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6.1991-2820

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GENERAL ADAPTIVE GUIDANCE USING NONLTNEAR PRO
CONSTRAINT SOLVING METHODS (FAST)
Lisa Skalecki* and Marc Martin**
Boeing Defense and Space Group
Seattle, Washington
objectives and constraints are satisfied, and
modular software that can be used for a wide
variety of vehicles and mission phases without
recoding the on-board algorithm.
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820
Abstract
An adaptive, general purpose, constraint solving
guidance algorithm called FAST (Flight
Algorithm to Solve Trajectories) has been
developed by the authors in response to t h e
requirements for the Advanced Launch System
(ALS). The FAST algorithm can be used for all
mission phases for a wide range of Space
Transportation
Vehicles
without
code
modification because of the general formulation
of the nonlinear programming (NLP) problem,
and the general trajectory simulation used to
predict constraint values. The approach allows
on board re-targeting for severe weather and
changes in payload or mission parameters,
increasing flight reliability and dependability
while reducing the amount of pre-flight analysis
that must be performed.
The algorithm is
described in general in this paper. Three degree
of freedom simulation results are presented for
application of the algorithm to ascent and reentry phases of an ALS mission, and Mars
aerobraking. Flight processor CPU requirement
data is also shown.
Currently, there are no such systems operating
in the field.
However, in response to the
requirements for the Advanced Launch System
(ALS), an adaptive guidance algorithm called
FAST (Flight Algorithm to Solve Trajectories) has
been developed by the authors. The algorithm
allows the vehicle to adapt to winds and
atmospheric perturbations in flight, as well as
autonomously retarget for changes in payload
prior to launch.
FAST combines nonlinear
programming with the shooting method for two
point boundary value problems to calculate a set
of command profiles which satisfy the mission
constraints.
At each guidance update, the on
board computer predicts the remainder of the
mission by explicitly integrating the trajectory,
and solves a nonlinear programming problem if
p y of the mission constraints are violated. It
has been coded such that it is efficient, general
and modular.
The FAST algorithm has been
successfully used for closed loop guidance
analysis for single and multi-stage vertical and
horizontal take-off vehicles, low L/D r e -e n t r y
and aerobraking.
Introduction
Current space transportation systems require
extensive pre-flight analysis in order to generate
and validate nominal trajectory profiles and
guidance commands for a given mission. Often,
multiple sets of command profiles must be
generated pre-flight and stored in the on-board
computer to ensure that the mission will not be
delayed d u e to environmental conditions,
contingencies, or minor last minute changes in
mission objectives and constraints.
This
approach is operationally slow, complex and
costly .
Prior applications of nonlinear programming
techniques to developing adaptive, autonomous
guidance algorithms focused on optimization and
concentrated on developing code for specific
missions
and vehicles.
Reference
1
demonstrated that the NLP2 optimization
package (Reference 2) could be used to
determine closed loop guidance commands for a
low L/D re-entry vehicle subjected to severe
atmospheric dispersions and winds. That work
dealt primarily with designing a nominal reentry command profile based on mission and
range safety constraints, and developing a multilevel optimization strategy which defines a
series of problems to be solved by the NLP2
optimization package.
The computational
requirements imposed on the flight processor by
such an approach, however, are too large for
near term application. In addition, while the
NLP2 optimization package has been applied to
An alternative approach is to make the vehicle
more autonomous so that the nominal commands
can be targeted and corrected by the vehicle's
on-board computer, both prior to and during
flight. This level of autonomy can be provided
by an integrated guidance and targeting
capability that utilizes trajectory optimization or
constraint solving techniques to tailor the
nominal commands such that the mission
* Specialist Engineer, Member AIAA
**Senior Engineer, Member AIAA
Copyright 0 1991, American Institute of Aeronautics
and Astronautics, Inc. All rights reserved.
