#
# ISC License
#
# Copyright (c) 2021, 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
# copyright notice and this permission notice appear in all copies.
#
# THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
# WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
# MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
# ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
# WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
# ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
# OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
#
r"""
Overview
--------
Demonstrates how to use magnetic torque bars to drive the angular momentum of RWs to desired values.
The basic spacecraft setup with RWs is similar to that seen in :ref:`scenarioAttitudeFeedbackRW`.
A magnetic field is simulated, and a three-axis magnetometer (TAM) sensor device is added. Three orthogonally
aligned magnetic torque bars (MTBs) (see :ref:`MtbEffector`) are included to provide a magnetic torque. Finally,
the RW angular momentum management module using MTBs, called :ref:`mtbMomentumManagement`,
is used to drive the RW spin rates
to desired values. The spacecraft is setup to stabilize and point in a fixed inertial direction while
this RW momentum control is engaged.
The script is found in the folder ``basilisk/examples`` and executed by using::
python3 scenarioMtbMomentumManagement.py
The RW momentum dumping strategy is taking from the paper
entitled `Three-Axis Attitude Control Using Redundant Reaction Wheels with Continuous Momentum Dumping <http://dx.doi.org/10.2514/1.G000812>`__ and authored by Erik Hogan.
Illustration of Simulation Results
----------------------------------
::
show_plots = True
The first plot illustrates that the :ref:`Inertial3D` module is able to achieve a stable inertial pointing.
.. image:: /_images/Scenarios/scenarioMtbMomentumManagement1.svg
:align: center
The next plots illustrate the RW states. The motor torque are initially large to stabilize the
spacecraft orientation. After this they return to small values that are compensating for the
magnetic momentum dumping. The RW spin rates converge to the desired values over time.
.. image:: /_images/Scenarios/scenarioMtbMomentumManagement3.svg
:align: center
.. image:: /_images/Scenarios/scenarioMtbMomentumManagement4.svg
:align: center
The following plots illustrate the sensed magnetic field as well as the TAM commanded dipoles.
.. image:: /_images/Scenarios/scenarioMtbMomentumManagement6.svg
:align: center
.. image:: /_images/Scenarios/scenarioMtbMomentumManagement7.svg
:align: center
"""
#
# Basilisk Scenario Script and Integrated Test
#
# Purpose: Integrated test of the spacecraft with RWs, TAMs and MTBs to perform RW momentum dumping.
# Author: Henry Macanas and Hanspeter Schaub
# Creation Date: June 22, 2021
#
import os
import matplotlib.pyplot as plt
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,
inertial3D, rwMotorTorque,
tamComm, mtbMomentumManagement)
from Basilisk.simulation import (reactionWheelStateEffector,
simpleNav,
magneticFieldWMM, magnetometer, MtbEffector,
spacecraft)
from Basilisk.utilities import (SimulationBaseClass, macros,
orbitalMotion, simIncludeGravBody,
simIncludeRW, unitTestSupport, vizSupport)
bskPath = __path__[0]
fileName = os.path.basename(os.path.splitext(__file__)[0])
# Plotting functions
# Plotting functions
[docs]
def plot_attitude_error(timeData, dataSigmaBR):
"""Plot the attitude errors."""
plt.figure(1)
for idx in range(3):
plt.plot(timeData, dataSigmaBR[:, idx],
color=unitTestSupport.getLineColor(idx, 3),
label=r'$\sigma_' + str(idx) + '$')
plt.legend(loc='lower right')
plt.xlabel('Time [min]')
plt.ylabel(r'Attitude Error $\sigma_{B/R}$')
plt.grid(True)
[docs]
def plot_rw_cmd_torque(timeData, dataUsReq, numRW):
"""Plot the RW command torques."""
plt.figure(2)
for idx in range(3):
plt.plot(timeData, dataUsReq[:, idx],
'--',
color=unitTestSupport.getLineColor(idx, numRW),
label=r'$\hat u_{s,' + str(idx) + '}$')
plt.legend(loc='lower right')
plt.xlabel('Time [min]')
plt.ylabel('RW Motor Torque [Nm]')
plt.grid(True)
[docs]
def plot_rw_motor_torque(timeData, dataUsReq, dataRW, numRW):
"""Plot the RW actual motor torques."""
plt.figure(2)
for idx in range(numRW):
plt.plot(timeData, dataUsReq[:, idx],
'--',
color=unitTestSupport.getLineColor(idx, numRW),
label=r'$\hat u_{s,' + str(idx) + '}$')
plt.plot(timeData, dataRW[idx],
color=unitTestSupport.getLineColor(idx, numRW),
label='$u_{s,' + str(idx) + '}$')
plt.legend(loc='lower right')
plt.xlabel('Time [min]')
plt.ylabel('RW Motor Torque [Nm]')
plt.grid(True)
[docs]
def plot_rate_error(timeData, dataOmegaBR):
"""Plot the body angular velocity rate tracking errors."""
