Baseline guidance and navigation strategy for an ecliptic projection of the Encke flyby mission consider solar electric propulsion stage parameters in generating optimized and targeted trajectory control. Results show the Encke relative approach error to be dominated by ephemerical uncertainties, particularly the velocity components

Hong, P.

English

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SYSTEM DESIGN IMPAm OF GUIDANCE AND 
NAVIGATION ANALYSIS FOR A SEPS 1979 
ENCKE FLYBY 
Philip Hong 
Martin Marietta Cwporatbn 
Denver, Cobmdo 
This is a report on a study that Martin Marietta did for Rockwell, who in turn was doing a 
feasibility study for the solar electric propulsion stage (SEPS). The emphasis was on system 
feasibility, and we tried to  merge the guidance and navigation reqdrements into the total 
system. The primary emphasis :';as th2 1979 Comet Encke flyby, which at that time was 
the first proposed SEIS mission. We also looked at some system requirements for other 
missions. 
Many of the system mameters are affected by guidance and navigation requirements. The 
most important ones art thrust control authority (that is, how much additional control is 
needed in the thrust subsystem to implement trajectory corrections), thrust performance 
tolerances, thrust vector control, propulsion time, the additional time required for adjust- 
ing the trajectories, fuel requirements, guidance updates, and the types of earth-basd 
navigation and communications needed. Other parameters affected are the onboard naviga- 
tion subsystem (how good must it be, if it is indeed needed) and the type of trajectory and 
terminal errors that occur (that is, control and knowledge). Control is the dispersion of the 
actual about the reference, and knowledge is the dispersion of the estimated about the 
actual. 
The baseline mission for this particulm stage was a launch in March 1979 and encounter in 
November 1980. Figure 1 shows an ecliptic projection of the flyby. 
L - LAUNCH POS1110N 
E - INCOUNTER I L  +Sa2 DAYS1 
Figure 1. Ecliptic projection of the 1979 earth-to-Encke flyby. 
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https://ntrs.nasa.gov/search.jsp?R=19760003098 2020-03-22T19:27:48+00:00Z
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One of the fm things we did was to take the mission analysis results that Rockwell gen- 
erated and produce a more realistic, optimized and targeted trajectory in which we imposed 
reasonable control policies. Listed below are the mission data: 
e 
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Launch date-March 25,1979 
Arrival date-November 7,1980 
Launch VHE-7.18 km/s 
Initial mas4-1988 kg 
Initid powm-2 1 kW 
Housekeeping power4650 kW 
Thruster efficiency44 percent 
Propdsion time-523 days 
Coast time-Initial, 64 days; fmal, 5 days 
Arrival VHP-3.16 km/s 
Arrival RCA-1 lo0 km 
Arrival mas-1456 kg 
We employed constant cone, clock, and thrust over fixed time segments, and we imposed 
whatever constraints were necessary; for example, the final coast time of 5 days was the 
minimum acceptable for science. There was also an initial coast and a total thrust time of 
523 days We arrived at 3 km/s at 1 100 km closest approach The encounter was 30 days 
prior to perihelia for this particular study. 
The baseline guidance and navigation strategy-and we are talking mostly about the approach 
phase now-assumed simultaneous or continuous coverage from three Deep Space Network 
(DSN) stations over the last 40 days. We assumed an onboard optical system similar to 
Mariner-IO. Optical or onboard observations were taken twice per day starting at 30 days 
prior to.encounter, and each optical measurement contained Encke and three identifiable 
stars. We estimated the vehicle state, thrust biases, and the Encke ephemeris, and we con- 
sidered the process noise that is generated by the thrusters. Guidance 111 'ates were per- 
formed every 4 days, and we assumed that we could control the trajectory just by biasing 
the nominal thrust controls. The baseline strategy was not intended to meet all the system 
requirements, but it was our first try at it. 
The dynamic and measurement error sources that we assumed are listed below: 
0 Dynamic error sources 
a. 
b. 
Launch error - Position, 3 km; velocity, S m/s; mass, 1 kg 
Thrust bias -Magnitude, 2.2 percent; direction, 0.035 rad 
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c. Thrust noise - Magnitude, 3.5 percent; conelation time, 5 days: direction: 
0.010 rad; correlation time, 3 hours 
Encke - Position, 10,OOO km; velocity, lo00 km/day d. 
0 Measurement emr sources 
a. 
b. 
c 
d. 
DSN station location - Spin radius, 1.5 m; longitude, 3.0 m; height, 10.0 m 
Doppler noise - Two-way, 1 mm/s; three-way, 0.1 mm/s 
Range noise -Tw*way, 3 m; three-way, 10 m 
Optical - Resolution, 30 arcseconds; center finding, 10 km 
S E E  is launched with the Titadentaur,  so we had typical insertion uncertainties. The 
thrust uncertainties consisted of both bias and noise. We estimated the bias and the noise, 
which has a timevarying component, hence the correlation times associated with them were 
considered. The values listed are for a single thruster; there are eight operating thrusters for 
this vehicle. The a priori error for Encke was assumed to be very pessimistic, although at 
that time it was a reasonable uncertainty of l0,OOO km and IO00 km per day, or about 10 
Typical station location uncertainties were assumed. Since we used simultaneous range and 
range rate data from earth to the spacecraft, we also included three-way uncertainties. Our 
onboard optical uncertainties consisted of an error ot 30 arcseconds noise and an uncer- 
tainty of 10 km to approximate the uncertainty between the comet's center of brigtr.:r 
and the center of gravity. 
One of the first things we studied was the approach geometry, to see if we could get an idea 
of what was happenhg. Figure 2 is a view of the last 30 dabs prior to encounter. It can be 
seen that the thrust vector is almost retrogrdde, which means Vut it is on a flat trajectory 
relative to Encke, and there is very little curvature. There is also the possibiiity of the 
thrust plume interfering with any instruments that are sensing as Encke is agproacbed. 
However, cutoff occurs at 5 days prior to encounter. The position of the earth is changing 
very rapidly both in direction and in declination, which would indicate that earth-based 