1843
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820
closed loop guidance for other missions and
vehicles (Reference 3). separate sets of code had
to be developed and maintained for each
because the code was not generalized to handle a
wide variety of vehicles or missions.
Analysis showed that using constraint solving
only, rather than optimizing an objective
function subject to constraints, resulted in
feasible CPU requirements as well as improved
targeting accuracy for low L/D re-entry.
The
FAST constraint solving guidance algorithm was
then developed based on the NLP approach of
Reference 1 with the additional requirements
that the code be:
1) modular and general such that it can be
applied to many types of vehicles and
missions without recoding
2) computationally efficient such that is is
feasible for real time implementation on
a currently available flight processor
3) robust such that it can be applied to
problems such as retargeting for weather,
changes in payload, inclination etc.,
without extensive pre-flight analysis.
The FAST guidance algorithm currently offers
advantages
not
only
over
other NLP
implementations, but also over other guidance
approaches such as calculus of variations (COV),
finite element methods, and collocation.
COV
approaches, such as the GUIDE algorithm
described in Reference 4, provide the capability
to efficiently generate optimal trajectories for
closed loop guidance.
They are, however,
limited in that they must be explicitly recoded
for each application and mission.
While
symbolic manipulation algorithms can be used to
make the process more efficient, an "expert"
level of human effort is required and separate
algorithms would have to be coded for each
mission as well as each phase of the mission
(ascent, re-entry).
Another optimal control approach based on
finite element
methods and the weak
Hamiltonian principle is described in Reference
5. While it was demonstrated that the weak
Hamiltonian approach could accurately and
efficiently
s o l v e trajectory
optimization
problems, again, the method implies that
separate sets of code must be developed for each
particular problem.
Another disadvantage is
that the weak Hamiltonian formulation has not
yet been developed to the extent that it can
handle inequality constraints.
solution in the presence of large dispersions.
However, work to date has shown that they are
too computationally demanding for near term
guidance application.
Improvement in flight
processor
speeds
and
s p a r s e nonlinear
programming methods are necessary before
such methods become feasible for real time
application.
The key to developing cost effective, adaptive
and autonomous guidance algorithms is that
they be general as well as efficient. The cost of
software design is not minimized if the software
has to be recoded for new vehicles, missions, or
such simple changes as new constraints. Nonlinear programming shooting methods have
traditionally been CPU intensive and therefore
not considered feasible for real time application.
The IUS Gamma Guidance algorithm (Reference
7), which uses nonlinear programming for
exoatmospheric
g u i d a n c e , uses
analytic
relationships rather than the shooting method to
evaluate the sensitivity of the constraints to the
command variables.
The shooting method is
used during the iterative steps taken by t h e
algorithm. While this approach works well for
exo-atmospheric application, it is difficult to
derive general and accurate analytic sensitivity
matrices for endo-atmospheric flight. Recent
improvements in flight processor speeds have
eliminated the need for this simplification,
e
enabling shooting methods to become feasible.
I n this paper we present a nonlinear
programming, constraint solving algorithm that
uses the shooting method and is feasible for on
board guidance with currently available flight
processors. The algorithm is easily applied to a
variety of missions and vehicles.
The key to
developing this algorithm was designing an
efficient, general trajectory simulation a n d
modularizing
the software.
This was
accomplished by using modern programming
languages and techniques, and considering t h e
implications of
flight processor timing
requirements during algorithm development.
FAST Guidance Algorithm Overview
The FAST adaptive guidance algorithm can be
used to solve linear and/or nonlinear, equality
and/or inequality constraints imposed at specific
points or over regions of flight. The algorithm
essentially has three components:
1) Constraint Solving Non-Linear Programming
Algorithm
2) General 3 DOF Vehicle Simulation
3) Guidance Executive Logic
Collocation methods such as those described in
Reference 6 are promising, as they can be
generalized, and can reliably converge to a
1844
Inputs to the guidance algorithm required prior
to flight are obtained from a mission data load,
which defines the current mission objectives and
constraints, and the on-board database, which
contains vehicle specific data such as
aerodynamic characteristics, etc. During flight,
the guidance algorithm requires the current
vehicle state to initialize the guidance
simulation.
