A spacecraft attitude and/or velocity control system includes a controller which responds to at least attitude errors to produce command signals representing a force vector F and a torque vector T, each having three orthogonal components, which represent the forces and torques which are to be generated by the thrusters. The thrusters may include magnetic torquer or reaction wheels. Six difference equations are generated, three having the form ##EQU1## where a.sub.j is the maximum torque which the j.sup.th thruster can produce, b.sub.j is the maximum force which the j.sup.th thruster can produce, and .alpha..sub.j is a variable representing the throttling factor of the j.sup.th thruster, which may range from zero to unity. The six equations are summed to produce a single scalar equation relating variables .alpha..sub.j to a performance index Z: ##EQU2## Those values of .alpha. which maximize the value of Z are determined by a method for solving linear equations, such as a linear programming method. The Simplex method may be used. The values of .alpha..sub.j are applied to control the corresponding thrusters

Paluszek, Michael A.

Piper, Jr., George E.

NASA Technical Reports Server

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US005130931A 
United States Patent [19] [11] Patent Number: 5,130,931 
Paluszek et al. [45] Date of Patent: Jul. 14, 1992 
[54] SPACECRAm ATTITUDE AND VELOCITY 
[75] Inventors: Michael A. Paluszek, Lawrenceville; 
George E. Piper, Jr., Plainsboro, both 
of N.J. 
[73] Assignee: General Electric Company, East 
Windsor, N.J. 
[21] Appl. No.: 552,& 
[22] Filed: Jul. 13,1990 
[51] Int. (3.5 ................. .............................. B64G 1/26 
244/171 
[58] Field of Search ............................... 364/434, 459; 
244/158 R, 164, 169, 172, 171, 3.21 
~561 References Cited 
COhTROL SYSTEM 
p21 U.S. a. .................................... 3641459; 2441164, 
U.S. PATENT DOCUMENTS 
3,866,025 2/1975 Cavanagh ........................... 364/459 
4,537,375 VI985 Chan ................................... 244/171 
4,599,697 7/1986 Chan et al. .......................... 244/169 
4,758,957 7/1988 Hubert et al. ....................... 364/459 
4,961,551 10/1990 Rosen .................................. 244/164 
OTHER PUBLICATIONS ’ 
“An Advanced Spacecraft Autopilot Concept”, by 
Edward V. Bergmann et al. Journal of Guidance and 
Control, May-Jun. 1979, vol. 2, No. 3, Article No. 
Primaly Examiner-Gary Chin 
Attorney, Agent, or Firm-William H. Meise; Stephen A. 
Young; Clement A. Berard 
1571 ABSTRACT 
A spacecraft attitude and/or velocity control system 
includes a controller which responds to at least attitude 
77-1071, pp. 161-168. 
errors to produce command signals representing a force 
vector F and a torque vector T, each having three or- 
thogonal components, which represent the forces and 
torques which are to be generated by the thrusters. The 
thrusters may include magnetic torquer or reaction 
wheels. Six difference equations are generated, three 
having the form 
and 
N 
j =  1 
Ai+3 = Ti - I a,pj 
where ai is the maximum torque which the j t h  thruster 
can produce, bj is the maximum force which the j l h  
thruster can produce, and aj is a variable representing 
the throttling factor of the j f h  thruster, which may range 
from zero to unity. The six equations are summed to 
produce a single scalar equation relating variables aj to 
a performance index Z: 
6 N 
I =  1 i= 1 
Z =  - .L [Ail  - L ai 
Those values of a which maximize the value of Z are 
determined by a method for solving linear equations, 
such as a linear programming method. The Simplex 
method may be used. The values of ajare applied to 
control the corresponding thrusters. 