plt.figure(3)
for idx in range(3):
plt.plot(timeData, dataOmegaBR[:, idx],
color=unitTestSupport.getLineColor(idx, 3),
label=r'$\omega_{BR,' + str(idx) + '}$')
plt.legend(loc='lower right')
plt.xlabel('Time [min]')
plt.ylabel('Rate Tracking Error [rad/s] ')
plt.grid(True)
[docs]
def plot_rw_speeds(timeData, dataOmegaRW, numRW):
"""Plot the RW spin rates."""
plt.figure(4)
for idx in range(numRW):
plt.plot(timeData, dataOmegaRW[:, idx] / macros.RPM,
color=unitTestSupport.getLineColor(idx, numRW),
label=r'$\Omega_{' + str(idx) + '}$')
plt.legend(loc='lower right')
plt.xlabel('Time [min]')
plt.ylabel('RW Speed [RPM] ')
plt.grid(True)
[docs]
def plot_magnetic_field(timeData, dataMagField):
"""Plot the magnetic field."""
plt.figure(5)
for idx in range(3):
plt.plot(timeData, dataMagField[:, idx] * 1e9,
color=unitTestSupport.getLineColor(idx, 3),
label=r'$B\_N_{' + str(idx) + '}$')
plt.legend(loc='lower right')
plt.xlabel('Time [min]')
plt.ylabel('Magnetic Field [nT]')
plt.grid(True)
[docs]
def plot_data_tam(timeData, dataTam):
"""Plot the magnetic field."""
plt.figure(6)
for idx in range(3):
plt.plot(timeData, dataTam[:, idx] * 1e9,
color=unitTestSupport.getLineColor(idx, 3),
label=r'$TAM\_S_{' + str(idx) + '}$')
plt.legend(loc='lower right')
plt.xlabel('Time [min]')
plt.ylabel('Magnetic Field [nT]')
plt.grid(True)
[docs]
def plot_data_tam_comm(timeData, dataTamComm):
"""Plot the magnetic field."""
plt.figure(7)
for idx in range(3):
plt.plot(timeData, dataTamComm[:, idx] * 1e9,
color=unitTestSupport.getLineColor(idx, 3),
label=r'$TAM\_B_{' + str(idx) + '}$')
plt.legend(loc='lower right')
plt.xlabel('Time [min]')
plt.ylabel('Magnetic Field [nT]')
plt.grid(True)
[docs]
def plot_data_mtb_momentum_management(timeData, dataMtbMomentumManegement, numMTB):
"""Plot the magnetic field."""
plt.figure(8)
for idx in range(numMTB):
plt.plot(timeData, dataMtbMomentumManegement[:, idx],
color=unitTestSupport.getLineColor(idx, numMTB),
label=r'$MTB\_T_{' + str(idx) + '}$')
plt.legend(loc='lower right')
plt.xlabel('Time [min]')
plt.ylabel('Torque Rod Dipoles [A-m2]')
plt.grid(True)
[docs]
def plot_data_rw_motor_torque_desired(dataUsReq, tauRequested_W, numRW):
"""Plot the RW desired motor torques."""
plt.figure(9)
for idx in range(numRW):
plt.plot(tauRequested_W[idx],
color=unitTestSupport.getLineColor(idx, numRW),
label='$u_{s,' + str(idx) + '}$')
plt.legend(loc='lower right')
plt.xlabel('Time [min]')
plt.ylabel('RW Motor Torque (Nm)')
plt.grid(True)
[docs]
def run(show_plots):
"""
The scenarios can be run with the followings setups parameters:
Args:
show_plots (bool): Determines if the script should display plots
useJitterSimple (bool): Specify if the RW simple jitter model should be included
useRWVoltageIO (bool): Specify if the RW voltage interface should be simulated.
"""
# Create simulation variable names
simTaskName = "simTask"
simProcessName = "simProcess"
# Create a sim module as an empty container
scSim = SimulationBaseClass.SimBaseClass()
# set the simulation time variable used later on
simulationTime = macros.min2nano(120.)
