NASA Technical Reports Server (NTRS) 20110020554: Mars Science Laboratory Entry Guidance Improvements for Mars 2018 (DRAFT)

2.9 MB·English

by  NASA Technical Reports Server (NTRS)

(DRAFT) Mars Science Laboratory Entry Guidance
Improvements for Mars 2018 (DRAFT)
EduardoGarc´ıa-Llama RichardG.Winski JeremyD.Shidner
GBTech,Inc. AnalyticalMechanicsAssociates AnalyticalMechanicsAssociates
NASA/JSC/EG5 NASA/LaRC/D205 NASA/LaRC/D205
Houston,TX77058 Hampton,VA,23681 Hampton,VA,23681
281-483-8223 757-864-4116 757-864-4516
[email protected] [email protected] [email protected]
MarkC.Ivanov MyronR.Grover RaviPrakash
JPL JPL JPL
Pasadena,CA91109 Pasadena,CA91109 Pasadena,CA91109
888-888-8888 818-393-2478 888-888-8888
[email protected] [email protected] [email protected]
Abstract—(DRAFT) In 2011, the Mars Science Laboratory MSL mission of 2011. This paper will discuss the main
(MSL) will be launched in a mission to deliver the largest and elements of the modified 2018 EDL preliminary design that
most capable rover to date to the surface of Mars. A follow willincreaseperformanceontheentryphaseofthemission.
onMSL-derivedmission, referredtoasMars2018, isplanned In particular, these elements will reduce the delivery ellipse
for2018. Mars2018goalsincludeperformanceenhancements
size at parachute deploy and increase the parachute deploy
oftheEntry, DescentandLandingoverthatofitspredecessor
altitudetoallowformoretimemarginduringthesubsequent
MSLmissionof2011.Thispaperwilldiscussthemainelements
descentandlandingphases.
ofthemodified2018EDLpreliminarydesignthatwillincrease
performance on the entry phase of the mission. In particular,
these elements will increase the parachute deploy altitude to To accomplish the goal of improved performance on entry,
allowformoretimemarginduringthesubsequentdescentand Mars 2018 will extend the limits of the entry technologies
landingphasesandreducethedeliveryellipsesizeatparachute andentryguidancedesignqualifiedbyMSL.Thispaperwill
deploy through modifications in the entry reference trajectory showthemaineffectsofspecificnewfeaturesoftheentryde-
design,guidancetriggerlogicdesign,andtheeffectofadditional signontheimprovedEDLperformancesuchastheselection
navigationhardware.
ofanewentryvehicle’slifttodragratio(L/D),modifications
intheentryreferencetrajectorydesign,guidancetriggerlogic
design,andtheeffectofadditionalnavigationhardware.
TABLE OF CONTENTS
Intermsofthedeliveredaltitudeatparachutedeploy,atrade
1 INTRODUCTION(DRAFT) ...................... 1 with selected L/D and entry mass as inputs will show the
potentialbenefitinaltitudethatcouldbereachedatparachute
2 ENTRYGUIDANCE(DRAFT) ................... 1
deploytakingintoaccountdipaltitudeanddynamicpressure
3 CONCEPTS(DRAFT) ........................... 2 considerations as well as constraints on guidance saturation
4 INCREASEDDELIVERYALTITUDEATPARACHUTE andpeakloads.
DEPLOY(DRAFT) .............................. 2
5 ELLIPSE SIZE REDUCTION AT PARACHUTE In terms of the ellipse size at parachute deploy, this paper
DEPLOY(DRAFT) .............................. 5 willshowimprovementinreducingtheellipsesizewhenthe
6 SUMMARY(DRAFT)............................ 7 parachutedeploytriggerisrange-basedratherthanvelocity-
based as is the case in MSL. Besides the obvious gain in
APPENDICES..................................... 7
range accuracy, it will be shown how the dispersed Mach
A PARTIALDERIVATIVESWITHGUIDANCESAT- andaltitudesatparachutedeploycomparedtothoseresulting
URATIONCONSTRAINT.......................... 7 from a velocity-based parachute deploy trigger. Also, the
B PARTIAL DERIVATIVES WITH ADDITIONAL paper will show the improvement in ellipse size reduction
PEAKLOADCONSTRAINT....................... 7 when the range-based trigger is combined with a smaller
ACKNOWLEDGMENTS ........................... 9 attitudeinitializationerrorwhichcanbeobtainedviaadding
REFERENCES .................................... 9 astartrackerdevicethatwilldeterminetheinitialattitudeof
thevehiclepriortoentryinterface.