6 Claims, 2 Drawing Sheets 
m THRUSTERS 
https://ntrs.nasa.gov/search.jsp?R=20080004324 2019-08-30T02:19:03+00:00Z
U.S. Patent July 14, 1992 Sheet 1 of 2 5,130,931 
\ 
c/ PITCH 
20i, 20j 
FIG. 7b 
204 2ov 
\ r  
12 I 
26L 
ROLL 
FIG. IC 
-- 
-- 
20s, 2ot 
U.S. Patent July 14, 1992 
21 6 214- 
1 7 
READSTORED , b 
a i &  bi  
Sheet 2 of 2 
FORM SIX EQUATIONS 
N 
j=l 
N 
A i + 3  =Ti -C  ai, aj 
Ai = F i - C  b.. a 
j=I I J  j 
FOR i = 1,2,3 
5,130,93 1 
218 --.- 
I I 
FORMULATE COST FUNCTIONAL 
6 N 
Z =-x IAil - C a, 
i=l j=l 
4 
I GENERATE DESIRED FORCE 212-d EANDTORQUE 1 
FIG. 2 
SOLVE FOR ds USING 
A METHOD FOR SOLVING 
LINEAR EQUATIONS 
220’ 4 
APPLY ds TO 
222 THRUSTERS 
1 
SPACECRAFT ATTITUDE AND VELOCITY 
CONTROL SYSTEM 
5,130,93 1 
2 
-continued 
A;+3 = Ti- ,Z a ,p j  
N 
J =  1 
amended (72 Stat. 435; 42 USC 2457). 
BACKGROUND OF THE INVENTION 
This invention relates to the control of the thrusters 
of a spacecraft, and more particularly, to attitude and 
velocity control by the use of throttleable or pulse- 
modulated thrusters. 
Spacecraft are widely used for communications, 
earth sensing and exploration, vehicle locating, and for 
surveillance. All of these uses require that the orienta- 
tion of the spacecraft in space, and possibly its location, 
be accurately controlled. The spacecraft attitude may 
be controlled by magnetic torquers, by momentum or 
reaction wheels, or by the use of thrusters. 
Since each spacecraft at launch has a slightly differ- 
ent configuration than other spacecraft, its thrusters 
will be placed at slightly different locations relative to 
the center of gravity than in other spacecraft. Also, the 
specific impulse characteristics of the thrusters may 
differ from one to the next. As a consequence, the logic 
for controlling the thruster system is ordinarily custom- 
written for each spacecraft. During the construction 
phase for a spacecraft, it may be found to be necessary 
to alter the configuration or thruster characteristics, 
which may require costly rewriting of software. 
Control arrangements ordinarily provide torques by 
preselected combinations of thrusters. The selected 
thrusters are ordinarily located on opposite sides of the 
center of gravity. When in orbit, a spacecraft thruster 
may fail or may have a significant change in specific 
impulse characteristics. When a thruster fails, those 
combinations of torque for which the failed thruster is 
an element cannot be used. This may adversely affect or 
limit control of the spacecraft. 
A spacecraft velocity and attitude control arrange- 
25 
30 
35 
40 
- 45 
ment k desired in which a change in specific impulse of 
a particular thruster need not necessarily eliminate its 
use in controlling the spacecraft. 
The difference signals A are summed to form a single 
lo scalar equation relating variable a to a scalar perfor- 
mance index Z. The single scalar equation is solved for 
that value of a,which maximizes Z, and the thrusters are 
controIled in a manner directly related to the corre- 
sponding value of aj. 
DESCRIPTION OF THE DRAWING 
FIG. la is a perspective or isometric view of a space- 
craft including a plurality of thrusters, FIG. lb illus- 
2o trates a simplified side view of the spacecraft of FIG. 
15 
SUMMARY OF THE INVENTION 
A method for controlling the attitude and velocity of 
a spacecraft includes the steps of generating sensed 
signals representative of pitch, roll and yaw. A velocity 
error signal may also be generated. Command signals 
are generated representing force and torque vectors F 55 
and T, respectively, which are to be generated by the 
thrusters. The force vector includes mutudly orthogo- 
nal components F1, F2 and F3, and the torque vector 
includes mutually orthogonal components TI,  T2 and 
T3. When unidimensional corrections are to be made, 60 
some or most of these components may take on zero 
magnitude. Six difference equations A of the form: 
50 
and 
65 
la, and FIG. IC is a simplified side view of the space- 
craft of FIG. la; and 
FIG. 2 is a flow chart illustrating a control method 
according to the invention. 
