mars aerocapture

(c)2000 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

AOO-39726

AIAA-2000-4116

AN ANALYTIC AEROCAPTURE GUIDANCE ALGORITHMFOR THE MARS SAMPLE RETURN ORBITER

James P. Masciarelli*NASA Johnson Space Center

Houston, TXand

Stephane ROUSSEAU*, Hubert FRAYSSEf, Etienne PEROT1Centre National d'Etudes Spatiales

Toulouse, France

Abstract

The Mars Sample Return mission calls for the first useof an aerocapture trajectory to insert a vehicle into orbitabout Mars. A joint CNES-NASA effort is underwayto study this very critical phase of the mission andchoose the best guidance algorithm to be used for thisatmospheric trajectory. This paper discusses an ana-lytic predictor corrector guidance algorithm, beingjointly developed by CNES and NASA. The algorithmis being considered for the Mars Sample Return Orbitervehicle, which will be developed, launched, and oper-ated by France. Nominal and Monte Carlo trajectoryresults are presented for two different versions of thealgorithm. These results show that the algorithm is agood candidate for the given mission.

Nomenclature

AFE Aeroassist Flight ExperimentAPC Analytic Predictor CorrectorCD Aerodynamic drag coefficientCL Aerodynamic lift coefficientCNES Centre National d'Etudes SpatialesD Deceleration due to dragEMCD European Martian Climate DatabaseE,0, Total orbital energyg Gravitational accelerationGd Drag error gainG^ Altitude rate error gainh Altitude rate

Reference altitude rateAtmosphere scale heightOrbit inclinationJohnson Space CenterEquilibrium glide factorVehicle massMars Global Reference AtmosphereModelMars Sample Return OrbiterPlanet gravitational constantNational Aeronautics and SpaceAdministrationBank angle commandDynamic pressureDistance from center of planetApoapsis radiusAtmospheric exit radiusDesired velocity at atmospheric exitPredicted velocity at atmospheric exitInertial velocityVelocity error ( Vai, -Vdes,Kd)

Introduction

The Mars Sample Return mission is a joint CNES andNASA mission of the Mars Exploration Program1. Themission requires an orbiter vehicle that will enter Marsorbit, locate and retrieve the samples, and return themto Earth. This Mars Sample Return Orbiter (MSRO),which is scheduled for launch in 2005, will be devel-oped, launched, and operated by France.

hs/JSCKmMars GRAM

MSROHNASA

0cmdqRRaRod,

* Engineer, Aeroscience and Flight Mechanics Division, Member AIAA+ Engineer, Mission Analysis Department* Engineer, COFRAMI, Toulouse, FranceCopyright 2000 by the American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in theUnited States under Title 17, U.S. Code. The U.S. Government has a royalty-free license to exercise all rights underthe copyright claimed herein for Governmental Purposes. All other rights are reserved by the copyright owner.

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(c)2000 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)1 Sponsoring Organization.

The MSRO mass is limited to 2700 kg on the launchpad. In order to maximize the amount of useful massdelivered to Mars orbit within this limit, the MSRO willuse a guided aerocapture trajectory to insert itself into a1400 km by 250 km altitude orbit with 45 degree incli-nation. Over the past year, a joint CNES-NASA teamhas been working to study this very critical phase of themission, demonstrate its robustness, and choose the bestguidance algorithm to be used for this atmospheric tra-jectory. A group of atmospheric trajectory specialistsfrom CNES, NASA-Langley and NASA-JSC has beenworking to propose and test guidance algorithms, crossvalidate trajectory simulators, and analyze the valida-tion methodology and assumptions for the aerocapturetrajectory. Five guidance algorithms (3 from NASAand 2 from CNES) are being evaluated. Two of the al-gorithms are analytical predictor-corrector (APC) algo-rithms derived from the guidance algorithm developedfor the Aeroassist Flight Experiment (AFE) program2.These two versions of the APC algorithm were devel-oped independently, one by CNES and one by JSC3.

This paper investigates the use of the APC aerocaptureguidance algorithms for the MSRO vehicle and missionrequirements. First, an overview of the APC guidancealgorithm is given, and the differences between theCNES derived and the JSC derived versions are dis-cussed. Nominal and Monte-Carlo trajectory simula-tion results using the two guidance algorithms are thenpresented for the expected orbiter arrival conditions atMars. These results show that the guidance perform-ance satisfies the MSRO mission requirements and thatthe two approaches lead to very similar results. Finally,the direction of future work on this algorithm is dis-cussed.

