureStopTime(simulationTime) scSim.ExecuteSimulation() # Change back to hill point for 60% of transfer orbit scSim.modeRequest = 'hillPoint' simulationTime += macros.sec2nano(0.6 * time_Transfer) scSim.ConfigureStopTime(simulationTime) scSim.ExecuteSimulation() # Change to second burn orientation in preparation for second burn scSim.modeRequest = 'secondBurn' simulationTime += macros.sec2nano(0.2 * time_Transfer) scSim.ConfigureStopTime(simulationTime) scSim.ExecuteSimulation() # Get the latest velocity and position vectors rN = scRec.r_BN_N[-1] vN = scRec.v_BN_N[-1] # Conduct the second burn of a Hohmann transfer from rFirst to rSecond rData = np.linalg.norm(rN) vData = np.linalg.norm(vN) at = (rData + rSecond) * .5 vt2 = np.sqrt((2 * mu / rData) - (mu / at)) Delta_V_2 = vt2 - vData vHat = vN / np.linalg.norm(vN) # unit vec? new_v = vN + Delta_V_2 * vHat velRef.setState(new_v) # Find the period for second orbit a2 = rSecond P2 = 2 * np.pi * np.sqrt(a2 ** 3 / mu) # Continue the simulation with new delta v simulationTime += macros.sec2nano(0.1 * P2) scSim.ConfigureStopTime(simulationTime) scSim.ExecuteSimulation() # Change back to Hill Point on second orbit scSim.modeRequest = 'hillPoint' simulationTime += macros.sec2nano(0.2 * P2) scSim.ConfigureStopTime(simulationTime) scSim.ExecuteSimulation() # Retrieve logged data timeAxis = attErrorLog.times() posData = scRec.r_BN_N # inertial pos. wrt. earth (central body) attData = attLog.sigma_BN attErrorData = attErrorLog.sigma_BR attRefData = attRefLog.sigma_RN # Plot the results plt.close("all") # clears out plots from earlier test runs figureList = {} plotOrbit(rFirst, rSecond, posData) pltName = fileName + "1" figureList[pltName] = plt.figure(1) plotAttitudeError(timeAxis, attErrorData) pltName = fileName + "2" figureList[pltName] = plt.figure(2) plotAttitude(timeAxis, attData) pltName = fileName + "3" figureList[pltName] = plt.figure(3) plotReferenceAttitude(timeAxis, attRefData) pltName = fileName + "4" figureList[pltName] = plt.figure(4) if show_plots: plt.show() # close the plots being saved off to avoid over-writing old and new figures plt.close("all") return figureList
# # This statement below ensures that the unit test scrip can be run as a # stand-along python script # if __name__ == "__main__": run( True, # show_plots 7000000, # major axis first orbit (m) 42164000 # major axis second orbit (m) )