DESCRIPTION OF THE INVENTION 
FIG. la illustrates a spacecraft which is controlled in 
accordance with the invention. In FIG. la, a spacecraft 
10 having a body 12 includes a omnidirectional antenna 
illustrated as 14 which may be used for communication 
and command, and also includes attitude sensors for 
roll, pitch and yaw, which are illustrated together as a 
block 16. Roll, pitch and yaw axes 4, 6 and 8 are associ- 
ated with spacecraft body 12. Attitude signals represen- 
tative of roll, pitch and yaw are coupled (by means 
which are not illustrated) to a controller illustrated as a 
block 18 for generating thruster control signals. A plu- 
rality of thrusters illustrated as 200-207 are associated 
with spacecraft body 12 and are connected (by means 
not illustrated) to controller 18 for being controlled 
thereby. 
FIG. 16 illustrates spacecraft 10 in simplified form, 
looking along the yaw axis. Elements of FIG. 16 corre- 
sponding to those of FIG. la are designated by the same 
reference numerals. FIG. lb is simplified, in that only 
thrusters 20i and 20j of FIG. la are illustrated, together 
with additional thrusters 20s, 201 which are not visible 
in FIG. la. Thrusters 20i, 20j, 20s and 202 when oper- 
ated together are capable of generating a torque in the 
direction of arrow 22 about a center of gravity (CG) 24. 
FIG. IC is similar to FIG. 16, and illustrates additional 
thrusters 20u, 20v which, together with thrusters 20s, 
2 0 2  are capable of creating a force for accelerating the 
spacecraft in the direction of arrow 26. Since the center 
of gravity 24 is not equidistant between the projections 
of the direction of thrust of thrusters 20s, 20t, 2Ou and 
20v, a torque will be created. Such a torque may be 
undesirable when only acceleration in a given direction 
is desired. Such a torque may be countered by operating 
thrusters 2Oh and 20k sufficiently to oppose the torque. 
Alternatively, translation may be accomplished without 
the torque by producing less thrust from thrusters 20s, 
20t than from 2Ou, 20v. 
The attitude of the spacecraft can be determined in 
any conventional manner. A method for determining 
the attitude of a spacecraft using a polar star sensor is 
described in U.S. Pat. application Ser. No. 07/511,169, 
filed Apr. 19, 1990 in the name of Paluszek. A method 
5,130,93 1 
3 4 
for determining the attitude of a spacecraft by the use of 
Doppler information measured from a ground station is 
described in U.S. Pat. application Ser. No. 07/397,939, 
filed Aug. 24, 1989 now U.S. Pat. No. 5,070,338 in the 
name of Cohen. Spacecraft velocity may also be deter- 5 
mined in any conventional manner, such as by the use of 
radar either from the spacecraft or from a ground sta- 
tion. If a ground station determines the velocity or the 
attitude, the information may be transmitted to the 
spacecraft for reception by antenna 12 and for commu- 10 
nication to controller 18. In general, attitude control 
requires that the spacecraft be torqued, and station 
keeping requires that forces be imported to the space- 
application of forces in turn may require application of 15 University Press* 19861 PP. 2*9-293. 
torque to correct for residual torques imparted by the 
thrusters. 
single scalar equation relating variable a to a scalar 
performance index Z. 
6 N (7) Z =  - Z IAjl - ,Z aj 
i= 1 I =  I 
Block 220 of FIG, represents the solving of equa- 
tion for those values of a which maximize z. The 
solution is achieved by some method for solving linear 
equations, such as a linear programming method. In 
particular, the Simplex method may be used. The Sim- 
plex method is described in standard texts, such as “NU- 
craft. As mentioned in relation to FIGS. 1b and IC, merid Recipes,” H. Press et d ~ ?  Cambridge 
as ‘lustrated by 222 Of 2* the 
values of a as determined in block 216 are applied for 
Controller 18 of FIG. 10 responds to the attitude 
signals and, as appropriate, to the velocity signals in a 
control of the thrusters to achieve the 
desired control resu1t. This requires only a proportional 
conventional manner to produce command signals rep- 20 throttling of the thrusters. If pulse-width modulation 
resenting a force vector F and a torque vector T, which is used* the ON to OFF durations are set to the 
represent the force and torque vectors which are to be required Proportion for each thruster. 