tracking of the spacecraft would be very good. On the other hand, because of the flatness 
of the trajectory, the onboard optics probably will not be as good. 
Figure 3 is a plot of the inertial position uncertainties due to the estimation of both Encke 
and SEPS. Because simultaneous data are employed, we get near-ballistic results for the 
spacecraft. However, our mboard optics just barely get below the a p.-iori level. 
Most of this is along-track error. However, a 6000-km along-track error i!: about 10 minutes 
uncertainty, and that would seriously affect pointing and slewing rate= Because the stage 
and Encke are dynamically uncoupled, the Encke relative uncertainty is basically the RSS 
of these two, which is then dominated by the Encke uncertainties. 
m / s  
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T . THRUST - 
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(10*UY) 
Figure 2. Encke ‘lyby relative approach geometry for last 30 days pior to encounter. 
As shown in faure 4, the velocity shows only fair improvement. It is still not very good, 
either that of Encke or of the stage. 
Since we found that the Encke relative uncertainties are dominated by the a priori ephemeris 
mar, we looked at a number of different a prioris and found that Encke relative uncertain- 
ties are a pr?ori sensitive, prharily in the velocity component ( f i  5).  For example, we 
found that, if we have velocity uncertainty, we will get mry good estimaticn errors 
However, if we ha;? any reasonable amount of a priori velocity uncertainty, the optics 
cannot compei t L ,  which means that the comet’s relative uncertainty remains unchanged. 
We did takr Pme covariances from Bob Farquhar and used them as our a priori. They looked 
more likr b u r  zero velocity case, although not quite as good, or about 400 km terminal 
uncer’. . Intv. 
F ~ de 6 iliustrates the magnitude of the thrust guidance corrections, that is, biases to the 
nominal thrust contrcr: policy. The biases never exceed more than 3 percent in thrust mag- 
nitude and are itregularly shaped because of our strategy. The curve could have been smoothed 
out by pk- *in * the guidance updates at different intervals and by employing a different 
control p bilcy. But in magnitude, the bias is not more than 3 percent, and in pointing, it 
is its man 2 O ,  1 u. 
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c A BEGIN O I T I C S  
E 4 0  E -30 E -20 E-10 ENCOUNTER 
Figure 3. Endre flyby approach phase baseline position uncertainties. 
A 
THRUST CUTOFF 
0.01 I I I 
E 4 0  E 40 c -10 L.10 
I E 4 0  E 40 c -10 L.10 LNCCIINTER 
I INTER 
Figure 4. Encke flyby approach phase baseline velocity uncertainties. 
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10.000 
8000 
6000 
4000 
. .  - 3 - 2000 
z 
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t - 1000 
2 800 
Y) 
Y) 
a 600 
0 
400 
200 
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BASELINE A PRIORI - 10,000 km. loo0 km/DAY 
- -  .- -~ 
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3000 km, 0 kmlDAY 
E 40  E-30 E-20 E-10 ENCOUNTER 
TRAJECTORY TIME (DAYS) 
Fgwe 5. Encke ephemeris Uncertainty. 
Figure 7 illustrates the terminal control error; that is, the error obtained after all the orbit 
determination and guidance have been employed. The shaded area is the inertial spacecraft 
uncertainty, and the total bar is the Encke relative uncertainty. We chose lo00 km as a 
guidance success zone, which is our maximum acceptable error for a successful mission. 
Obviously our baseline m i d  that by quite a bit. If we look at the effect of a priori 
ephemeris uncertainties, we could get within the success zone if we have zero velocity un- 
certainty in Encke. However, that is not a realistic case. If we assume some currently reason- 
able error, we will probably just barely make the guidance success zone. Because of the 
dominance of the ephemeris uncertainty, even if we eliminated earth-based ranging of the 
stage, the Encke relative uncertainty wovld not be affected, but the stage uncertainty would 
be. If we ever do reduce the ephemeris error down to some low level, we will still need 
earth-based ranging, and the same thing goes for simultaneous range and range rate data 
from the earth. 
The conclusions for this particular study are as fdlows: Cruise guidance and navigation 
requirements (not discussed) were minimal compared to the approach phase. The Encke 
relative approach error was dominated by the ephemeris uncertainties, particularly the 
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2.0 
1.6 
1.2 
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E -1 00 E-36 E-32 E-28 E-24 E-20 E-16 E-12 € 4  
Figure 6. Encke flyby thrust guidance corrections. 
GUIDANCE 
SUCCESS ZONE 
k -CEPHEMEAIS:  3000 km and 0 kmlDAY 
NO SIMULTANEOUS D A T A  
I I I I I I I I I 
0 km 2000 4000 6000 8000 km 
Figure 7. Encke encounter unawtaintia; (lo). 
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velocity components. The earth-bas4 trhcking was very good; however, quality three-way 
data are still needed from the DSP; >;:;ions. Optical navigation was only fair, due primarily 
to  the flat trajectory. Finally, the thrust control authority, that is, the thrust updates, were 
within acceptable tolerances. 
Table 1 lists some other missions which might drive the design of this stage, which is supposed 
to be a multimission spacecraft. and we identified a few missions which might drive the 
g,iidance and navigation subsystem design. One was the Encke flyby, because that was the first 
yoposed SEPS mission. The next was an earth+rbital mission, because of its unique char- 
acteristics. The Encke rendezvous was chosen primarily because it might place great demands 
on an onboard sensor and also because it was the second interplanetary mission. The 
Mercury orbiter was chosen because it had a high thrust acceleration at approach, which 
meant that the process noise in the thrust would dcminate this particular mission. Finally, 
we chose an outer planet mission, or an outbound mission, in this case a Phobos/Deimos 
rendemom. The data in the table are just guesses as to  what the impact might be on these 
subsystem. 
Table 1 
Mission/Subsystem Impact * 
Minion Launch 
Encke Flyby 
Earth Orbital 
Phobos/Deimos 
Rendezvous 
Flight 
Time 
(days) 
6 3c 
50-100! 
I 1 0 0  
400 
2 60 
Thrust 
Vector and 
Control Trackmg 
Earth- Approach Thrust Guidance Attitude 
M 
H - M 
 
