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Advanced Guidance and Control Methods for Reusable Launch 

Vehicles: Test Results 

Draft 
John M. Hanson 1 , Robert E. Jones 2 , Don R Krupp 1 

Abstract 

There are a number of approaches to advanced guidance and control (AG&C) that have 
the potential for achieving the goals of significantly increasing reusable launch vehicle 
(RLV) safety/reliability and reducing the cost. In this paper, we examine some of these 
methods and compare the results. We briefly introduce the various methods under test, 
list the test cases used to demonstrate that the desired results are achieved, show an 
automated test scoring method that greatly reduces the evaluation effort required, and 
display results of the tests. Results are shown for the algorithms that have entered testing 
so far. 

Introduction 

Advanced guidance and control has a significant potential to increase the safety of future 
reusable launch vehicles, as well as to reduce the cost of performing guidance and control 
analysis, both in the design and in the operational phases. This potential has been 
documented elsewhere (Ref 1). The Advanced Guidance and Control Project, supported 
by the NASA X-33 Program Office, had as its purpose to develop and test some of the 
potential methods. The testing was to be in a high-fidelity simulation, against a number of 
stressing conditions, in order to discern the most flexible approaches. 

In this paper, we examine approaches in the areas of ascent/abort guidance, entry 
guidance, and flight control. We summarize an initial phase of testing performed to 
examine the various methods and describe these methods. Some lessons were learned 
from the initial phase of testing. Some of the algorithms performed well, but for the most 
part the methods were not ready to address all the RLV needs. We planned a second 
phase of testing to more completely examine the performance of the algorithms versus 
the safety/cost requirements. This paper includes a description of the test cases for the 
second phase of testing. This paper also describes an automated method of scoring, for 
evaluating the results of tests, that results in a significant reduction of effort. We include 
results of the second phase of testing at the end of the paper. 

First Phase of Testing 

An original goal in this effort was to include as many approaches as possible within the 
resources of the effort, with an eye toward not missing what may be the best approach. 
The methods had to be openly available (not proprietary), and available with a relatively 
small budget. This led to an emphasis on university grants and in-house efforts. Some of 



1 Aerospace Engineer, NASA Marshall Space Flight Centet/ID54, Huntsville, AL 35812. 

2 Senior Engineer, Sverdrup Technology, Inc., MSFC Group, 6703 Odyssey Drive, Suite 303, Huntsville, 
AL 35806 



the methods' development was funded separately but was furnished by the authors for 
testing in this environment. 

A test series was conducted in September 2000. No ascent/abort guidance algorithms 
were available for this first phase of testing. Four entry guidance methods were tested, as 
were five control approaches. The test environment was the high-fidelity X-33 Marshall 
Aerospace Vehicle Representation in C (MAVERIC) simulation (Ref 2). The X-33 was 
planned to fly a number of sub-orbital test flights, so these tests encompassed primarily 
ascent followed immediately by entry on sub-orbital trajectories. For the entry guidance 
methods, additional tests were run for entry from various orbits, with differing crossrange 
requirements and heat constraints. 

Tests included different nominal missions, engine-out aborts, dispersion Monte Carlo 
runs for both nominal missions and aborts, and significant engine over and under 
performance. Failures and mis-modeling not associated with the propulsion system were 
not explicitly considered for this Phase 1 testing. Algorithm size, speed of execution, 
memory, complexity/effort required, and performance against a variety of criteria were 
all compared. 

Of all the methods tested, the linear quadratic regulator entry guidance was the only one 
that performed quite well. In all cases, it became clear that more work was necessary to 
develop the algorithms to their full potential, so that they would successfully attack the 
various test cases. This led to the definition of a second set of tests, as described below, 
and to more work on the algorithms, as described in the references. 

Methods to be Examined 

The work in this paper continues from work first described in Reference 2. The methods 
under examination are described in that paper, but are listed below for reference, along 
with the current status. 

Ascent guidance 

• In the first method, judicious approximations are made to reduce the order and 
complexity of the state/costate system, and multiple shooting is used. It re- 
optimizes the ascent trajectory every guidance cycle from liftoff to engine burnout 
(Ref. 3). Ascent and abort are both covered. Results for Phase 2 testing are 
included in this paper. 