This includes the current time,
position, velocity, propellant levels, and
command values.
Position and velocity i s
obtained from the navigation system while
current propellant levels are estimated based on
the number of engines operating.
Command
values (such as the position of flaps, etc) are
obtained from other sensors. Output consists of
the table of guidance commands, which is used
by the control system.
The constraint solving algorithm is loosely based
on a subroutine in the NLP2 optimization
package which is used to find a feasible point
before optimizing. The problem is to solve for
the n command variables u such that the m
constraint equations:
Ce ( x, u, t ) = 0
Ci ( x, u, t ) 2 0
(Equality constraints)
(Inequality constraints)
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820
are satisfied, where x is the state of the vehicle
and t is time.
The constraint values are predicted using an
explicit 3 degree of freedom trajectory
simulation with a 4th order Runge-Kutta
integrator, which has been generalized to allow
application to a wide variety of environments
and vehicles.
The environmental models allow
general oblate planet models, atmospheres, and
winds to be included in the guidance trajectory
predictor.
The vehicle models allow multiple
stages, multiple engines,
and
complex
descriptions of the aerodynamic force a n d
moment coefficients. The mission is simulated
as a series of events, which represent changes in
the environmental or vehicle definition. A static
moment balance option, which gimbals the
engines to balance the aerodynamic moment in
the pitch and yaw planes, increases simulation
accuracy for non symmetric configurations.
Vehicle attitude may be specified using inertial
euler angles, relative euler angles, o r
aerodynamic angles.
The guidance executive logic includes the code
used to read and process the guidance input file,
which models the on-board database and
mission data load, and controls communication
between the guidance algorithm and the onboard computer.
The algorithm makes minimal assumptions on
the vehicle characteristics, steering command
profiles, mission objectives or constraints. These
parameters are obtained either from the onboard database or /mission data load, which can
"be standardize
to p r o v i d e operational
efficiency.
Bas'cally, the modular guidance
approach is similqr to the concept of a fighter
pilot loading a tape of his flight plan - he doesn't
need to remove and reprogram his on-board
computers. The mission data load (information
that changes depending on mission or day of
launch) is minimized because the vehicle would
be able to autonomously target the initial flight
profile on-board prior to launch from a set of
standard nominal command profiles stored in
the on-board database.
3
The algorithm can be applied to a wide variety
of vehicles and missions because of the
capability to define variables, equations, and
tables within an on board database or mission
data load. A standard equation reader has been
built into the algorithm, with multidimensional
table lookups treated as standard functions.
Therefore, the basic trajectory sirnulation
modelled within the algorithm can be easily
extended with user defined constants, variables,
and integrals.
Figure 1 shows a portion of the guidance input
file used to simulate the mission data load and
on-board database for closed loop computer
simulations, to illustrate how easy it is to define
the mission and the constraints.
The guidance
command tables are initialized in the COMMAND
section.
Inertial pitch angle (inpitch) and
inertial roll angle (inRoll) are standard
commands for launch vehicles.
Anything that
makes sense and has an effect on the vehicle's
flight can be commanded.
The
sign
designates commands that the guidance can vary
to satisfy the constraints, while an "=" sign
designates a fixed value that cannot be altered.
The mission constraints are defined in the
CONSTRAINT section.
Constraints can be
standard trajectory variables or user defined
Since the algorithm can predict the remaining
trajectory, commands are generated to the e n d
of the mission or phase, resulting in a table of
commands rather than simply instantaneous
commands (See Table 1). This table is modified
during each guidance update if any constraints
are not satisfied. The control system then can
get instantaneous commands by interpolating
from this table. This feature aids in increasing
flight reliability, since a set of converged
guidance commands is always available for the
entire mission.