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*(L = low, M = moderate, H = high). 
tPer one-way trip. 
If we dismiss ephemeris uncertainties for the time being, the limiting factor is the thrust 
uncertainty; that is, the noise or  uncertainty in the performance of the engines. Figure 8 
shows the closest approach uncertainty. The Encke flyby is relatively insensitive t o  thrust 
magnitude uncertainties, primarily because of the good tracking from the earth, which can 
minimize the effect of the thrust uncertainties. The Encke rendezvous in 1981, which is a 
1984 encounter, does not do as well, because the earth geometry relative to  the spacecraft 
and Encke is not as good. The Mercury orbiter, because of the high acceleration at approach, 
is ;very sensitive: to  thrust error. Of course, this means that if we have a 1000-km guidance 
success zone, we had better reduce the thrust errors considerably for the Mercury orbiter. 
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5000 I 
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CLOSEST 
APPROACH 
UNCERTAINTY t km ( 1 0 )  0 
2000 
1000 
100 
200 
X THRUST MAGNITUDE i lo l  
2 3 4 5 6 7 
100 
0 
Figwe 8. Sensitivity of encounter error to thrust error. 
The following recommendations were made and will probably be conducted in a fol1ow-on 
study: 
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Improve the small body, both comet and astroid, ephemeris determination. Part 
of this involves integrating the earth-based telescope observations of Encke with 
the DSN and onboard optics measurements. 
Reduce thrust noise level, either through hardware changes or through better 
orbit determination and measurement. 
Continue development of the simultaneous and/or differenced data types, that is, 
the quality earth-based three-way data. 
Investigate the impact of other missions and combine their requirements into a 
common spacecraft. 
Study alternate mission strategies. For example, since we d o  have thrust at the end, 
we might shape the trajectory and possibly get some curvature to minimize the 
along-track error. 
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System design impact of guidance and navigation analysis for a SEPS 1979 Encke flyby

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