Relative Navigation of Multiple Spacecraft during Proximity Maneuvers

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 We he re f ocus on  t he ut ilization o f low f requency update a nd l ow c ost 
sensors, s uch a s C ommercial O ff-The-Shelve ( COTS) de vices. I n particular, t he 
spacecraft a re e nvisioned to have the a vailability of  r ange m easurements a nd relative 
attitude measurements. 
This work presents the design of a spacecraft relative navigation system robust to 
frequent signal loss and/or darkening of the sensors, where the information of the other 
vehicles maneuvers is not available. 
Two dynamics m odels a re h ere c onsidered: 1)  t he classical K alman f ilter 
technique, [13], considering the unknown input (the maneuver command) modeled as a  
random process, and 2) the MIE (Modified Input Estimation) technique [5], [8] and [14], 
where the maneuver is estimated in real time as additional variable in an augmented state 
vector. 
Between the two approaches, the MIE proves to be the most successful. It yields 
satisfactory performances without constant acceleration or small sampling time 
assumptions. F urthermore, i t no t on ly provides f ast initial convergence rate, bu t it c an 
also track a maneuvering target w ith a  good  accuracy under r andom loss of  signal and 
slow data rate, allowing the spacecraft to perform critical maneuvering such as docking 
and multi-vehicle assembly. 
A. BACKGROUND 
The topic of autonomous interacting s pacecraft is gaining popularity as space 
launch remains h igh cost, and automated space s ystems c ould be e conomical a nd 
beneficial f or c ertain commercial a nd military operations. A few real-world p rojects of  
autononmy through the use artificial vision are given here for contextual background. 
1. European Space Agency’s (ESA) Automated Transfer Vehicle (ATV) 
The A TV i s a  E uropean de veloped s pacecraft f or pr oviding t he I nternational 
Space S tation w ith t he a utomated transfer o f s upplies. T he f irst o f i ts c lass, t he J ules 
Verne s uccessfully c ompleted t he a utonomous r endezvous a nd doc king s ystem i n 
Europe’s l argest s hip hu ll test f acility in S eptember, 20 06 a nd pl ans to replicate tha t 
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success in space in 2007. Its primary mode of navigation comes from the use of 
independent supervision laser scanning device.  
2. National Space Development Agency (NASDA) of Japan’s ETS-7 
The ETS-7 program consisted of a pair of satellites, a chase satellite and a target 
satellite, that successfully undocked and re-docked autonomously in July o f 1998.  Also 
known a s K iku-7, t he pa ir of  i nteracting s pacecraft pe rformed multiple t ests, i ncluding 
degraded equipment tests and several tele-robotic experiments that boosted Japan’s hopes 
for f uture unmanned space f lights. Scientists a t NASDA c laim tha t th is e xperiment ha s 
proven the cost e ffectiveness of autonomous, interacting spacecraft. However, s ince the 
system w as bui lt a nd launched t ogether be fore i t w as t ested, there i s s ome doub t the 
system could be as effective with other types of spacecraft. 
3. AFRL’s XSS-11 
The XSS-11 Demonstration Mission was launched in April o f 2005. Its purpose 
was to demonstrate robust, extended duration proximity operations. It is a micro-satellite 
class v ehicle t hat could autonomously r endezvous with m ultiple s pace obj ects using a 
scanning L IDAR for n avigation. I t a lso h as s everal gui dance modes, s uch a s forced- 
motion trajectories, closed loop proximity operations, or collision avoidance that could be 
switched from ground control or autonomously.  
4. NASA’s Hubble Robotic Vehicle (HRV) 
NASA was developing a robotic vehicle to service the Hubble Space Telescope 
(HST) in FY08. Its purpose was to lengthen the life of the HST by taking it new batteries, 
propellant i nside of  a  d e-orbit module, a nd an ejection module w ith r obotic uni ts. The 
HRV w ould be  partially controlled f rom the ground to install ne w instruments, a nd 
reroute power u sing the n ew bat teries. The HRV project was r ecently cancelled due to 
budget constraints. 