"-"
1845
varied (eg. drop booster weight at "dropBoost"
event), and are designated by "+" signs on the
graphics. The inertial pitch angle is commanded
at 12 "nodes" along the trajectory, while the
inertial roll angle is commanded at only 5 nodes.
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820
variables. The example shown in Figure 1 is for
a vehicle delivering a payload to a 28.5 degree
orbit with perigee at 80 nautical miles. Note
that this is an input file, and modification or
recompilation of the guidance algorithm is not
required to create new variables, events, or
constraints.
The retargeted trajectory satisfies all of the
mission constraints, and the vehicle is ready to
be launched.
The algorithm used 3.04 CPU
seconds to perform the pre-launch targeting
shown in Figure 2, assuming a MIPS R3000 flight
processor with a 20 MHz clock rate.
The FAST algorithm is written entirely in
Modula-2 (Reference 8), a modern programming
language based on Pascal. Use of Modula-2 has
allowed the on-board database and mission data
load to be modelled in a format that is easy to
read and understand (See Figure l), as well as
allowing a general, yet efficient, high fidelity
trajectory simulation to be developed. Modula-2
is very similar to Ada, and is, in fact, often used
as an Ada training tool.
This feature will
simplify the eventual conversion of the
algorithm to Ada for implementation on a flight
processor.
The benefit of using Modula-2 for
algorithm development is that it is easier to
learn than Ada and does not have the slow
compilation or overhead of Ada, which allows
rapid prototyping on time shared computers.
The results of guidance dispersion analysis on
the two stage ALS launch vehicle ascent
trajectory are tabulated in Table 2. The nominal
reserve propellant for this case is 12699 lbs,
with approximately 5200 lbs allocated for
dispersions (the rest is for engine out).
The
vehicle follows open loop commands during first
stage flight.
The FAST guidance algorithm
performs updates every 20 seconds after
booster separation.
The guidance injection accuracy requirements
for the generic ALS launch vehicle are:
To demonstrate the FAST adaptive guidance
algorithm, results of three degree of freedom
closed loop simulations are presented for a
generic ALS launch vehicle, a low L/D re-entry
vehicle and an aerobraking vehicle.
The
algorithm has also been successfully applied to
single stage to orbit (SSTO) vertical and
horizontal take-off.
apogee
perigee
inclination
+/- 1 nm
+/- 1 nm
+/- 0.1 degree
Rote that the algorithm is relatively insensitive
to the dispersions, resulting in small injection
accuracy e r r o r s and r e s e r v e propellant
requirements within the allocated margin,
Therefore, the overall GN&C injection accuracy
error will be primarily due to navigation errors
(particularly errors in knowledge of the engine
cut-off velocity), which cannot be corrected by
guidance.
ALS Ascent
The closed loop simulation that incorporates t h e
FAST guidance algorithm includes interactive
graphics capability.
Figure 2 shows a screen
dump of the algorithm in target mode for ALS
ascent application. Prior to launch, the vehicle's
on-board computer would be able to retarget the
initial standard optimal trajectory stored in the
database for current weather conditions or
changes in payload, etc.
Figure 3 shows the detailed results from the 100
closed loop simulations through winter dispersed
GRAM (Global Reference Atmospheric Model)
winds and atmospheres.
The FAST guidance
algorithm is given only the monthly mean wind
and atmosphere profile in order to predict the
trajectory. The actual vehicle flies through the
dispersed profiles.
Note that the resulting
apogee, perigee and inclination errors are well
within the guidance tolerances.
While q-alpha
and q-beta were not imposed as guidance
constraints for this example, their resulting
maximum values were monitored and plotted.
The ALS vehicle used for this example can
tolerate q-alphas near 6500 p,sf-deg.