• Neighboring optimal control (NASA Langley Research Center). This method has 
not been available for testing yet. 

• Trajectory-following guidance (NASA MSFC). This method was not pursued 
due to a lack of available manpower. 

• There are two more approaches under development that have not been tested in 
this environment yet. One is being developed by Iowa State University (Ref. 4) 
under subcontract to Ohio University on a NASA 2 nd Generation RLV contract, 
and the other is being developed by Guided Systems Technology Inc. (Ref. 5) 



under a Phase 2 Small Business Innovative Research (SBIR) contract with the Air 
Force Research Lab. We are hoping to include these two approaches in testing. 



Entry guidance 



Linear quadratic regulator. This method (Ref 6) was not listed in Ref 2 but has 
performed very well in test. Results for Phase 2 testing are included in this paper. 
Predictor-corrector. This method (Ref. 7) has been adapted to provide a trajectory 
for another entry guidance method to follow. It is functioning as a trajectory 
generator rather than as a guidance scheme. Results for Phase 2 testing are 
included in this paper. 

A trajectory design method that uses quasi-equilibrium glide, combined with a 
predictor-corrector method, to choose parameters for entry. (Ref 8). Guidance 
flies these profiles. The guidance method was also tested during Phase 2 testing. 
An entry trajectory design and guidance procedure based on extension of the 
Shuttle trajectory design methods to three dimensions. The planning algorithm 
generates reference drag acceleration and lateral acceleration profiles, along with 
the reference state and bank angle profiles. A feedback linearization control is 
used to track the reference profiles (Ref 9). This method is not available for 
testing as of this writing. 



Flight control 



Sliding mode controller (Ref 10). This controller showed some promise in phase 

1 testing. This work has been combined with controller design by trajectory 

linearization (Ref 14) and reconfigurable control allocation (Ref 13). Results for 

Phase 2 testing are included in this paper. 

Fault tolerant nonlinear adaptive controller using neural nets (Ref 11). This 

controller showed some promise in phase 1 testing. Results for Phase 2 testing 

are not available of this writing. 

Dynamic inversion (Ref 12). Phase 1 testing was for ascent only, as the control 

method was not ready for entry flight. The algorithm had trouble for ascent 

primarily due to some cases where a subroutine bombed and also due to not 

following the guidance overall throttle command. The investigator has had 

insufficient time available to pursue this work during the current testing period. 

Robust inversion and data compression in control allocation. This work has been 

updated to provide reconfigurable control allocation (Ref. 13). It has been 

combined with the sliding mode controller work (Ref 10) and trajectory 

linearization control work (Ref 14) in a single algorithm architecture. Test results 

are included in this paper. 

Linear parametrically varying controller. This control approach was nowhere 

close to being ready for testing when the first phase of testing occurred, and was 

dropped from consideration. 

Controller design by trajectory linearization (Ref. 14). This method showed some 

promise in Phase 1 testing and was tested during Phase 2 as part of an overall 



algorithm architecture that includes the sliding mode controller (Ref 10) and 
reconfigurable control allocation (Ref 13). 

Test Cases and Test Criteria 

For the second phase of tests, we included many of the first set of tests again, since the 
methods did not in most cases perform satisfactorily. We also added tests for various 
failure and mis-modeling cases that seemed appropriate. The test environment was a 
newer version of MAVERIC that models the X-33 vehicle in more detail and automates 
some of the test processes required. A list of the test cases follows in Table 1 . Table 2 
shows the motivation for each set of tests. Table 3 lists the criteria compared for each of 
the various tests. The actual parameters scored, weights, and limit values vary between 
test cases and are too extensive to list here. See Ref 15 for a complete description. 