APC Guidance Algorithm Overview

The APC guidance algorithm consists of two phases.The first phase, or capture phase, provides bank com-mands to stabilize the trajectory and drive the vehicletoward equilibrium glide conditions. When the vehicledecelerates to a specified velocity, the second phase, orexit phase, begins. The exit phase analytically predictsthe velocity vector at atmospheric exit altitude, thenadjusts the lift vector magnitude (through bank com-mands) so that the velocity achieved at exit altitude willproduce an orbit with the target apoapsis. A significantfeature of the APC algorithm is that no reference tra-jectories are computed prior to flight; all references arecomputed and updated during flight.

The original version of the APC algorithm was devel-oped for the AFE program, and its derivation can befound in [2]. CNES and JSC both independently devel-

oped modified versions of the original guidance. Thechanges that were made are discussed below.

Capture Phase

For both the CNES and JSC versions of the guidance,the capture phase is the same as in [2] except that thedynamic pressure term in the control equation is re-placed by a drag acceleration term. With this change,the control equation becomes

(*-*// s-i J

where $cmd is the commanded bank angle, h is thealtitude rate, q is the dynamic pressure, and D is thedeceleration due to drag. Gh and Gd are gains selectedto provide the controller with a low response time(-100 sec), minimum overshoot of the drag reference,and a smooth bank angle profile.

During the capture phase, when equilibrium glide istargeted, the reference altitude rate,/zrey, is zero, andthe reference drag deceleration is given by

where V, is current inertial velocity, R is current radiusvector magnitude, g is acceleration due to gravity, CLand CD are lift and drag coefficients, and AT is a factor todetermine how much of the lift vector should be used tomaintain equilibrium glide. Since (g-V?IK) is alwaysnegative, the bank angle must be between 90 and180 deg hi order to maintain equilibrium glide. To pro-vide the controller with some robustness margin, K isselected to be 1.5, producing a mean value for equilib-rium glide bank angle near 135 deg.

Exit Phase

In the exit phase of the guidance, the drag accelerationterm is omitted from the control equation, and the refer-ence altitude rate is chosen to be a constant such thatthe velocity at atmospheric exit will provide the desiredtarget apoapsis altitude. This results in the followingcontrol equation, which is identical to the original ver-sion outlined in [2]:

h-h= COS AM,. - -


During the exit phase, Gh is tuned to provide the con-troller with a response time of 20 to 30 seconds.

In the original version of the guidance, the referencealtitude rate was chosen by a time consuming iterativeprocedure. JSC and CNES developed the followingequation to adjust the reference altitude rate based onthe difference between the predicted and desired exitvelocity instead of using the iterative procedure:

nrefdesired

(dVmissldh)

where F , is the predicted velocity at exit, Fdw/red isvelocity at exit to achieve the apoapsis target with givenhref, and Vmiss = Fra/, - Vdesired. The difference betweenthe CNES and JSC versions of the guidance is in howVexit and Visited are computed. The CNES version fol-lows a method similar to that in [2], which assumes anexponential atmosphere and constant radial velocity toatmosphere exit for estimating velocity loss due to drag.The JSC version uses these assumptions and the fol-lowing additional assumptions: Velocity loss due to drag is instantaneous and can

be applied at any point in the exit phase to estimateapoapse altitude.

Desired velocity (a square root function of the visviva integral) can be approximated by a quadraticexpression and can be calculated at the current al-titude rather than the exit altitude.

With these assumptions, a simplified sequence of cal-culations is obtained to compute Fra;, and Vdesired. Thedetails of this derivation can be found in [3]. Figure 1shows the differences between the original, CNES, andJSC sequence of computations for the exit phase.

Estimation of Atmosphere Density

In all of the sequences above, it is necessary to have anestimate of the current atmospheric density. Densitycan be derived from measured drag deceleration, as-suming a nominal CD:

Pmes =2mDnSCDV;

The guidance models the density as a simple exponen-tial law of altitude

h-h0

Pmod = Poe

where p0 and h0 are reference density and altitude, andthe scale height, hs, is a constant. The scale height isselected to provide the best compromised performancewith the anticipated different atmospheric profiles.

A density scale multiplier Kp is defined as the ratiobetween the expected density (from the guidance's ex-ponential model) and the measured density. A first or-

Original Sequence CNES Sequence JSC Sequence

K = V1

V an r~ -il Seal 1m

AF=-

h = "* P"exit n Seal

AF = -

v desired" * yv. y desirecT~

hrefmCDSqesths Vr

Fn =

-1"factor , 2

2FJ4-1'P\ R2

; 2desired

AF

wish

Figure 1. Comparison of Exit Phase Computation Sequences

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der low-pass filter is used to smooth high frequencyatmosphere disturbances:

Pmod

The density scale multiplier is initialized to 1. A typi-cal value of 0.2 is used for the filter gain, K.