#
# create the simulation process
#
dynProcess = scSim.CreateNewProcess(simProcessName)
# create the dynamics task and specify the integration update time
simulationTimeStep = macros.sec2nano(2.0)
dynProcess.addTask(scSim.CreateNewTask(simTaskName, simulationTimeStep))
#
# setup the simulation tasks/objects
#
# initialize spacecraft object and set properties
scObject = spacecraft.Spacecraft()
scObject.ModelTag = "bsk-Sat"
# define the simulation inertia
I = [0.02 / 3, 0., 0.,
0., 0.1256 / 3, 0.,
0., 0., 0.1256 / 3]
scObject.hub.mHub = 10.0 # 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, 1)
# clear prior gravitational body and SPICE setup definitions
gravFactory = simIncludeGravBody.gravBodyFactory()
# setup Earth Gravity Body
earth = gravFactory.createEarth()
earth.isCentralBody = True # ensure this is the central gravitational body
mu = earth.mu
# attach gravity model to spacecraft
gravFactory.addBodiesTo(scObject)
#
# add RW devices
#
# Make a fresh RW factory instance, this is critical to run multiple times
rwFactory = simIncludeRW.rwFactory()
# store the RW dynamical model type
varRWModel = messaging.BalancedWheels
beta = 52. * np.pi / 180.
Gs = np.array([
[0., 0., np.cos(beta), -np.cos(beta)],
[np.cos(beta), np.sin(beta), -np.sin(beta), -np.sin(beta)],
[np.sin(beta), -np.cos(beta), 0., 0.]])
# create each RW by specifying the RW type, the spin axis gsHat, plus optional arguments
RW1 = rwFactory.create('BCT_RWP015', Gs[:, 0], Omega_max=5000. # RPM
, RWModel=varRWModel, useRWfriction=False,
)
RW2 = rwFactory.create('BCT_RWP015', Gs[:, 1], Omega_max=5000. # RPM
, RWModel=varRWModel, useRWfriction=False,
)
RW3 = rwFactory.create('BCT_RWP015', Gs[:, 2], Omega_max=5000. # RPM
, RWModel=varRWModel, useRWfriction=False,
)
RW4 = rwFactory.create('BCT_RWP015', Gs[:, 3], Omega_max=5000. # RPM
, RWModel=varRWModel, useRWfriction=False,
)
# In this simulation the RW objects RW1, RW2 or RW3 are not modified further. However, you can over-ride
# any values generate in the `.create()` process using for example RW1.Omega_max = 100. to change the
# maximum wheel speed.
numRW = rwFactory.getNumOfDevices()
# create RW object container and tie to spacecraft object
rwStateEffector = reactionWheelStateEffector.ReactionWheelStateEffector()
rwStateEffector.ModelTag = "RW_cluster"
rwFactory.addToSpacecraft(scObject.ModelTag, rwStateEffector, scObject)
# add RW object array to the simulation process. This is required for the UpdateState() method
# to be called which logs the RW states
scSim.AddModelToTask(simTaskName, rwStateEffector, 2)
# add the simple Navigation sensor module. This sets the SC attitude, rate, position
# velocity navigation message
sNavObject = simpleNav.SimpleNav()
sNavObject.ModelTag = "SimpleNavigation"
scSim.AddModelToTask(simTaskName, sNavObject)
# create magnetic field module
magModule = magneticFieldWMM.MagneticFieldWMM()
magModule.ModelTag = "WMM"
magModule.dataPath = bskPath + '/supportData/MagneticField/'
epochMsg = unitTestSupport.timeStringToGregorianUTCMsg('2019 June 27, 10:23:0.0 (UTC)')
magModule.epochInMsg.subscribeTo(epochMsg)
magModule.addSpacecraftToModel(scObject.scStateOutMsg) # this command can be repeated if multiple
scSim.AddModelToTask(simTaskName, magModule)
# add magnetic torque bar effector
mtbEff = MtbEffector.MtbEffector()
mtbEff.ModelTag = "MtbEff"
scObject.addDynamicEffector(mtbEff)
scSim.AddModelToTask(simTaskName, mtbEff)
#
# setup the FSW algorithm tasks
#
# setup inertial3D guidance module
inertial3DObj = inertial3D.inertial3D()
inertial3DObj.ModelTag = "inertial3D"
scSim.AddModelToTask(simTaskName, inertial3DObj)
inertial3DObj.sigma_R0N = [0., 0., 0.] # set the desired inertial orientation
# setup the attitude tracking error evaluation module
attError = attTrackingError.attTrackingError()
attError.ModelTag = "attErrorInertial3D"
scSim.AddModelToTask(simTaskName, attError)
# setup the MRP Feedback control module
mrpControl = mrpFeedback.mrpFeedback()
mrpControl.ModelTag = "mrpFeedback"
scSim.AddModelToTask(simTaskName, mrpControl)
mrpControl.Ki = -1 # make value negative to turn off integral feedback
mrpControl.K = 0.0001
mrpControl.P = 0.002
mrpControl.integralLimit = 2. / mrpControl.Ki * 0.1
# add module that maps the Lr control torque into the RW motor torques
rwMotorTorqueObj = rwMotorTorque.rwMotorTorque()
rwMotorTorqueObj.ModelTag = "rwMotorTorque"
scSim.AddModelToTask(simTaskName, rwMotorTorqueObj)
# Make the RW control all three body axes
controlAxes_B = [
1, 0, 0, 0, 1, 0, 0, 0, 1
]
rwMotorTorqueObj.controlAxes_B = controlAxes_B
# create the minimal TAM module
TAM = magnetometer.Magnetometer()
TAM.ModelTag = "TAM_sensor"
# specify the optional TAM variables
TAM.scaleFactor = 1.0
TAM.senNoiseStd = [0.0, 0.0, 0.0]
scSim.AddModelToTask(simTaskName, TAM)
# setup tamComm module
tamCommObj = tamComm.tamComm()
tamCommObj.dcm_BS = [1., 0., 0., 0., 1., 0., 0., 0., 1.]