The constraints imposed are listed on the left
side of the screen. When a constraint is satisfied
a "*" is shown after the constraint value. The
number of function evaluations, which includes
evaluations to form the Jacobian matrix, is
shown above the constraint values. The Jacobian
is the matrix of sensitivities of the constraints to
perturbations in the command variables and is
used by the constraint solver to update the
command tables.
The resulting reserve propellant is shown in
Figure 3 to illustrate that the constraint solver
does not drive the solution away from the
optimum.
Thus, adding optimization of
Events are used to define the steering command
nodes as well as points along the guidance
simulated trajectory where input data is to be
1846
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820
parameters such as final reserve propellant
would only increase the amount of CPU used per
update, with negligible impact on the final
injection accuracy and actual reserve propellant.
Optimization would only serve to improve t h e
pre-launch or on-orbit targeting capabilities, and
will eventually be added to the FAST algorithm
for these purposes only.
Reference 1 where the third phase angle of
attack command was not used until the vehicle
was actually flying in the third phase. The use
of nodes, as done here with the FAST algorithm,
rather than phases of constant commands, as
done in Reference 1, allows greater flexibility in
defining a strategy.
During ascent, guidance update rates are on the
order of 20-30 seconds. Table 2 and figure 3
illustrate that the maximum CPU used for each
dispersed case is well below 2 seconds. The CPU
intensive guidance updates occur early in the
ascent phase where the atmospheric and wind
effects have the most impact and the predicted
trajectories are the longest. A two second delay
in obtaining the updated guidance command
tables has a negligible effect on the final
accuracy since any errors incurred due to t h e
delay are corrected in later updates. To verify
this, the closed loop simulation was modified to
implement a computer delay such that the
updated guidance commands could not be used
until the CPU time required for processing h a d
elapsed.
There was no significant change in
orbital injection accuracy, CPU requirements, or
constraint values.
The constraints imposed on the re-entry
problem are the aeromaneuver terminal latitude
and longitude error in nautical miles at 15,000 ft
altitude, as well as the maximum bank angle
rate. Figure 4 shows two sets of targeting errors
for 100 closed loop simulations through GRAM
dispersed winter winds and atmospheres. Both
sets use vehicle atmospheric angle of attack and
bank angle command profiles as guidance
variables. For the first case, the guidance uses
monthly mean wind and atmospheric data, and
is able to guide the vehicle to within 1.5 nm of
the target. The second case utilizes a ground or
aircraft based lidar system which measures a n d
uplinks the eastward and northward wind
components from 0 to 60,000 f t altitude. With
the lidar system, the FAST guidance algorithm is
able to obtain pinpoint accuracy (within 0.02 nm
122 ft) for all 100 cases.
-
Low L/D R e - e m
e
The constraint solving algorithm was also
applied to re-entry of a generic, low L/D (-0.2)
vehicle. Re-entry typically consists of a de-orbit
burn to t h e proper re-entry orbit, an
aeromaneuver phase, and a parachute or other
terminal guidance phase.
The goal is to
minimize the aeromaneuver targeting error so
that recovery operations are simplified, reducing
the operating cost of the system.
The FAST guidance algorithm can also be applied
to high L/D re-entry.
For this application,
however, the bank angle should not be directly
commanded due to its highly nonlinear nature.
An alternate command, such as the vertical or
horizontal component of the L/D, is more linear
and therefore would be more reliable.
Mars Aerobraking
The FAST algorithm has also been applied to an
aerobraking Mars mission with a vehicle L/D of
0.5.
The approach trajectory is a hyperbolic
orbit with C3 (twice the specific mechanical
energy) of 50 k m 2 / s e c 2 . The targeted final
orbit is highly elliptic (3644 km by 37183 km
radius). The imposed constraints are velocity at
periapsis to give the correct apoapsis, the final
inclination (30 deg), the final longitude of
ascending node (0 deg), and the maximum bank
rate (30 deg/sec). The bank angle at 18 nodes is
used as the guidance command, with a fixed
angle of attack.