Table 1. Phase 2 Test Series 

DOF: Degrees of Freedom; MCD: Monte Carlo Dispersions; PPO: Power Pack Out (Engine Failure, time of failure 
indicated); AGC is a vehicle with X-33 characteristics with specific impulse doubled so it can reach orbit; Michael 
(nominal) and Ibex (low energy) are X-33 landing sites; MichlOal and lOdl are planned X-33 trajectories; MECO: 
main engine cutoff; alpha is angle of attack; Q is dynamic pressure; Q-alpha is dynamic pressure times angle of attack; 
seed indicates whether a new random number was used to start certain test cases; season is which part of the year is 
used for environmental dispersions. All environments are for the month of April unless noted. EAFB is Edwards AFB 
GRAM is Global Reference Atmosphere Model. ISS is International Space Station; LEO is low Earth orbit. TVC is 
thrust vector control. 

ASCENT GUIDANCE TEST SERIES 



Test Number & Description 

1 ) 'X-33 Mich 1 0a 1 , thrust dispersion increased so 3 sigma is 20% 

2) "X-33 MichlOal PPO at 50 sec, to Michael (early PPO to Michael) 

3 ) "X-33 Mich 1 Oa 1 PPO at 50 sec to Ibex (late PPO to Ibex) 

4) *X-33 MichlOal PPO at 40 sec to Ibex (early PPO to Ibex) 

5) AGC to 28.5 deg. 100 nm circular orbit Wind profile available is mean annual only. 

6) »AGC to 5 1 .6 deg. orbit, 40x1 50 nm orbit, in-plane (maximum payload) injection. 

7) * AGC to 51.6 deg. orbit, 40x150 nm orbit, rendezvous mission 5 minutes after in-plane launch. 

8) *Same as 7 with launch 5 minutes before in-plane launch 

9) *AGC abort to orbit for 5 1 .6 deg. case (40x150) with loss of 50% thrust at 122.9 sec (early failure) 

10) * AGC abort to orbit for 51.6 deg. case (40x150) with 67% propulsion loss 10 sec, prior to MECO 

11) *AGC abort to downrange landing site (from 51.6 deg. case) for early engine loss (50% of total thrust 
is lost, time of loss 48 sec), alpha and Q-alpha are control-power limited. 

12) *Same as 1 1 (ascent mission), but downrange abort after late (223 sec) 50% propulsion loss. 

1 3) *AGC abort to launch site (5 1 .6 deg., 40x1 50 case), 20% thrust loss at T=0. Alpha and Q-alpha are 
control-power limited. 



141 



'Same as 13 for 33% thrust loss at max Q. Alpha and Q-alpha are control-power limited. 



♦Same as 1 3 for late 20% thrust loss. Alpha and Q-alpha are control-power limited. 



DOF 



#Runs 



100 MCD 



100 MCD 



100 MCD 



100 MCD 



100 MCD 



100 MCD 



100 MCD 



100 MCD 



100 MCD 



100 MCD 



100 MCD 



100 MCD 



100 MCD 



100 MCD 



100 MCD 



Wind provided to guidance is mean annual for EAFB; wind seen in simulation is randomized from GRAM. 
The cases all involve day of launch wind measurement. A smoothed wind profile is available to guidance. Another 
profile, measured a few hours later, is the wind that the vehicle must fly. Tests 5-15 are launches from Cape 
C ana veral 

ENTRY GUIDANCE TEST SERIES 



Test Number & Description 



1) MichlOal 



2) MichlOal, February environment, different random seed 

3) MichlOdl 



4) Mich lOdl, August environment, different random seed 



5) MichlOal, PPO time 50 sec (early abort to Michael) 



6) MichlOal, PPO time 60 sec 



7) MichlOal, PPO time 112 sec 



DOF 



#Runs 



100 MCD 



200 MCD 



100 MCD 



200 MCD 



100 MCD 



100 MCD 



100 MCD 



8) MichlOal, PPO time 40 sec (early to Ibex), different random seed 



200 MCD 



9) MichlOdl, PPO time 38 sec (early to Ibex), different random seed 



200 MCD 



10) MichlOal, +4 sigma thrust dispersion from ascent 



1 



1 1 ) MichlOal, +6 sigma thrust dispersion from ascent 



12) MichlOal, -12 sigma thrust dispersion from ascent 



1 



13) 51.6 deg. ISS orbit entry, low crossrange, high peak heat rate limit, input profile to guidance is from 
this trajectory's design. 