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B.        RESEARCH GOALS 
This research is intended to advance the field of multiple spacecraft navigation by 
developing an autonomous navigation algorithm f or multiple spacecraft in c lose 
proximity operations, including s imultaneous rendezvous and docking. The a rchitecture 
of t he na vigation a lgorithm is de signed to pe rmit a  relative na vigation i n autonomous 
manner, without any data exchange and with only relative sensors. The adaptive tracking 
algorithm permits the use of low frequency sensors and allow also quite number of signal 
interruptions. The developed approach, also minimize the fuel consumption with a better 
estimation of the relative state and the Target’s control estimation. 
The navigation algorithm takes in to account considerations on realistic actuators 
and sensors p erformances and was tested and evaluate b y implementation in the 
Spacecraft R obotics L aboratory located at the Naval P ostgraduate S chool (NPS). This 
allows f or validation of t he na vigation a lgorithm ba sed o n l ow r ate a nd limited d ata 
sensors. 
The t estbed w as a dvanced b y incorporating a  large, f lat e poxy surface a nd an 
indoor-GPS system into the laboratory f ramework. The epoxy f loor a llows a  vehicle to 
emulate t he s pace environment by f loating o n a  ne ar-frictionless s urface r epresenting 
motion i n t wo d imensions. P seudo-GPS w as i ntegrated i nto t he t estbed t o a llow f or 
independent verification and validation of a vehicle’s performance. 
The do cking simulator w as de veloped by i ntegrating computer h ardware and 
attitude sensors in to a newly-designed vehicle architecture to support i ts navigation and 
control needs. A position and attitude estimator was created to fuse the vehicle’s sensor 
inputs. A control system was designed to allow for position control through eight 
thrusters and attitude control through the use of a reaction wheel. 
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II. OVERVIEW OF MULTIPLE SPACECRAFT MISSIONS 
A. MULTIPLE SPACECRAFT NAVIGATION 
The controlled spatial interaction of s ystems involving multiple vehicles, robots, 
aircraft, or spacecraft in  c lose pr oximity i s a  c omplex ta sk. How mu ltiple vehicles are 
controlled depends on a wide range of operating environments, missions, objectives, and 
organizational combinations. Developing systems consisting of multiple autonomous 
vehicles that cooperatively perform a task or behavior is of paramount importance to the 
engineering c ommunity. The di stinctive s pace e nvironment makes f or par ticularly 
interesting and challenging navigation and control algorithm requirements based on 
orbital d ynamics, communication l imitations, and tight spacecraft s ensitive t o 
disturbances and constraints. The dynamics of the orbital spacecraft is affected by 
disturbances and perturbations. Traditionally, individual spacecraft maneuvers have been 
based on fuel e fficiency r equirements, since f uel i s a  c ritical r esource i n the l ife of  a  
spacecraft. During large e arly staging maneuvers, the c onservation of f uel is gener ally 
more critical then the timeliness of any particular task. Once in the desired mission orbit, 
the only regular translational maneuvers which most individual spacecraft perform are for 
general station keeping. Also, due to the relatively large distances between typical orbital 
objects c ollision avoidance maneuvers a re r arely necessary and s eldom e xecuted. 
However, due t o spacecraft t echnology improvements, there is now  a  g reater d esire t o 
control multiple spacecraft in close proximity operations. These multiple spacecraft, close 
proximity operations r equire a l arge r obust t o t he s ignal l oss a nd pr ecise na vigation 
algorithm. 
Advances i n t echnology c ontinue to de crease t he s ize, w eight o f c omponents 
while increasing the capability of payloads, sensors and processors. This trend has 
enabled the space industry to decrease the s ize of spacecraft. Small satellites with mass 
less than a few hundred kg are becoming more common. Launch opportunities are more 
readily available f or smaller spacecraft s ince more launch vehicle can support them. 