generated by the thrusters. The force vector F includes For North-South keeping for a 
mutually orthogonal components F], F~ and F ~ .  The geosynchronous satellite, to correct orbital inclination 
torque vector T includes mutually orthogonal torque 25 errors, translational forces in a North-South direction 
components Ti, T2 and T3. Naturally, depending upon be necessary. If the spacecraft is too far Noah, 
the attitude error, some or most of the components may maximum Av in a Southerly direction may be neces- 
take on zero value for all or part of a maneuver. The sary. In principle, this requires that the thrusters on the 
method illustrated in FIG. 2 shows the reading of the North face of the Spacecraft be operated to Provide 
attitude control signals as a block 210, and the genera- 30 thrust along the Pitch axis. However, differences in 
tion of vectors F and T as a block 212. thrust among the North-face thrusters, attitude errors 
and the like may result in net thrust in undesired direc- 
includes the generation of six different equations A: tions. Prior to starting the maneuver, attitude-sensing 
gyros are initialized by the use of Earth sensor data. 
35 Attitude errors sensed by the gyros during the maneu- 
ver are applied to the control arrangement, correspond- 
ing to block 212 of FIG. 2. The control arrangement 
N (2) may use a proportional-derivative algorithm, or a pro- 
portional-integral-derivative (PID) algorithm. A PID 
40 controller is described in US. Pat. application Ser. No. 
N (3) 07/459,627, filed Jan. 2, 1990 now U.S. Pat. No. 
5,025,381 in the name of Goodzeit et al. The controller 
calculates control torques T about pitch, roll and yaw 
axes which are required for stabilizing the spacecraft. 
In accordance with the invention, the control method 
N 
j= 1 A1 = F1 - Z blpJ 
6 2  = F2 - j= z 1 bzpj 
A3 = F3 - Z b3p1 
j= 1 
N 
j= 1 
(4) a4 = TI - Z alpJ 
N 
j= 1 
A s  = T2 - P a2pj 
N 
j =  1 
A6 = T3 - I a3pj 
45 Torques T are used in block 214 to generate A4, A5 and 
A6. For this particular application, the cost functional Z 
produced in block 218 of FIG. 1 has the form: 
50 
In equations 1-6, ajis the maximum torque which the 
jth thruster can produce, and relates to the force which 
the j t h  thruster can produce and its distance from the 
center of gravity. There are a total of N thrusters. The 
term bj is the maximum force which the jth thruster can 
produce. The values of aj and bj are predetermined, and 
may be established by prelaunch measurements or by 
on-orbit tests performed from time to time. Variable zy 
represents the throttle setting of the j r*  thruster, which 
may take on values ranging from zero to unity. The step 
of forming equations 1-6 is illustrated in FIG. 2 as a 
block 214. The step represented by block 214 uses val- 
ues ai and bi which are read from memory, as repre- 
sented by block 216. 
Block 218 of FIG. 2 illustrates a further step of the 
control method according to the invention, namely that 
of summing the difference equations 1-6 to produce a 
55 
6 N2 N 
Z =  - Z [Ail + .Z  a j -  ,Z aj 
i=4 J = p  J = 1  
which is generated by substituting 
N 2  3 
I ajfor  I [Ail  
j = p  i-1 
in equation 6. 
In equation 7, thrusters with indices ranging from p to 
60 N2 are oriented for thrust in the direction opposite to 
the desired AV direction. The values of a are applied to 
the corresponding thrusters, so that attitude control 
about roll and yaw axes is accomplished by throttling or 
modulating the North-face thrusters. Attitude control 
65 about the pitch axis (the AV axis) is exerted by pulsing 
ON the East and West face thrusters. 