100 MCD 



14) 51 .6 deg. ISS orbit entry, high right crossrange, high peak heat rate limit, input profile from 1 3. 



100 MCD 



15) 51.6 deg. ISS orbit entry, high left crossrange, high peak heat rate limit, input profile from 1 3 



100 MCD 



16) 51.6 deg. ISS orbit entry, low crossrange, low peak heat rate limit, input profile from this trajectory's 
design. 



100 MCD 



17) 51.6 deg. ISS orbit entry, high right crossrange, low peak heat rate limit, input profile from 16. 



100 MCD 



18) 51.6 deg. ISS orbit entry, high left crossrange, low peak heat rate limit, input profile from 16 



100 MCD 



1 9) 28.5 deg. LEO orbit entry, low crossrange, low peak heat rate limit, input profile from 1 6 



20) 28.5 deg. LEO orbit entry, high right crossrange, low peak heat rate limit, input profile from 16. 



100 MCD 
100 MCD 



2 1 ) 28.5 deg. LEO orbit entry, high left crossrange, low peak heat rate limit, input profile from 16 



100 MCD 



22) MichlOal, aerosurface failure result: angle of attack limited to 5 deg. less that nominal entry value 



23) MichlOal, aerosurface failure result: angle of attack and bank rates limited to 2 deg./sec. maximum. 



24) Mich lOdl, aerosurface failure: angle of attack limited to 5 deg. less that nominal entry value 



25) MichlOdl , aerosurface failure: angle of attack limited to 5 deg. less that nominal entry value, and angle 
of attack and bank rates limited to 2 deg./sec. maximum 



26) MichlOal, unknown to guidance, first flight aerodynamics mis-modeling: aerodynamic lift coef 20% 
less than vehicle database model. 



27) MichlOal, unknown to guidance, first flight aerodynamics mis-modeling: aerodynamic lift coef. 20% 
more than vehicle database model. 



28) MichlOal, unknown to guidance, first flight aerodynamics mis-modeling: aerodynamic lift coef. 20% 
less and aerodynamic drag is 20% more than vehicle database model. 



FLIGHT CONTROL TEST SERIES 



Test Number & Description 



DOF 



1) MichlOal 



2) MichlOdl 



3) MichlOal, PPO time 36 sec (early to Ibex) 



4) MichlOdl, PPO time 50 sec (early to Michael) 



5) TVC command bias on Engine A: Roll/Pitch TVC commands +0.5% 



6) TVC command bias on Engine B: Roll/Pitch TVC commands -1 .0% 



7) TVC command bias on Yaw: TVC commands +1.0% 



8) +3 sigma Fz, My on Engine A, -3 sigma Fz, My on Engine B 



9) Right inboard elevon fails to +10 deg. 50 seconds into flight for 30 seconds. 



10) Left outboard elevon fails to -1 5 deg. 275 seconds into flight for 45 seconds. 



1 1 ) Right flap fails to +2 deg. 1 50 seconds into flight for 20 seconds. 



12) Right flap fails to +2 deg. 300 seconds into flight for 20 seconds 



13) Right rudder fails to -30 deg. 30 seconds into flight for remainder of flight 



14) Left inboard elevon fails to null 35 seconds into flight for remainder of flight 



15) Right outboard elevon fails to null 250 seconds into flight for remainder of flight. 



16) Right flap fails to null at 20 seconds into flight for remainder of flight 



17) Left flap fails to null at 21 5 seconds into flight for remainder of flight. 



1 8) Right outboard elevon jams 58 seconds into flight for remainder of flight. 



1 9) Left inboard elevon jams 208 seconds into flight for remainder of flight. 



20) Right flap jams 170 seconds into flight for remainder of flight 



21) Left flap jams 280 seconds into flight for remainder of flight. 