Many of these relatively small satellites can be deployed into orbit from the same launch 
vehicle. Once in orbit the spacecraft will need to disperse or converge, relative to each 
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other de pending on t heir m ission. A s s pacecraft ge t c loser t o e ach ot her t he 
execution of  7c ollision avoidance, r endezvous, a nd doc king m aneuvers o ver a  s hort 
timeline m ay t ake pr iority o ver opt imizing i ndividual s pacecraft's f uel c onsumption. 
During these c lose pr oximity maneuvers, the des ires a re to maintain e fficient fuel 
management while accomplishing the maneuver objective quickly. The longer each 
spacecraft stays in t ransition during close proximity the more p recise s tation keeping is 
required; therefore more propellant may be used. 
B. MULTIPLE SPACECRAFT MISSIONS 
Navigation a nd C ontrol a lgorithms f or m ultiple s pacecraft ne ed t o t ake t he 
similarity a nd differences o f e ach spacecraft i nto consideration, which is d iscussed in 
detail in Chapter II.B.1. In this research cooperative homogeneous spacecraft with similar 
sensors and navigation algorithms are considered. Additionally, it is useful to define the 
phase of the spacecraft mission in relationship to the d istances from other spacecraft or  
the goal position. A discussion of relative orbital mission phases is presented in Chapter 
II.B.2. Also, the organizational g rouping of spacecraft depends on t he manner in which 
the s pacecraft maintain position w ith r espect t o each other. The various or ganizational 
groupings of spacecraft are discussed in Chapter II.B.3. Precision control, that requires a 
high a ccurate na vigation, m ay be de sired i n s ome a pplications, s uch a s po inting 
spacecraft w ith h igh r esolution imagery p ayloads, a nd l oose control may b e de sired in 
other applications, such as station keeping of communication satellites. Mission 
motivations for autonomously navigation and synchronized multiple spacecraft in precise 
spatial c onfigurations a re num erous, a nd i nclude i nterferometry, c ommunications, a nd 
power ge neration. These c ooperative s pacecraft m ay ne ed to be  a ble t o c onverge or  
diverge in a  safe and e fficient fashion. For s ervicing missions, it may be  necessary for 
two or more spacecraft to rendezvous, or even dock. 
First, multiple s pacecraft interferometry is ba sed on t he i dea that t he p recise 
configuration o f t he relative pos ition a nd or ientation of  multiple s pacecraft pa yloads 
could r esult in pe rformance equivalent t o a  m uch l arger spacecraft pa yload. M ultiple 
spacecraft are positioned in order to form a  distributed array. Distributing spacecraft 
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payloads ( e.g., sensors) into pr ecise s patially c onfigurations, or  a ssembling multiple 
spacecraft o n or bit, r equire hi gher level navigation a lgorithms. B ecause it is r equired 
control a lgorithm capabilities inc lude the  e stablishment a nd maintenance of  a  given 
formation and a ny po ssible r econfiguration of t he formation, i t i s necessary a robust 
navigation algorithm.  
Second, reconfigurable cooperative formation mission concepts are based on 
collectives o f small spacecraft working in unison to perform a greater function. For the 
purpose of spacecraft formation navigation and control it is generally assumed that each 
spacecraft is relatively homogeneous and executes centralized control strategies in order 
to minimize fuel consumption during formation flight. Each small spacecraft coordinates 
with others in the group and shares processing, communication, and payload or mission 
functions. Defense Advanced Research Projects Agency (DARPA) is currently studying 
the idea of fractionated spacecraft architectures which decompose the overall spacecraft 
function i nto a  f ree-flying ne twork of  c omponent m odules. T he t raditional m onolithic 
spacecraft m ight be  r eplaced with a gr oup of smaller s pacecraft i nteracting w irelessly. 