Thus, maximizing the cost functional Z will maximize 
AV, and will minimize errors between the desired con- 
5,130,93 1 
5 6 
-continued 
A6 = T3 - I a3,nJ 
trol torques and the actual control torques. The cost 
functional equation (equation 6 or 7) is solved during N 
j =  1 each control cycle using linear programming method to 
maximize Z, and the throttle settings a, always remain 
in the range of 0 to 1. The throttle values a, are used to 
set the pulse width (or other throttle control) for each 
thruster, so that the pulse width equals IaJ, where I is 
the control period. 
advantage, in that the control algorithm which gener- 
ates the desired F and T can be common among a plu- 
rality of spacecraft, thereby achieving a cost reduction 
and an increase in effective reliability. Since only the 
thruster characteristics and their number and location 3 
relative to the center of gravity change from spacecraft 
to spacecraft, only the values of a,j and bi, need be 
changed in the equations represented by block 216 of 
these minor changes. 
be apparent controlling each thruster in a manner directly related 
to those skilled in the art. In particular, this approach 
could be used with other actuators such as magnetic 2. A method according to claim 1 wherein said ~ I V -  
torquers and reaction wheels. It could be used with 25 ing step comprises the step of applying a linear pro- 
combinations of momentum exchange devices and low gramming method algorithm for solving said scalar 
thrust thrusters. It could be used solely as part of a equation. 
change devices were used for control. In addition, pre- Progrm-g method algorithm 
defined weighting factors could be added to increase or 30 
decrease the significance of a term in the cost equation. 
What is claimed is: 
1. A method for controlling the attitude and velocity 
generating sensed signals representative of pitch, roll, 
5 
where: 
N is the total number of thrusters; 
au, azJ and are the maximum torques which the jth 
thrusters can produce about the Ist, 2nd and 3nd 
axes; 
bkbtbyare the maximum forces which the jrhthmst- 
ers can produce along the lst, 2nd and 3rd axes; 
and 
aj is a variable representing the throttle setting of the 
jth thruster, which can take on volumes ranging 
from zero to unity; 
said difference signa1s to form a singie sca- 
lar equation relating the variable a j  to a scalar 
performance index Z; 
aj which maximizes said Z, and 
to the corresponding value of said aj. 
The method according to the invention has a further 10 
2' and the logc may be reused but for 20 solving said scalar equation for a value ofthe variable 
Other embodiments Of the invention 
momentum unloading system in which momentum ex- 3. A method according to claim 2 wherein said h e a r  
a Simp1ex 
4. A method according to claim 1, wherein said sum- 
ming step forms a single scalar equation in which the 
equation defining said scalar Z includes at least the term 
of a spacecraft, comprising the steps of: 35 
N2 
from said sensed signals, generating command signals r=m J=P 
6 . yaw and at least velocity error of said spacecraft; - P IArl + P aj 
representing a force vector F, and torque vector T 
to be generated by said thrusters, said force vector 40 
F including mutually orthogonal components F1, 
F2 and F3, and said torque vector T including mu- 
tu& oflhogonal components TI, T2 and T39 Some 
or all of which said Fi, F2, F3 and TI,  T3 and T3 can 45 
from time to time take on zero magnitude; 
ence equations A of the form: 
where thrusters which indices ranging from P to N2 
are oriented for thrust in the direction opposite to 
the desired AV direction, and m= 1. 
5. A method according to claim 4, wherein p= 1 and 
N2 equals the total number of thrusters. 
6. A method according to claim 4, wherein said equa- 
tion defining said scalar Z includes, in addition to the 
term generating difference signals representing six differ- 
6 Ni 
- . Z  141 + .I aJ 
r=m J=P N 50 A1 = F1 - P blpJ 
J= 1 
the additional term 
N 
j =  1 
N 
j =  1 
N 
j =  1 
N 
j =  1 
A 2 = F 2 -  P &j 
A3 = F3 - Z b3pj 
4 = TI - P a lp j  
A5 = T2 - I aipj  
55 NI - P aj 
j =  r 
where p=N1, and thrusters having indices ranging 
from 1 to N1 do not have their thrust vectors 
aligned with a desired direction of acceleration, 
while thrusters having indices ranging from N1 to 
N2 have their thrust vectors aligned with the de- 
sired direction of acceleration. 
60 
* * . *  * 
65 


Spacecraft attitude and velocity control system

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