1. INTRODUCTION (DRAFT)
2. ENTRY GUIDANCE (DRAFT)
In 2011, the Mars Science Laboratory (MSL) will be
Mars 2018 will utilize, as in MSL, an offset center of
launchedinamissiontodeliverthelargestandmostcapable
mass to create a nominal angle of attack. This angle of
rovertodatetothesurfaceofMars.AfollowonMSL-derived
attack generates lift which is used to reduce the landing
mission,referredtoasMars2018,isplannedfor2018. Mars
error ellipse size and increase the parachute deploy altitude.
2018 goals include performance enhancements of the Entry,
Entry guidance provides bank angle commands throughout
Descent and Landing (EDL) over that of its predecessor
entry that orient the vehicle lift vector to compensate for
dispersions in initial delivery state, atmospheric conditions,
978-1-4577-0557-1/12/$26.00(cid:13)c2012IEEE. and aerodynamic performance. This enables the vehicle to
1IEEEACPaper#xxxx,Versionx,Updateddd/mm/yyyy.
1
Theearlyandlatebankangles,thetransitionvelocitytolate
bank, the entry mass, the total L/D and the entry flight path
angleofthevehicleareparametersofthereferencetrajectory
designmap. Oncerunundernominalconditions, thedesign
mapcanbefilteredtoobtainthereferenceprofilethatresults
in the highest parachute deploy altitude under some specific
conditionsforeachentrymassandtotalL/Dcombination.
GuidanceSaturation
In a vehicle that modulates its vertical L/D using the bank
angle only, the control response is said to saturate when the
bank angle command results in the maximum or minimum
verticalL/D.MaximumandminimumverticalL/D’shappen
whenthebankangleis0◦and180◦,respectively.
Figure1. Referenceprofiledefinition.
Following the guideline that was set for MSL, guidance
saturation is defined in this paper as the percentage of time
during the entry phase that guidance is commanding a bank
arriveclosetothedesiredstateatparachutedeployment. whoseabsolutevalueiswithin15◦awayfromsaturation.
The Mars 2018 will use an Apollo-derived entry guidance Theguidanceisnotsaturatedwhenflyingatrajectoryunder
algorithm[1],[2]. Thealgorithmisdividedintothreephases. nominal conditions; it can be saturated when flying under
Entry interface marks the start of guided entry: guidance is dispersed conditions. Guidance saturation for a particular
initializedinthepre-bankphaseandthecontrollercommands trajectoryprofileisassessedinworstcaseconditionsinorder
bank attitude hold until the sensed acceleration exceeds 0.1 toinformhowthereferencetrajectoryisexpectedtoperform
Earthg’s. Oncethesensedaccelerationexceedsthespecified prior to its evaluation in a Monte Carlo simulation. Worst
triggerlimit,therangecontrolphasebegins. caseconditionstoassessguidancesaturationdefinedforMSL
account for a L/D that is 20% smaller than the nominal, an
Duringtherangecontrolphase,thebankangleiscommanded atmosphericdensity15%largerthanthenominal, aballistic
tominimizepredicteddownrangeerroratparachutedeploy- number 15% smaller than the nominal and an entry flight
ment. Throughoutthisphase,crossrangeerrorismaintained path angle 0.2◦ steeper than the nominal [7]. Under these
with a manageable deadband limit by executing bank rever- stress conditions, the guidance will try to fly more lift-up in
sals as necessary. Peak heating and peak deceleration occur ordertoreachitstargetand,therefore,itwillbemoreprone
duringthisguidancephase. tosaturate.