Now, the density estimate, dynamic pressure estimate,and drag deceleration estimate used in the controllerequations are computed as:

1Pest = Kppmod, qest = pestVr , Dest =2 m

qesl.

Note that with this approach, the density scale multi-plier will compensate for both density variations and CDdispersions.

Lateral Logic

For the MSRO mission, orbit inclination is specified,but node location is unspecified. Therefore, bank re-versals are performed to target only for the desired orbitinclination. The CNES and JSC versions of the guid-ance initiate a bank reversal whenever the current incli-nation exceeds some limit. For the results presented inthis paper, both algorithms used the same lateral logic.

The lateral logic uses an inclination deadband that is afunction of inertial velocity. Whenever the inclinationerror exceeds this deadband, a roll reversal is com-manded. In this case, the allowable inclination error,iaiimabie, is given by

manded. Finally, the angular distance to roll is exam-ined. If the distance to roll through lift down is lessthan 245 deg, then roll through lift down is com-manded, otherwise a roll through lift up is commanded.

APC Performance for the MSRO Mission

MSRO Vehicle Definition

The MSRO vehicle has a mass of 2200 kg at entry. Thevehicle's aeroshell has a reference area of 8.647 m2.The nominal angle of attack is 2 deg, and for continuumflow, the nominal values for lift and drag coefficientsare 0.426 and 1.723 respectively. With these charac-teristics, the vehicle has a nominal lift-to-drag ratio of0.25, and a ballistic coefficient of 148 kg/m2. The ve-hicle's attitude control system is capable of producingbank accelerations of 6.8 deg/s2, and the roll rate islimited to 20 deg/s. These assumptions correspond tothe CNES MSRO phase A mission design.

Aerocapture Mission Requirements

Mission requirements dictate that the post-aerocaptureapoapsis altitude must be 1400 100 km, that the peri-apse altitude must be greater than -50 km, and that theorbit inclination must be 45 0.5 deg (Phase A hy-potheses). The total AV allocated for post-aerocaptureis 100 m/s. In addition, the aerocapture trajectory mustsatisfy the following constraints on deceleration, heatflux, heat load, and dynamic pressure:

maximum deceleration of 2.8 g's (27.46 m/s2), maximum heat flux of 460 kW/m2, maximum total heat load of 70 MJ/m2, maximum dynamic pressure 4.6 kPa.

allowable + a(v, - V \i 11 Mars Arrival Conditions-t- U\Y/ vminj, imax ;j

where V, is the current inertial velocity, a is the changeof allowable inclination error with velocity, /,, and imaxare values that specify the minimum and maximum in-clination limits, and Vmin is the velocity where imin is ap-plied.

The roll direction is selected through a series of teststhat examine current velocity, angular distance to roll,and difference between reference and navigated altituderate. First, if the inertial velocity is greater than5.8 km/s, the direction is commanded based on theshortest distance to roll. If that condition is not met,then if the current altitude rate is greater than the refer-ence altitude rate, a roll lift-down is commanded. Thenext test computes an allowable error between the ref-erence altitude rate and the current altitude rate. If thecurrent altitude rate is a certain amount below the refer-ence altitude rate, then a roll through lift up is corn-

The arrival conditions corresponding to launch at theclose of launch window were estimated to impose themost demanding requirements on the aerocapture guid-ance. Therefore, these conditions were examined firstand are presented in this paper. A launch at the close oflaunch window gives an arrival time at Mars of August.27, 2006 10:28:23 UT. With entry interface defined tobe at a radial distance of 3522.2 km from the center ofMars, the entry velocity is 5.9 km/s and the flight pathangle is -10.5 deg. The arrival conditions correspond-ing to launch at the open of the launch window werelater investigated with similar results.

Simulation Overview

The CNES and JSC versions of the APC algorithmwere implemented as subroutines within a 3-degree offreedom trajectory simulation program. Inputs to theguidance subroutine include current time, position, ve-

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locity, sensed acceleration, and estimated bank angle.The subroutine outputs commanded bank angle and thedirection to roll. Both versions of the APC algorithmrequire on the order of 150 executable lines ofFORTRAN code for the guidance subroutine

The guidance algorithms were tested with two differentMars atmosphere models: the Mars GRAM, providedby NASA, and the ESA European Martian ClimateDatabase (EMCD) atmosphere model, provided byCNES. The vehicle aerodynamic coefficients are de-termined from tabular data of Q. and CD versus Knud-sen number and angle of attack, which was generatedfrom computational fluid dynamics analysis and windtunnel tests of the aeroshell configuration.