tamCommObj.ModelTag = "tamComm"
scSim.AddModelToTask(simTaskName, tamCommObj)
# setup mtbMomentumManagement module
mtbMomentumManagementObj = mtbMomentumManagement.mtbMomentumManagement()
# setting the optional RW biases
mtbMomentumManagementObj.wheelSpeedBiases = [800. * macros.rpm2radsec, 600. * macros.rpm2radsec,
400. * macros.rpm2radsec, 200. * macros.rpm2radsec]
mtbMomentumManagementObj.cGain = 0.003
mtbMomentumManagementObj.ModelTag = "mtbMomentumManagement"
scSim.AddModelToTask(simTaskName, mtbMomentumManagementObj)
# mtbConfigData message
mtbConfigParams = messaging.MTBArrayConfigMsgPayload()
mtbConfigParams.numMTB = 4
# row major toque bar alignments
mtbConfigParams.GtMatrix_B =[
1., 0., 0., 0.70710678,
0., 1., 0., 0.70710678,
0., 0., 1., 0.]
maxDipole = 0.1
mtbConfigParams.maxMtbDipoles = [maxDipole]*mtbConfigParams.numMTB
mtbParamsInMsg = messaging.MTBArrayConfigMsg().write(mtbConfigParams)
#
# Setup data logging before the simulation is initialized
#
numDataPoints = 200
samplingTime = unitTestSupport.samplingTime(simulationTime, simulationTimeStep, numDataPoints)
rwMotorLog = rwMotorTorqueObj.rwMotorTorqueOutMsg.recorder(samplingTime)
attErrorLog = attError.attGuidOutMsg.recorder(samplingTime)
magLog = magModule.envOutMsgs[0].recorder(samplingTime)
tamLog = TAM.tamDataOutMsg.recorder(samplingTime)
tamCommLog = tamCommObj.tamOutMsg.recorder(samplingTime)
mtbDipoleCmdsLog = mtbMomentumManagementObj.mtbCmdOutMsg.recorder(samplingTime)
scSim.AddModelToTask(simTaskName, rwMotorLog)
scSim.AddModelToTask(simTaskName, attErrorLog)
scSim.AddModelToTask(simTaskName, magLog)
scSim.AddModelToTask(simTaskName, tamLog)
scSim.AddModelToTask(simTaskName, tamCommLog)
scSim.AddModelToTask(simTaskName, mtbDipoleCmdsLog)
# To log the RW information, the following code is used:
mrpLog = rwStateEffector.rwSpeedOutMsg.recorder(samplingTime)
scSim.AddModelToTask(simTaskName, mrpLog)