Once the navigated relative velocity drops below a certain AltitudeDipConstraint
value, guidance transitions to a heading alignment phase.
Duringthisphase,theguidancenolongercontrolsdownrange Toachievemaximumaltitudeatparachutedeploy,thetrajec-
error. Instead, the guidance commands a bank angle to toriestendtodivesteeplyintheatmospheretoriseup,orloft,
minimizeresidualcrossrangeerrorandazimutherrorbefore attheendofthetrajectory[3],[4]. Insomecases,especially
parachutedeployment.However,thebankangleduringhead- whentheL/D’sandballisticnumbersarehigh,thetrajectories
ing alignment is limited to ensure that a sufficient amount maytendtodiveintoosteeply,potentiallyreachingverylow
of lift is commanded to achieve the desired altitude perfor- altitudesinthemiddleofthetrajectorybeforegainingaltitude
mance. again at the end. Those low altitudes are called herein dip
altitudesandmaybetoolowinsomecases.
Justpriortoparachutedeployment,thevehicleangleofattack
isadjustedto0◦byejectingbalancemasseswhiletheazimuth Thedipaltitudeconstraintistheminimumacceptablealtitude
isalignedforbetterradarperformancelaterduringparachute in the middle of a trajectory in a nominal case. In selecting
descent. Parachute deployment is triggered at a navigated thedipaltitudeconstraint,itisimportanttokeepinmindwhat
velocityofover450m/swhenavelocitytriggerisused. happensunderdispersedconditions. Underdispersedcondi-
tions, the worst case dip altitude may be a few kilometers
belowthenominaldipaltitude.
3. CONCEPTS (DRAFT)
A 10 km dip constraint is selected in this study. This is
Someconceptsthatwillbeusedindifferentpartsofthepaper the value that has traditionally been used for different final
willbedefinedinthissection. altitude maximization studies that have been carried out to
date [3],[4]. In any case, the dip constraint of 10 km is an
ReferenceTrajectoryDesignMap arbitrary value and therefore can be changed. The selected
value depends on the acceptable minimum altitude for dis-
Thereferencetrajectorydesignmapconsistsofaparametric
persedtrajectories.
study used to determine the entry flight path angle and the
shape of the reference profile that maximizes the parachute
deploy altitude under certain conditions for each L/D and
entrymasscombination.Theshapedefinitionofthereference 4. INCREASED DELIVERY ALTITUDE AT
profile in terms of bank angle vs. relative velocity employs PARACHUTE DEPLOY (DRAFT)
the same parameters that define the MSL reference profile
In order to find the maximum altitude at parachute deploy
(see Figure 1): an early bank angle at entry interface that
thatcouldbeachievedforeachpossibleL/Dandentrymass
linearlyrampsdowntoalatebankanglethatremainsconstant
combination, the reference trajectory design map was run.
untiltheheadingalignmentvelocityisreached.
2
Table1. ReferenceTrajectoryDesignMap
Parameter Rangeofvalues Increment
L/D 0.24-0.36 0.01
EntryMass(mt) 3-4.2 0.3
EntryFlight
PathAngle(deg) -13to-19 0.5
EarlyBank(deg) 55-135 10
TransitionVelocity
toLateBank(km/s) 2-3 0.25
The ranges of values used in the design map in this paper
foreachoftheparametersareshowninTable1.
Figure2. Parachutedeployaltitude(km).
DuringtheMSL’sreferencetrajectorydesignprocess,itwas
learned that, for a given L/D and entry mass, the entry
flight path angle and the early bank are the parameters that
influencethemostintheparachutedeployaltitude. Thelate
bank affects the parachute deploy altitude as well but it has
a more significant influence in the ability of the guidance to
accommodatedispersionsattheendofthetrajectoryandthus
toreducetheellipsefootprintatparachutedeploy.