22) Fail l&lOatMECO (loss of pure yaw capability) 



23) Fail 5&9 at MECO (loss of pure yaw capability) 



24) Fail 4 at MECO (loss of yawroll capability) 



25) Fail 8 at MECO (loss of yawroll capability) 



26) +3 sigma Cm, +3 sigma Ca, +3 sigma CN 



27) -4 sigma Cm, -4 sigma Ca, -4 sigma CN 



28) -3 sigma CY, -3 sigma CI, -3 sigma Cn 



29) -4 sigma rotary derivative increments 



30) -3 sigma Cm, Ca, CN (body flap), +3 sigma CY, CI, Cn (body flap) 



1 



# Runs 



31 ) +3 sigma CY, CI, Cn (elevons) 



32) +4 sigma jet effect increments on control surface effectiveness 



33) +3 sigma adverse yaw moment increments on elevons & body flaps 



34) 2 Hz, 10% nominal pitch signal magnitude, 30 deg. phase angle signal added to nominal navigation 
output to account for vibrational mode mis-modeling (simplified test of mis-modeling) 



35) 2 Hz, 10% nominal yaw/roll signal magnitude, 30 deg. phase angle signal added to nominal navigation 
output 



vuii^ui ________________________________ 

36) 2 Hz, 20% nominal pitch signal magnitude, 30 deg. phase angle signal added to nominal navigation 
o utput 



— 'UlL/Uk „___________________-———— - ■ — 

37) 2 Hz, 20% nominal yaw/roll signal magnitude, 30 deg. phase angle signal added to nominal navigation 
o utput 



uutpui . 

38) 2 Hz, 10% nominal pitch signal magnitude, 45 deg. phase angle signal added to nominal navigation 
output 



uutpm. 

39) 2 Hz, 10% nominal yaw/roll signal magnitude, 45 deg. phase angle signal added to nominal navigation 
output 



ompui __ 

40) 4 Hz, 5% nominal pitch signal magnitude, deg. phase angle signal added to nominal navigation output 

a 1 \ a tt_ _n/ : 1 /__11 _:~ Mr .i -n^nitn/la ft /-!_— — .Viaco onnlp ciormi aAAf^A in nnminal nflvioatinn 



41 ) 4 Hz, 5% nominal yaw/roll signal magnitude, deg. phase angle signal added to nominal navigation 
output 



42) 10 Hz, 10% nominal pitch signal magnitude, 60 deg. phase angle signal added to nominal navigation 
output 



UUl^Ul __ __ __ - 

43) 10 Hz, 10% nominal yaw/roll signal magnitude, 60 deg, phase angle signal added to nominal navigation 
output 



44) MichlOal 



45) MichlOal, February environment, different random seed 



46) MichlOdl 



47) MichlOdl, August environment, different random seed 



48) MichlOal, PPO time 60 sec 



49) MichlOal, PPO time 1 12 sec 



50) MichlOal, PPO time 40 sec, different random seed 



5 1 ) Mich 1 Od 1 , PPO time 38 sec, different random seed 



100 MCD 



200 MCD 



100 MCD 



200 MCD 



100 MCD 



100 MCD 



200 MCD 



200 MCD 



Table 2. Motivation for the Tests 



Tests 



1-4 



5-15 



6-8 



9-15 



1-4 



5-9 



10-12 



13-21 



Motivation 



Ascent Guidance 



X-33 missions with dispersions and engine failures. Launch from EAFB. 
Guidance robustness and adaptability. 



AGC vehicle launched from CCAFS/KSC. 



28.5 deg. orbit. Actual winds randomized from GRAM. 
when a measured wind is not available to guidance. 



Examine loads 



51.6 deg. orbit; measure performance and adaptability to different orbits. 



Abort to orbit, abort from orbit to landing site, abort to launch site. Ability 

of guidance/trajectory design to adapt to a range of failure cases. 