During the aeromaneuver phase, the guidance
commands consist of the bank angle and angle of
attack at various nodes along the trajectory.
Low L/D, precision re-entry is a much more
difficult problem than ascent.
As the vehicle
approaches the target, it loses control authority
(the bank angle and angle of attack become less
effective) and experiences severe atmospheric
and wind perturbations. This is in contrast to
the ascent case, where atmospheric and wind
perturbations are less significant since the
vehicle exits the sensible atmosphere as it
approaches the target.
Figure 5 shows resulting trajectories for flight
through 5 different atmospheres including t h e
Viking1 and Viking2 measured atmospheres.
The guidance has information only on the mean
(Marsnhme) atmosphere.
The resulting delta-V
required to correct the final apoapsis and
periapsis are shown as well as the resulting
inclination errors, argument of periapsis errors
Therefore, the guidance commands at each node
are not always active. Instead, commands near
the end of the trajectory are reserved for use
during later updates, so that corrections made
during upper atmospheric flight do not saturate
the commands near the end of the trajectory.
1847
ascent, re-entry and aerobraking missions for a
variety of space transportation vehicles.
The
same algorithm was used for all of the
applications, with no recoding required in order
to perform the analysis, demonstrating that a
single guidance algorithm can be used for all
mission phases as well as for a wide variety of
vehicles.
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820
and longitude of ascending node errors.
Since
there were no specified accuracy requirements
when this study was performed, the constraint
tolerances were arbitrarily set at 50 m/sec, 1
deg and 1 deg respectively for velocity at
periapsis, inclination and longitude of ascending
node constraints.
Figure 6 shows results of 100 closed loop
simulations through dispersed winds and
atmospheres generated using the MarsGRAM
(Reference 10) model for a low density day. The
statistical mean and standard deviation,
assuming a normal distribution, are also shown
for each parameter.
The CPU data presented for applications of the
FAST guidance algorithm demonstrates that
nonlinear programming shooting methods are
feasible
for
current
flight
processor
implementation.
Restrictive approaches that
involve using analytic sensitivity matrices are no
longer advantageous. In view of the historically
rapid improvement in processor speed, CPU
requirements will become even less of an issue
in the years to come. The benefits to operational
efficiency and in-flight reliability of a general
approach such as the FAST algorithm are too
significant to ignore.
T h e ability to
autonomously and quickly perform pre-launch
targeting within the vehicle's flight computer
simplifies the ground operations (no need to
upload a new solution since the computer can
generate the retargeted solution by itself) and
increases
the
launch
reliability
and
dependability (the vehicle can retarget for actual
environmental conditions).
The resulting inclination and longitude of
ascending node errors are well within t h e
specified tolerances of 1 deg.
While the
argument of perigee was not constrained, as
there was insufficient control authority using
only the bank angle profile for guidance
commands, the results show that 'the. errors are
at least bounded.
Further research is required
to determine an approach for actively
constraining the argument of perigee.
The resulting delta V's to correct the final orbit
are relatively small, indicating that the FAST
guidance algorithm is a good candidate for
application to aerobraking flight. The maximum
CPU used per run is also plotted, again assuming
a MIPS R3000 processor with a 20 MHz clock
rate. The guidance update rate varies from 5 to
20 seconds during the aeromaneuver phase.
While 2 CPU seconds may seem to be rather
large for an update rate of 5 seconds, it is
important to keep in mind that processors
historically double in speed every 18 months on
the average. Figure 7 shows the historical trend
for MIPS CMOS processors and VAX CMOS
processors.
CMOS processors do not r e q u i r e
cooling, so their performance can be related to
flight processor performance.
0
However, while the shooting method works well
when the initial estimate of commands is close
enough to the actual solution, and the constraints
are well behaved, it is difficult to apply to
problems where a reasonable estimate of the
solution is not available. An example of this is
engine out during ascent. Unless multiple initial
command profiles are stored pre-flight, or some
correction factor is developed and applied to the
stored profile in order to force the initial guess
to be in the neighborhood of the final solution,
the algorithm may not be able to converge. A
solution to this problem is to utilize multiple
shooting, which is more capable of solving
problems with poor initial estimates, or highly
nonlinear constraints.