Since the conceptual design phase of MSL starting in 2000,
reference trajectories usually had a 45◦ late bank. Lower
late bank angles would result in higher parachute deploy
altitudes as well as in larger ellipse footprints. Higher late
banks would have the opposite effect. At this early stage in
thedesignofthereferencetrajectory, alatebankof45◦ has
been selected because it offers a good compromise between
parachutedeployaltitudeandellipsesizefootprint.
The transition velocity to late bank has a small influence in
thealtitudeatparachutedeploy. MSL’stransitionvelocityis
often2.0km/s. Inthispaper,thepossiblerangeofvaluesfor
this parameter was extended to 3 km/s. The entry velocity Figure3. Entryflightpathangle(deg).
was selected to be 6 km/s. In all the cases, the heading
alignmentstartsat1km/s,0.1km/slowerthaninMSL.This
difference has practically no effect in the parachute deploy
conditions. Giventhefactthattheworstcasedipaltitudesin
altitude. Future refinements in the selection of these values
thedesignmapwerestillhigh,thealtitudedipconstraintwas
shouldbeexpected.
disregarded at this stage of the design. Therefore Figure 2
showstheparachutedeployaltitudecontourlinesforthecase
WithGuidanceSaturationConstraint
inwhichthe10kmdipconstraintwasnotused.
Figure2showstheparachutedeployaltitudecontourlinesas
a function of L/D and entry mass resulting from the design Each point in figure 2 is associated to a particular reference
map with the altitude being referenced to the Mars MOLA trajectory and entry flight path angle. Figures 3, 4 and 5
(Mars Orbiting Laser Altimeter) areoid surface definition show the entry flight path angles, early banks and transition
[8]. The results from the design map have been filtered to velocitiesofthereferencetrajectoriesassociatedtotheresults
find those that provide the highest parachute deploy altitude shown in Figure 2. Figures 3, 4 and 5 show that the
under the condition that the worst case guidance saturation parameterstheypresentare,forthemostpart,independentof
is smaller than 20% (this is the design value used in MSL). theentrymass. Inaddition, Figure5showslargeareaswith
Thisconstraintimprovestherobustnessoftheentryguidance transition velocities equal to 3 km/s. Because 3 km/s is the
by ensuring sufficient vertical L/D is held in reserve to upperlimitvalueusedinthedesignmap,thistrendindicates
accommodatedispersions. that higher parachute deploy altitudes could be expected
shouldthetransitionvelocitytolatebankbeenlargedinthe
A10kmdipconstraintwasoriginallyaddedasaconditionin design map. In any case, this possibility was not explored
theselectionofthereferenceprofileandentryflightpathan- furtherinthispaper.
gle. Whenthisconstraintwasused,onlythecaseswithhigh
entry mass and high L/D were affected. Later Monte Carlo Figure 2 constitutes a useful tool in the design process be-
simulationsshowedthatthelowestdipaltitudeswerehigher cause it shows how much L/D is required in order to obtain
than7kminallthecaseswiththeexceptionofthecasewith a desired parachute deploy altitude for a given entry mass.
highest L/D (0.36) and highest entry mass (4.2 mt) which Appendix A shows the partial derivatives for all L/D and
hadaminimumdipaltitudeofabout6.5kmunderdispersed entrymasscombinations.
3
Figure4. Earlybank(deg).
Figure6. DynamicPressure(Pa).
Figure5. Transitionvelocitytolatebank(km/s).
Figure7. Maximumload(g’s).
Figure6showsthedynamicpressureatparachutedeploy. It
can be observed that the dynamic pressures are well within
theMSL’sparachutedeployqualificationlimitof850Pa[9].
WiththeAdditionofPeakLoadConstraint
MSL entry vehicle structure is designed for 15g peak loads
during entry. During the design of MSL’s entry guidance it
was observed that if the nominal trajectory had a peak load
smallerthan13gthenthedispersedpeakloadswouldremain
below15g. Whenthedesignmapisnotfilteredwiththe13g
peak constraint, the cases with L/D higher than 0.3 surpass
that value with a maximum at about 15g as it is shown in
Figure7.