Entry Guidance 



Nominal X-33 missions with dispersions; robustness to dispersions 



Engine failures; robustness to large off-energy cases and alternate landing 

sites 



Large thrust dispersions; ability to maximize probability of successful 
landing 



Entry from orbit; ability to adapt to different heating requirements and 
crossrange requirements with dispersions. _____ 



22-25 



26-28 



1-2 



3-4 



5-8 



9-21 



22-29 



30-36 



37-44 



Effects from failures causing a change in maneuverability 



Mis-modeling of aerodynamics on first flight 



Control System 



Nominal X-33 missions; robustness to differing missions 



Engine failures; robustness to different thrust levels 



Thrust Vector Control Failure 



Aerosurface failure 



Modeling erroes 



Mis-modeling of vibrational modes 



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Automated Scoring 

The Phase 1 test evaluation involved a number of guidance and control experts reviewing 
the results (both graphical and numerical) and determining how well the method flew the 
vehicle. This approach worked, but had two drawbacks: 1) It requires a large amount of 
engineer time for evaluation of many parameters on many tests for multiple algorithms, 
and 2) the final evaluation has some subjectivity in it (and could potentially result in 
uneven evaluation). There was a benefit to this method, however. In evaluating the 
methods, it became clear to the evaluators what parameters were important to them and 
what values of these parameters were acceptable. As a result, we were able to automate 
the scoring process for the Phase 2 tests. 

Tests are numerically scored, and then each test is weighted, with the scores added, so 
that the algorithms have a final numerical score. Normalization results in a perfect score 
being given a value of 1 .0. For each parameter to be tested, there is a weight, and these 
multiply that parameter's score and add into the total. Single tests (not Monte Carlo 
dispersions) are scored as in this example: 

Normal acceleration: 0-3. 5g, 1.0-2.5g means the score is 1 .0 for normal acceleration 
magnitudes below 2.5, 0.0 for values above 3.5, and linearly varying in between the two 
limit values. The parameter score is multiplied by the weight for that parameter (normal 
acceleration) and added into the total score for that test. 

For Monte Carlo dispersion tests, the overall score is the average of the individual scores. 
A final criteria used for the entry guidance and flight control tests regards accuracy in 
reaching the TAEM targets. If the range, altitude, and heading angles are not sufficiently 
controlled in order to be able to land successfully, the test was considered a failure (score 
of 0) even if other criteria were met. Typical values used for the required accuracy at 
hitting the TAEM condition were 7 nm, 7000 ft, and 10 deg, respectively. If more than 
10% of Monte Carlo cases fail to meet these TAEM conditions, then the entire Monte 
Carlo run is given a score of 0.0. 

The detailed scoring parameters and weights appear in Reference 15. 
Results 

Results of the tests are shown in the following figures. A couple of examples from early 
tests are below. The baseline X-33 guidance and control (G&C) will be used for 
comparison for tests where the baseline G&C is able to fly the vehicle. (The baseline 
G&C consists of PID control, open-loop ascent guidance in the atmosphere, linear 
tangent steering vacuum closed-loop guidance, and Shuttle-derived entry guidance). 
Results from testing the rest of the algorithms will appear in the final paper. Complete 
test results are in Ref 15. 

Figure 1 shows the performance for each test case. A score of 0.0 may mean the 
algorithm failed the test or that the algorithm is not ready to perform that test case yet. 



We expect the final paper will include more complete test results for each algorithm, 
more algorithms in test, and ascent guidance and control system tests as well as entry 
guidance tests. 

The criteria graph (Fig. 2) shows the performance on the various criteria from each 
algorithm. The criteria are in Table 3. The performance is shown only for those tests 
that did not fail (did not score a zero on the test cases graph). This way, the reader will 
see information on how the method performed for the various criteria. The number of 
successful tests for each algorithm can be determined from the test cases graph. 



• 
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Figure 1. Entry Guidance Test Scores 



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10 15 20 25 30 35 

Criteria number 



Summary 

This paper gives the results of testing of a number of advanced guidance and control 
methods for application to future reusable launch vehicles. The methods were tested in 
high-fidelity simulation to determine their performance with respect to nominal missions, 
engine-out situations, dispersions, various failures, and vehicle mis-modeling. We expect 
that the best of these methods will yield improved safety and reduced cost for future 
reusable launch vehicles. Summarize any relevant results here. A final version of this 
paper will contain complete test results, and will be submitted for publication. Follow-on 
work is planned to choose between the various guidance and control options and to 
integrate them into a single G&C architecture that meets the safety and cost needs of the 
2 nd Generation RLV Program. More complete testing will be conducted on the integrated 
architecture. 