Nominal Trajectory Results

Nominal trajectory results obtained with both versionsof the guidance for all of the different atmosphere mod-els look very similar. As an example, nominal trajec-tory results obtained with the CNES version of theguidance and the EMCD dusty atmosphere model are

shown in Figure 2. Target conditions and trajectoryconstraints are satisfied in all cases.

Monte Carlo Results

Monte Carlo simulations were performed to further testthe guidance algorithms. Each run randomly varied theactual entry position and velocity, the navigated posi-tion and velocity, trim angle of attack, aerodynamic co-efficients, vehicle mass, and used a perturbed atmos-phere density profiles generated with the atmospheremodels. A total of 4000 runs were completed for eachversion of the guidance, which includes 2000 caseswith the Mars GRAM, 1000 cases with the EMCDdusty atmosphere model, and 1000 cases with theEMCD clear atmosphere model.

Monte Carlo results obtained with the CNES and JSCversions of the guidance are shown in Figures. Asummary of the Monte Carlo statistics for the CNESand JSC versions of the guidance is shown in Table 1.Again, the two versions of the guidance produce similarresults.

D>CD

T3

200

100

_CDCCD-*

I-100

-2003500 4000 4500 5000 5500 6000

Inertia! velocity, m/s

500

CO 0

&S -500CDa

5 -1000

-15003500 4000 4500 5000 5500 6000

Inertial velocity, m/s

46.5

46

1*45.5

I4 5

44

43.53500 4000 4500 5000 5500

Inertial velocity, m/s6000

40

4230c"o

CDO


50

40

530in

10'1300

50

I

30CO

&CO

20

10'1300

1350 1400 1450Apoapsis Altitude, km

CNES Version

65

J2 60

*55c

JOQ.

^50

451500 44.5

JSC Version65

1350 1400 1450Apoapsis Altitude, km

1500

caa.^50

45

45Orbit Inclination, deg

45.5

44.5 45Orbit Inclination, deg

45.5

Figures. Monte Carlo Results

Table 1. Monte Carlo Statistics (4000 cases each)

Variable

Apoapsis altitude, kmPeriapsis altitude, kmInclination, degMax. acceleration, gMax. dynamic pressure, kPaMax. heat flux, kW/m2

Max. heat load, MJ/m2

In-plane AV, m/sTotal AV, m/s

CNES Version

Min

1332.6820.1044.58

1.522.24

324.6847.2346.5147.39

Mean

1393.4835.9444.902.283.33

404.5253.4452.4060.43

Max

1493.3643.8145.28

3.094.37

479.9762.1261.9675.12

Std. Dev.

30.123.970.160.150.27

19.191.623.145.09

JSC Version

Min

1338.3911.0244.59

1.522.24

324.6847.0146.7647.63

Mean

1396.7030.5544.892.393.44

411.8352.0752.4661.07

Max

1486.2342.3645.30

3.284.67

488.5961.9660.8974.38

Std. Dev.

22.054.130.170.230.35

23.471.381.924.91

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The Monte Carlo results show that target conditionswere achieved in all of the cases. In the cases with theEMCD atmosphere model, all trajectory constraints aresatisfied. With the Mars GRAM however, about 2 per-cent of the cases violated the maximum deceleration orheat flux constraints. Further investigation into thesecases revealed that the Mars GRAM produces somehigh frequency density perturbations that are not seen inthe EMCD model. These high frequency disturbancescaused the deceleration and heat rate limits to be ex-ceeded for very short periods. More work is needed todetermine if this behavior of the model is correct, and ifso, can the vehicle design accommodate these viola-tions of the constraints for the very short time durationsthat they occur.

Entry Corridor Width

Although the nominal and Monte Carlo results showthat bom versions of the guidance perform very well forthe MSRO mission, more work was completed to testthe robustness of the guidance. The uncertainty in entryflight path angle has a major effect on the guidance per-

formance. The Monte Carlo runs used a 3-sigma valueof 0.4 deg, uncertainty in flight path angle. In order tohave as robust a design as possible, it is desirable forthe guidance to not only handle this case, but to captureas much of the theoretical entry corridor as possible.

The steep side of the theoretical entry corridor is de-fined as the flight path angle where a full lift up trajec-tory just reaches the apoapsis target altitude. At steeperflight path angles, the vehicle does not have enough liftto be able to reach the target apoapsis. The shallowside of the theoretical entry corridor is found by flyingall lift down trajectories to determine the flight path an-gle where the vehicle just begins to exceed the apoapsistarget. At any shallower flight path angle, the vehicledoes not have enough lift to capture into the target or-bit, and faces the danger of skipping out of the atmos-phere.