Assuming that Mars 2018 will have the same entry vehicle
structural limit, and because the range control logic in the
entryguidanceisnotexplicitlycommandingtolimitacceler-
ationloads,thedesignmapwasadditionallyfilteredtoresult
onlyincaseswithapeakloadof13g.
Figure 8 shows how the parachute deploy altitude contour
lines get modified when the 13g peak load constraint is
Figure8. Parachutedeployaltitude(km).
applied to the design map. Appendix B shows the partial
derivativesforallL/Dandentrymasscombinationswhenthe
4
Figure9. Entryflightpathangle(deg). Figure11. Transitionvelocitytolatebank(km/s).
purposes (the entry mass will be the one used in the design
mapthathastheclosestvaluetotheMSL’sentrymass). The
reference trajectory that will be used in this section is that
whichcorrespondstoaL/D=0.24andanentrymass=3.3mt
inFigure2:-14.5◦entryflightpathangle,85◦earlybank,45◦
late bank, 2.75 km/s transition velocity to late bank and 1.0
km/stransitionvelocitytoheadingalignment(forreference,
since the conceptual design phase of MSL starting in 2000,
referencetrajectoriesusuallyhadnear-15.5◦entryflightpath
angle,65◦earlybank,and45◦latebankangle.Thevelocities
oftherampbetweenearlyandlatebankhavevariedbutthe
referencelatebankangleisoftenachievedat2km/s).
MonteCarloProducts(Thissectionisnotcompleteyet)
The following subsections will show Monte Carlo results.
The characteristics of the Monte Carlo simulations, the dis-
Figure10. Earlybank(deg). persionsused,andthestatisticsusedfortheevaluationofthe
datawillbediscussedinthissubsection.
Monte Carlo runs are conducted with 8,000 randomly per-
peakloadconstraintiscombinedwiththeguidancesaturation
turbed cases in addition to the nominal. Experience has
constraint.
shown this number to be a reasonable balance between sta-
tisticalaccuracyandcomputerruntime. Traditionally,inthe
Figures 9, 10 and 11 showing the entry flight path angles,
MSL project, performance metrics have been tracked by a
earlybanksandtransitionvelocitiesassociatedtothealtitude
0.13percentileor99.87percentilestatistics. Thisconvention
contourswith13gconstraintareincludedforreference.
is used to provide requirements with a high probability (3-
sigma percentile under the assumption of a Gaussian dis-
tribution) of success that is insensitive to the underlying
5. ELLIPSE SIZE REDUCTION AT PARACHUTE distributionorthenumberofcasesrun[5]. Continuingwith
DEPLOY (DRAFT) thispractice,performancemetricswillbetrackedbythesame
conventioninthispaper.
The dispersed ellipse size at parachute deploy is driven by
threefactors. Oneisthenavigatedpositionknowledgeerror
RangeTriggerVersusVelocityTriggerforParachuteDeploy
as the guidance cannot reduce the ellipse size any smaller.
Another factor is the residual downrange error that results In Reference [6], a side-by-side comparison of parachute
from a velocity-based parachute deploy trigger, although in deployment triggers was conducted for MSL. Two triggers,
MSLthiscontributionwassecondarytotheknowledgeerror the baseline velocity trigger and an alternate range trigger,
magnitude. Third, the guidance accuracy is sensitive to the were tuned to produce the same nominal parachute deploy
attitude initialization error prior to cruise stage separation Machnumber.Foreachtriggera6-DoF(DegreeofFreedom)
[5]. Thissectionwillshowtheimprovementinreducingthe MonteCarloanalysisof8,000runswasperformedusingthe
ellipse size at parachute deploy when the deploy trigger is MSL POST2 (Program to Optimize Simulated Trajectories
range-based rather than velocity-based and when a smaller II) end-to-end EDL performance simulation. The results
attitudeinitializationerrorisused.Inthissection,sinceaL/D of this study showed that a range trigger has the potential
andentrymasshasnotyetbeenselectedforMars2018, the to significantly reduce footprint size with negligible Mach
MSL’s L/D and entry mass will be selected for comparison increaseandnoaltitudeloss.