References 

1. Hanson, J., "A Plan for Advanced Guidance and Control Technology for 2 n 
Generation Reusable Launch Vehicles," 2002 AIAA Guidance, Navigation, and 
Control Conference, Monterey, CA, Aug 2002. 

2. Hanson, J., "Advanced Guidance and Control Project for Reusable Launch Vehicles," 
AIAA-2000-3957, Proceedings of the 2000 AIAA Guidance, Navigation, and Control 
Conference. 

3. Dukeman, G A., "Atmospheric Ascent Guidance for Rocket-Powered Launch 
Vehicles," paper 2002-4559, AIAA Guidance, Navigation, and Control Conference, 
Monterey, CA, Aug 2002. 

4. Sun, H., and Lu, P., "Closed-loop Endoatmospheric Ascent Guidance," paper 2002- 
4558, AIAA Guidance, Navigation, and Control Conference, Monterey, CA, Aug 
2002. 

5. Calise, A., and Brandt, N., "Generation of Launch Vehicle Abort Trajectories using a 
Hybrid Optimization Method," paper 2002-4560, AIAA Guidance, Navigation, and 
Control Conference, Monterey, CA, Aug 2002. 

6. Dukeman, G.A., "Profile-Following Entry Guidance Using Linear Quadratic 
Regulator Theory," paper 2002-4457, AIAA Guidance, Navigation, and Control 
Conference, Monterey, CA, Aug 2002. 

7. Zimmerman, C, Dukeman, G, and Hanson, J., "An Automated Method to Compute 
Orbital Re-entry Trajectories with Heating Constraints," paper 2002-4454, AIAA 
Guidance, Navigation, and Control Conference, Monterey, CA, Aug 2002. 

8. Shen, Z , and Lu, P., "On-Board Generation of Three-Dimensional Constrained Entry 
Trajectories," paper 2002-4455, AIAA Guidance, Navigation, and Control 
Conference, Monterey, CA, Aug 2002. 

9. Chen, D.T., Saraf, A., Leavitt, J.A., and Mease, K.D., "Performance of Evolved 
Acceleration Guidance Logic for Entry (EAGLE)," paper 2002-4456, AIAA 
Guidance, Navigation, and Control Conference, Monterey, CA, Aug 2002. 

10. Shtessel, Y., Zhu, J., and Daniels, D., "Reusable Launch Vehicle Attitude Control 
using a Time- Varying Sliding Mode Control Technique," paper 2002-4779, AIAA 
Guidance, Navigation, and Control Conference, Monterey, CA, Aug 2002. 



11. Johnson, E., Calise, A., and Corban, J.E., "A Six Degree-of-Freedom Adaptive Flight 
Control Architecture for Trajectory Following," AIAA-2002-4776, AIAA Guidance, 
Navigation, and Control Conference, Monterey, CA, Aug 2002. 

12. Doman, D., Leggett, D., Ngo, A., Saliers, M, and Pachter, M, "Development of a 
Hybrid Direct-Indirect Adaptive Control System for the X-33, AIAA-2000-4156, 
AIAA Guidance, Navigation, and Control Conference, Denver, CO, Aug 14-17, 
2000. 

13. Hodel, A. S., and Callahan, R., "Autonomous Reconfigurable Control Allocation 
(ARCA) for Reusable Launch Vehicles," paper 2002-4777, AIAA Guidance, 
Navigation, and Control Conference, Monterey, CA, Aug 2002. 

14. Zhu, J., Lawrence, D., Fisher, J., Shtessel, Y., Hodel, AS., and Lu, P., "Direct Fault 
Tolerant RLV Attitude Control— A Singular Perturbation Approach," paper 2002- 
4778, AIAA Guidance, Navigation, and Control Conference, Monterey, CA, Aug 
2002. 

15. Results of Phase 2 of Advanced Guidance and Control Project Testing, NASA 
Technical Memorandum, to be published.