This would further
increase the reliability and autonomy of the
algorithm. Multiple shooting takes advantage of
knowledge of the form of the state vector as a
function of time, which, for guidance application,
can be taken from the previous update.
The
application of multiple shooting to guidance is
the subject of another paper by the authors
(Reference 11).
Another advantage to using the FAST constraint
solving guidance algorithm for missions such as
this is that it can also be used for re-entry.
Thus, the same algorithm can be used for
landing on Mars. This reduces the amount of on
board software that must b e coded and
validated. The only additional data required is
defining the target conditions, constraints and
commands that should be used to guide the
vehicle during re-entry.
These are all part of
the mission data load.
Conclusion
The FAST constraint solving, adaptive guidance
algorithm has been successfully applied to
1848
References
1.
Cramer, Bradt, and Hardtla, "NLP Re-entry
Guidance: Developing a Strategy for Low
L/D Vehicles", AIAA-88-4123-CP, AIAA
Guidance,
Navigation
and
Control
Conference, August 1988.
2.
Betts, John T., "Nonlinear Programming
Algorithm NLP2 Documentation", The
Aerospace Corporation, April 1987.
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820
Command tables at time = 24 seconds
3.
Cramer, Bradt and Hardtla, "Launch
Flexibility Using NLP Guidance and Remote
Wind Sensing", AIAA-90-3330-CP, AIAA
Guidance,
Navigation
and
Control
Conference,. August 1990.
4.
Tylee, and Hardtla, "Adaptive Guidance for
Future Launch Vehicles", AIAA-88-4124CP, AIAA Guidance, Navigation and Control
Conference, August 1988.
5.
Hodges, Calise, Bless and Leung "A Weak
Hamiltonian Finite Element Method for
Optimal Guidance of an Advanced Launch
Vehicle", American Control Conference
Proceedings, 1989.
6.
Bradt, Jessick, Hardtla, "Optimal Guidance
for Future Space Applications", AIAA-872401-CP, AIAA Guidance, Navigation and
Control Conference, August 1987.
7.
Hardtla, John, "Gamma Guidance for the
Inertial Upper Stage (IUS)", AIAA-78-1292,
AIAA GN&C Conference, 1978.
8.
Wirth, Nicklaus, "Programming in Modula2", 3rd edition, Springer-Verlag, New York,
1985.
9.
time
inpitch
inRoll
25.0
30.0
68.2
11 2.7
155.9
180.3
205.4
229.7
251 .O
271.7
292.4
313.2
333.9
-17.4
-20.8
-46.7
-69.9
-80.0
-79.4
-87.1
-92.8
-96.8
-99.6
-103.2
-1 06.4
-1 09.6
-90.9
-91.o
-91.3
-91.6
-91.6
-91.6
-91.7
-91.7
-91.7
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-91.8
-91.8
-91.9
Table 1 : Sample FAST Comn md Tables
On Board Database:
(
- means command t h a t g u i d a n c e c a n v a r y )
COMMAND
0
DEFINE i n P i t c h
AT f i r s t
AT c l e a r T o w e r
AT d r o p B o o s t
AT time230
AT d r o p F a i r i n g
AT time350
AT time400
AT t i m e 4 2 5
AT l a s t
DEFINE inRoll
AT f i r s t
AT c l e a r T o w e r
AT d r o p B o o s t
AT d r o p F a i r i n g
AT l a s t
Justus, Fletcher, Gramling and Pace, "The
NASAMSFC Global Reference Atmospheric
Model", NASA Contractor Report 3256,
1980.