5
Figure12. 99.87%-tileEllipsefootprintatparachutedeploy Figure13. 99.87%-tileAltitudeovertheMarsMOLAareoid
(VT=VelocityTrigger,RT=RangeTrigger,AIE=Attitude vs.Machnumberatparachutedeploy(VT=VelocityTrigger,
InitializationError). RT=RangeTrigger,AIE=AttitudeInitializationError).
The same type of Monte Carlo comparison was performed
using the proposed new reference profile. The results show
the same trend as that presented in Reference [6] in terms
ofthesignificantreductionintheellipsesizefootprintwhen
the range trigger is used. Figure 12 shows thecomparison
of the ellipse footprint for the velocity trigger and the range
trigger when the attitude initialization error of 0.25◦ is used
(Figure12alsoshowstheellipsefootprintforthecasewhen
therangetriggerwithanattitudeinitializationerrorof0.025◦
isused.Thiscasewillbediscussedinthenextsection.Figure
12 also includes the velocity trigger case with an attitude
initializationerrorof0.025◦forreference).
Figure13showstheresultsforthealtitudevs. Machnumber
at parachute deploy where the altitude is referenced to the
MarsMOLAareoidsurfacedefinition. Figure13showsthat
there is not a significant difference in performance between
the velocity trigger case and the range trigger case when an Figure14. 99.87%-tileDynamicpressurevs. Machnumber
attitude initialization error of 0.25◦ is used (Figure 13 also at parachute deploy (VT = Velocity Trigger, RT = Range
shows the ellipse for the case when the range trigger with Trigger,AIE=AttitudeInitializationError).
an attitude initialization error of 0.025◦ is used. This case
willbediscussedinthenextsection. Figure13alsoincludes
thevelocitytriggercasewithanattitudeinitializationerrorof
of 0.25◦. The goal for Mars 2018 is to have this error
0.025◦forreference).
reduced as much as possible through the addition of a star
tracker in the entry vehicle that will determine the vehicle’s
Figure 14 showing the dynamic pressure vs. Mach at
attitudepriortoentry. Aspecificstartrackermodeltocarry
parachutedeployisincludedforreference.
out this operation has not been selected yet, however, low
cost and all purpose star trackers for space applications can
AttitudeInitializationErrorPriortoEntry
typically provide accuracies of about 20 arc-seconds (high
The attitude initialization error (IMU misalignment at the precision star trackers can be found capable of determining
last navigation upload prior to entry) results in velocity and theattitudebetterthan1arc-second)[10][11]. Inthispaper,
position knowledge errors perpendicular to the direction of a conservative attitude knowledge error of 90 arc-seconds,
deceleration during entry. This results in crossrange and whichisatenthofMSL’sattitudeinitializationerror(0.025◦),
altitude position knowledge errors. More importantly, it isconsidered.
also results in altitude rate estimation errors which directly
impacts the entry guidance predicted range errors because Figure 12 shows the improvement in ellipse size reduction
thealtituderateisaquantityusedbytheguidancetopredict when a range trigger with an attitude initialization error of
the range flown. Greater attitude initialization errors result 0.025◦ isused: thesizeoftheellipsefootprintinthiscaseis
in greater range deploy errors. Sufficiently large attitude 4.7 km by 2.6 km in size; that is almost 13.4 times smaller
initialization errors will dominate over other factors in the than that corresponding to the current baseline (velocity
ellipsesize[7]. trigger with attitude initialization error of 0.25◦). In terms
ofaltitudevs. Machperformanceatparachutedeploy,Figure
MSL has a maximum attitude knowledge initialization error 13showsamoreconfineddistributionofpointsintherange
6
trigger case with attitude initialization error of 0.025◦: the
99.87%-tile ellipse size in this case is almost 20% smaller
than that corresponding to the velocity trigger case with an
attitude initialization error of 0.25◦. The results also show
thattheminimumdeployaltitudeisraisedaboutonekilome-
terandthatthemaximumMachisreducedbyabout0.1when
therangetriggerwithattitudeinitializationof0.025◦isused.