# A message is created that stores an array of the \f$\Omega\f$ wheel speeds. This is logged
# here to be plotted later on. However, RW specific messages are also being created which
# contain a wealth of information. The vector of messages is ordered as they were added. This
# allows us to log RW specific information such as the actual RW motor torque being applied.
rwLogs = []
for item in range(numRW):
rwLogs.append(rwStateEffector.rwOutMsgs[item].recorder(samplingTime))
scSim.AddModelToTask(simTaskName, rwLogs[item])
#
# create simulation messages
#
# 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)
# Setup the FSW RW configuration to be the same as the simulated RW configuration
fswRwParamMsg = rwFactory.getConfigMessage()
#
# set initial Spacecraft States
#
# setup the orbit using classical orbit elements
oe = orbitalMotion.ClassicElements()
oe.a = 6778.14 * 1000. # meters
oe.e = 0.00
oe.i = 45. * macros.D2R
oe.Omega = 60. * macros.D2R
oe.omega = 0. * macros.D2R
oe.f = 0. * macros.D2R
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
# if this scenario is to interface with the BSK Viz, uncomment the following lines
viz = vizSupport.enableUnityVisualization(scSim, simTaskName, scObject
# , saveFile=fileName
, rwEffectorList=rwStateEffector
)
# link messages
sNavObject.scStateInMsg.subscribeTo(scObject.scStateOutMsg)
attError.attNavInMsg.subscribeTo(sNavObject.attOutMsg)
attError.attRefInMsg.subscribeTo(inertial3DObj.attRefOutMsg)
mrpControl.guidInMsg.subscribeTo(attError.attGuidOutMsg)
mrpControl.vehConfigInMsg.subscribeTo(vcMsg)
mrpControl.rwParamsInMsg.subscribeTo(fswRwParamMsg)
mrpControl.rwSpeedsInMsg.subscribeTo(rwStateEffector.rwSpeedOutMsg)
TAM.stateInMsg.subscribeTo(scObject.scStateOutMsg)
TAM.magInMsg.subscribeTo(magModule.envOutMsgs[0])
tamCommObj.tamInMsg.subscribeTo(TAM.tamDataOutMsg)
rwMotorTorqueObj.rwParamsInMsg.subscribeTo(fswRwParamMsg)
rwMotorTorqueObj.vehControlInMsg.subscribeTo(mrpControl.cmdTorqueOutMsg)
mtbMomentumManagementObj.rwParamsInMsg.subscribeTo(fswRwParamMsg)
mtbMomentumManagementObj.mtbParamsInMsg.subscribeTo(mtbParamsInMsg)
mtbMomentumManagementObj.tamSensorBodyInMsg.subscribeTo(tamCommObj.tamOutMsg)
mtbMomentumManagementObj.rwSpeedsInMsg.subscribeTo(rwStateEffector.rwSpeedOutMsg)
mtbMomentumManagementObj.rwMotorTorqueInMsg.subscribeTo(rwMotorTorqueObj.rwMotorTorqueOutMsg)
rwStateEffector.rwMotorCmdInMsg.subscribeTo(mtbMomentumManagementObj.rwMotorTorqueOutMsg)
mtbEff.mtbCmdInMsg.subscribeTo(mtbMomentumManagementObj.mtbCmdOutMsg)
mtbEff.mtbParamsInMsg.subscribeTo(mtbParamsInMsg)
mtbEff.magInMsg.subscribeTo(magModule.envOutMsgs[0])
# initialize configure and execute sim
scSim.InitializeSimulation()
scSim.ConfigureStopTime(simulationTime)
scSim.ExecuteSimulation()
# retrieve the logged data
dataUsReq = rwMotorLog.motorTorque
dataSigmaBR = attErrorLog.sigma_BR
dataOmegaBR = attErrorLog.omega_BR_B
dataOmegaRW = mrpLog.wheelSpeeds
dataRW = []
for i in range(numRW):
dataRW.append(rwLogs[i].u_current)
dataMagField = magLog.magField_N
dataTam = tamLog.tam_S
dataTamComm = tamCommLog.tam_B
dataMtbDipoleCmds = mtbDipoleCmdsLog.mtbDipoleCmds
np.set_printoptions(precision=16)
# plot the results
timeData = rwMotorLog.times() * macros.NANO2MIN
plt.close("all") # clears out plots from earlier test runs
plot_attitude_error(timeData, dataSigmaBR)
figureList = {}
pltName = fileName + "1"
figureList[pltName] = plt.figure(1)
plot_rw_motor_torque(timeData, dataUsReq, dataRW, numRW)
pltName = fileName + "2"
figureList[pltName] = plt.figure(2)
plot_rate_error(timeData, dataOmegaBR)
plot_rw_speeds(timeData, dataOmegaRW, numRW)
pltName = fileName + "3"
figureList[pltName] = plt.figure(4)
plot_magnetic_field(timeData, dataMagField)
pltName = fileName + "4"
figureList[pltName] = plt.figure(5)
plot_data_tam(timeData, dataTam)
pltName = fileName + "5"
figureList[pltName] = plt.figure(6)
plot_data_tam_comm(timeData, dataTamComm)
pltName = fileName + "6"
figureList[pltName] = plt.figure(7)
plot_data_mtb_momentum_management(timeData, dataMtbDipoleCmds, mtbConfigParams.numMTB)
pltName = fileName + "7"
figureList[pltName] = plt.figure(8)
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
)