=
0.000000EO
=
0.000000EO
- 74.873666
- 70.862320
- 81.765260
- 90.932520
- 97.843471
- 101.17229
- 103.89821
=
- 180.00000
- 180.00000
-91.217530
- 91.350888
- 91.547421
--
=
-
Mission Data Load:
CONSTRAINT
AT l a s t
AT l a s t
AT l a s t
AT l a s t
AT l a s t
10. Johnson, James, Justus and Chimonas, "The
Mars Global Reference Atmosphere Model
(Mars - GRAM)", Technical Report for NASA
Grant No NAG8-078, October, 1989.
coreprop
>
5000
height
80
0
inFlight
=
ink1
= 25766.0
inclination =
28.5
AUXILIARY
DEFINE h e i g h t
DEFINE qAlpha
11. Skalecki, L., and Martin, M., "Application of
Multiple Shooting to Closed Loop Guidance",
I A F -9 1 - 3 2 6 , IAF 42nd International
Astronautical Congress, 1991.
=
=
TOL
TOL
TOL
TOL
TOL
=
=
1
0.001
=
0.001
=
0.01
0.001
=
( r a d i u s - e q u a t o r b d ) /6076.1155
dynPres * a t t a c k
Figure 1: Sample Database and MDL
1849
FLIGHT
function
final
22
........................
,
(clearTower)
oostProp
coreprop
-
400000
21745.32*
25766.00 *
i n c l i n a t i o 28.50000*
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820
................ ,................500000
Retargetedbrajectory
f i n a l t r a j e c t o r y with outputs..
Figure 2: ALS Ascent Targeting
*
Table 2: ALS Ascent
1850
.
Max CPU (sec) vs Run I D
150
200
250
Reserve P r o p ( a s ) vs Run I D
,
:
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820
1080
2060
3040
,
j
.
.
j
;
i
i
j
4020
P e r i a e e E r r o r vs ADOUM E r r o r h m )
150
200
250
I n c l i n a t i o n E r r o r (deg) vs Run I D
- 0.25
0
150
0.25
U
2 00
250
AM Dispersions
WITH BANK AND ANGLE
OF ATTACK CONTROL
WITH BANK, ANGLE OF ATTACK
CONTROL, AND LIDAR
2
2
s i
h
h
E
Y
Y
L2
E o
t
1
o
t
longitude error (nm)
longitude error (nm)
erornanuever
Figure 4: LOW LI
1851
Guldance knows
Marsnhme,
Vehlcle flles through:
-..-...
MARSNHME
COSPARVL
xrmmm
100
VIKING1
...... VIKING2
3M)
200
COSPARVH
TIME (sec)
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820
I
!
I
DeltaV IncErr ArgPerErr
(m=)(deg)
-200
l i
........... 1......................
100
200
i .........
300
100
TIME (sec)
LonAsc
NCdeER
6%)
(deg)
MARSNHME
17.3
-.008 -.018
-.WOO5
COSPARVL
125.2
,139
-5.6
,056
COSPARVH
248.7
.i49
4.5
,015
,042 1.4
,002
VIKING1
89.6
VIKING2
40.5
-.024
-.0004
-.8
200 300
TIME (sec)
Figure 5: Mars Aerocapture Guided Trajectories
C3 = 50
I1A..................I
.................. i
RG PFR ERROR : Mean
2
.................i..................
...... .....
-2M)oo
125
150
175
-0.051, Slarna = 0.643 deg
.....
I
........... ...................
I
RUNID
125
150
RUNID
175
39 deg
150
..................
L
125
150
I
175
125
5 deg
150
175
RUN
ID
MAX GPU : Mean = 1.99. Siarna = 0.456 sec
3 ....................................
i................. j,..................
.................. .................. :................................
:
0
125
1852
150
o
:
0
RUNID
Downloaded by UNIVERSITY OF NEW SOUTH WALES (UNSW) on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.1991-2820
40
30
20
10
Introduction Date
.*
lntr
1853
n
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