6. SUMMARY (DRAFT)
The paper shows the main effects of specific new features
of the Mars 2018 mission that will result in improved EDL
performanceoverthecurrentMSLmission.
The entry flight path angles and reference trajectories that
resultinmaximumparachutedeployaltitudehavebeenfound
forasetofdifferentL/Dandentrymasscombinations,taking
intoaccountdipaltitudeanddynamicpressureconsiderations
Figure 15. Normal vectors to parachute deploy altitude
aswellasconstraintsonguidancesaturationandpeakloads.
surface.
These results constitute a useful tool in the design process
because they show how much L/D is required in order to
obtain a desired parachute deploy altitude for a given entry
From Equation 1, the different partial derivatives can be
mass.
calculated. ThechangeinaltitudewithL/Disthengivenby
Acomparisoninperformancebetweenarange-basedtrigger
and a velocity-based trigger for parachute deploy has been
∂h n
presented. The results show that the use of a range trigger =− L/D (2)
barelyaffectsthealtitudevs. Machdistributionatparachute ∂L/D nh
deploy while significantly reducing the ellipse size with re-
specttothatofMSL.
Similarly,thechangeinaltitudewithentrymassisgivenby
The paper also shows the effect of a significant reduction
in the attitude initialization error when it is combined with
∂h n
a range-based trigger for parachute deploy. The reduction =− me (3)
in attitude initialization error is assumed to be achieved via ∂me nh
adding a star tracker device that can determine the initial
attitude of the vehicle prior to entry interface. The paper
whereasthechangeinL/Dwithentrymassrequiredtokeep
shows that for a conservative attitude initialization error of
aconstantdeployaltitudeisgivenby
0.025◦ (90 arc-seconds), equivalent to a tenth of the atti-
tude initialization error in MSL, the resulting ellipse size at
parachute deploy is 4.7 km by 2.6 km which is 13.4 times
∂L/D n
smaller than that corresponding to the MSL baseline. The = me (4)
resultsalsoshowthattheminimumdeployaltitudeisraised ∂me nL/D
aboutonekilometerandthatthemaximumMachisreduced
byabout0.1whentherangetriggerwithattitudeinitialization
of0.025◦isused. The partial derivatives when only the guidance saturation
constraintisconsideredarepresentedinFigures16to18for
each L/D and entry mass combination. Figure 16 shows the
change in gained altitude at parachute deploy (expressed in
APPENDICES km)forachangeof0.02inL/D,Figure17showsthechange
A. PARTIAL DERIVATIVES WITH GUIDANCE inaltitudeforanincreaseof0.3mtinentrymass,andFigure
18 shows the increase in L/D required to keep a constant
SATURATION CONSTRAINT
deployaltitudewhenthereisanincreaseinentrymassof0.3
The shape of the altitude at parachute deploy as a function mt.
of L/D and entry mass in 3D can be decomposed into small
planesasdepictedinFigure15.
B. PARTIAL DERIVATIVES WITH ADDITIONAL
Each of the planes in Figure 15 is defined by its normal PEAK LOAD CONSTRAINT
unitvector(n ,n ,n )andthepointitisassociatedto
me L/D h
(m ,L/D ,h ). Theequationdefiningeachplaneisgiven FollowingthesameproceduredescribedinAppendixA,the
bye0 0 0 partial derivatives for all L/D and entry mass combinations
whenthepeakloadconstraintiscombinedwiththeguidance
saturationconstraintwerefound.Figure19showsthechange
ingainedaltitudeatparachutedeploy(expressedinkm)fora
changeof0.02inL/D,Figure20showsthechangeinaltitude
foranincreaseof0.3mtinentrymass,andFigure21shows
h= nme (m −m )+ nL/D (L/D −L/D)+h (1) theincreaseinL/Drequiredtokeepaconstantdeployaltitude
n e0 e n 0 0 whenthereisanincreaseinentrymassof0.3mt.
h h
7
Figure 16. Gained altitude at parachute deploy (expressed Figure 19. Gained altitude at parachute deploy (expressed
inkm)forachangeof0.02inL/Dwithguidancesaturation inkm)forachangeof0.02inL/Dwithadditionalpeakload
constraint. constraint.