The theoretical entry corridor width is dependent on theatmosphere model. For the EMCD model (consideringboth clear and dusty scenarios), the theoretical entrycorridor extends from -11.24 to -10.03 deg in flight

Mars GRAM 1600je- 1500j3

8- 1300

1200-11

1600

- 1500

< 1400en

55g-1300

.5 -11 -10.5 -10EMCD Dusty

-95

1200-11.5 -11 -10.5

EMCD Clear-10 -95

1600

1400

ONESJSC

ONESJSC

1200-11

ONESJSC

-11 -10.5Entry FPA, deg

-10 -9.5

Figure 4. Sensitivity to Entry Flight Path Angle

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path angle. For the Mars GRAM model, the theoreticalentry corridor is -11.14 to -9.71 deg.

The sensitivity of the 2 versions of the guidance to dis-persions in flight path angle were examined by takingthe nominal entry velocity magnitude and varying theflight path angle at entry interface over the theoreticalcorridor range. The results showing apoapsis altitudeachieved with guidance as a function of entry flightpath angle are shown in Figure 4. The dashed lines inthe figure show the theoretical corridor. As can beseen, both versions of the guidance capture most of thetheoretical corridor, but neither version captures the en-tire theoretical corridor. Most of the loss occurs at theshallow end of the corridor.

A New and Improved APC Algorithm

A joint CNES and JSC effort is in progress, underCNES responsibility, to develop a single APC algo-rithm that combines the best features of the CNES andJSC versions discussed above. In addition, variousmodifications are being investigated to further improvethe algorithm's performance and robustness.

Areas of current focus are on increasing the amount oftheoretical corridor captured by the guidance as well asincreasing guidance robustness to atmospheric disper-sions, aerodynamic dispersions, and system failure sce-narios. Some of the modifications being investigatedinclude corrections based on measured lift to drag ratio,and incorporation of a drag reference term in the exitphase logic. Gain tuning is another area of being in-vestigated, as finding the "best" values for gains re-quires a tradeoff between precision and robustness.This cooperative effort is proving to be fruitful, as pre-liminary results are showing improvements over thealgorithms discussed above.

Summary and Conclusions

This paper has examined two different versions of anAPC guidance algorithm for the MSRO mission. Bothversions were derived independently by CNES and JSCfrom an algorithm originally developed for the AFEprogram. JSC and CNES made similar but slightly dif-ferent modifications to the original algorithm. Bothversions replaced the dynamic pressure reference with adrag acceleration reference. Both versions also re-placed an iterative sequence to determine reference al-titude rate in the exit phase with a simpler calculusbased method. The main difference between the twoalgorithms is the method used to predict the atmos-pheric exit conditions.

Both versions of the guidance algorithm were tested intrajectory simulation programs. Nominal trajectories

and Monte Carlo results have been developed using twodifferent atmosphere models. In addition, performancesensitivity to large deviations from the nominal entryflight path angle has been investigated. These resultsshow that both versions of the APC guidance algorithmperform well for the MSRO mission. No significantperformance differences have been found between thetwo versions of the algorithm (with gains kept at thesame values). Some trajectory constraint violationswere discovered during the Monte Carlo analysis withthe Mars GRAM atmosphere, and effort is underway toaddress this issue.

The work completed by the CNES-NASA team overthat past year has shown that the APC algorithm is avery efficient and simple algorithm, and therefore agood candidate for the MSRO mission. The commonNASA and CNES work on this guidance algorithm hasbeen very fruitful. Future cooperative work will bedone to further improve and test this algorithm.

References

[1] Lee, Wayne; D'Amario, Louis; Roncoli, Ralph;Smith, John: "Mission Design Overview for theMars 2003/2005 Sample Return Mission," AAS99-305, AAS/AIAA Astrodynamics Conference,Girdwood, Alaska, August 1999.

[2] Cerimele, C.J.; Gamble, J.D.: "A Simplified Guid-ance Algorithm for Lifting Aeroassist OrbitalTransfer Vehicles," AIAA-85-0348, AIAA 23rdAerospace Sciences Meeting, Reno, Nevada, Janu-ary 1985.

[3] Bryant, L.E.; Tigges, M.A.; Ives, D.G.: "AnalyticDrag Control for Precision Landing and Aerocap-ture," AIAA-98-4572.

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mars aerocapture

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