Figure 17. Gained altitude at parachute deploy (expressed Figure20. Gainedaltitudeatparachutedeploy(expressedin
in km) for a change of 0.3 mt in entry mass with guidance km)forachangeof0.3mtinentrymasswithadditionalpeak
saturationconstraint. loadconstraint.
Figure 18. Required increase in L/D for an increase of 0.3 Figure21. RequiredincreaseinL/Dforanincreaseof0.3mt
mttokeepaconstantdeployaltitudewithguidancesaturation to keep a constant deploy altitude with additional peak load
constraint. constraint.
8
InFigure21, theplottedincreaseinL/Dhasbeencappedat
0.1toeasevisualization. Inreality,valueslargerthan0.1are
associatedtotheregionshowingaL/Dincreaseof0.1.
ACKNOWLEDGMENTS
The authors thank Gavin F. Mendeck and Lynn E. Craig for
theircommentsandhelp.
REFERENCES
[1] H.R.Morth,”ReentryGuidanceforApollo,”MITInstru-
mentationLab.,R-532,Vol.1,Cambridge,January1966.
[2] P.E. Moseley, “The Apollo Entry Guidance: A Review
of the Mathematical Development and Its Operational
Characteristics”, TRW Note No. 69-FMT-791, TRW,
December1,1969.
[3] J.M. Lafleur and C.J. Cerimele, ”Angle of Attack Mod-
ulation for Mars Entry Terminal State Optimization.”
AIAA2009-5611.AIAAAtmosphericFlightMechanics
ConferenceandExhibit,Chicago,Illinois,10-13August
2009.
[4] J.M.LafleurandC.J.Cerimele,”MarsEntryBankProfile
Design for Terminal State Optimization.” AIAA 2008-
6213.AIAAAtmosphericFlightMechanicsConference
andExhibit,Honolulu,Hawaii,Aug.18-21,2008.
[5] R. Prakash, et al. ”Mars Science Laboratory Entry,
Descent, and Landing System Overview,” 2008 IEEE
AerospaceConferenceProceedings,March1-8,2008.
[6] D. Way, ”On the Use of a Range Trigger for the Mars
ScienceLaboratoryEntry, Descent, andLanding”, 2011
IEEE Aerospace Conference Proceedings, March 5-12,
2011.
[7] G.F. Mendeck and L.E. Craig, ”Entry Guidance for the
2011 Mars Science Laboratory Mission.” AIAA 2011-
6639.AIAAAtmosphericFlightMechanicsConference
andExhibit,Portland,Oregon,Aug.8-11,2011.
[8] M.T.Zuber,etal.”MarsObserverLaserAltimeterInves-
tigation”, Journal of Geophysical Research, Vol. 97, pp.
7781-7797,May1992.
[9] D.Kipp,etal.”MarsScienceLaboratoryEntry,Descent,
and Landing Triggers,” 2007 IEEE Aerospace Confer-
enceProceedings,March3-10,2007.
[10] C. Liebe, ”Star Trackers for Attitude Determination”,
AerospaceandElectronicSystemsMagazine,IEEE,Vol.
10,Issue6,pp.10-16,June,1995.
[11] C. Liebe, ”Accuracy Performance of Star Trackers -
a Tutorial”, IEEE Transactions on Aerospace and Elec-
tronic Systems, Vol. 38, Issue 2, pp. 587 - 599, April,
2002.
9