Upgrading the group can be done iteratively in order to increase overall performance and 
mission dur ation. T his c an s ubstantially e nhances t he f lexibility, r esponsiveness, 
robustness, and lifecycle of the overall spacecraft function. 
Third, rendezvous mission concepts are usually based on a cooperative spacecraft 
approaching a nother s pacecraft w ithin a  c ommon s patial r egion. The goa l po sition i s 
usually occupied b y a cooperative spacecraft in t he s ame or bital plane a s t he 
maneuvering spacecraft. The Space Transportation System (STS), often referred to as the 
Space S huttle, a nd t he I SS a re of ten s hown doc king i n or bit. The S pace S huttle is 
astronaut controlled as it docks to the ISS. This process is no t autonomous, bu t there is 
autonomous docking of Russian Soyuz and Progress spacecraft with the ISS. The process 
of a utomated s pacecraft doc king w as pi oneered b y the S oviet U nion; how ever t he 
automated system occasionally f ails to complete the t ask. According to NASA, current 
state of the art Russian automated rendezvous and docking systems have a current failure 
rate of  approximately 10 -15 %. As a  result, ISS’s Zvezda module i s equipped w ith the 
Russian bu ilt T elerobotically O perated R endezvous U nit ( TORU) m anual doc king 
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system which can be operated by cosmonauts. However, manual rendezvous can not be 
relied upon since human space flight is very dangerous, impractical, and unnecessary for 
most on orbit missions. The European Space Agency (ESA) have lunched the Automated 
Transfer V ehicle (ATV) t o automatically dock with the ISS. However, close proximity 
operations of  spacecraft a re of ten complicated by momentary communication a nd 
autopilot navigation failures, from here the necessity of a robust navigation algorithm that 
could gua rantee the m ission s afety e ven i f interruption of  the s ignals w ill oc cur. F rom 
here t he i mportance of  t his s tudy, as in t he orbital application as in t he l aboratory 
experimentation. 
The motivation to rendezvous i s no t l imited to manned-spaceflight. Rendezvous 
technology ha s a lso e volved w ith s mall s pacecraft de velopment, s uch a s the N ASA’s 
Demonstration for A utonomous R endezvous Technology ( DART). The use of m icro-
satellites to monitor, inspect, service, repair, and re-fuel larger spacecraft is a  long term 
goal. The closest the XSS-11 approached and maneuvered around another object in space 
was approximately 500 meters. The XSS-11 used on-board laser range finders to measure 
the di stance t o t arget obj ects. Most o f t he X SS-11 f light is be ing c onducted manually 
with a utonomous pl anners running in the ba ckground. In addition, DARPA’s Orbital 
Express Advanced T echnology D emonstration P rogram i s intended to validate t he 
technology and t echniques f or on -orbit r efueling a nd r econfiguration of  two s atellites. 
The mission, w hich l aunched in l ate 2006, is i ntended t o pe rform s even a utonomous 
rendezvous a nd c apture s cenarios. These will include c omponent e xchange a nd 
propellant t ransfer e vents. T here i s a lso r esearch to a pply rendezvous t echnology to 
smaller spacecraft, such as DARPA’s Tiny, Independent, Coordinating Spacecraft (TICS) 
program. These small spacecraft programs are leading the way for advanced autonomous 
close proximity operations by supporting the development of enabling technologies. 
1. Homogenous and Heterogeneous Spacecraft 
Any given group of spacecraft may have characteristics that make them similar or 
different. The l ikeness among vehicles is of s ignificant consideration in the coordinated 
navigation of a group of spacecraft. Spacecraft are termed homogenous, if the spacecraft 
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are identical, or heterogeneous, if the spacecraft are different. The likeness evaluation of 
spacecrafts m ay be bas ed on a l arge variety of  par ameters, varying from ph ysical 
characteristics (e.g., mass, volume, a nd s tructure/configuration) to t he s pacecrafts 
capabilities (e.g., communication, data handling, power, payloads, and control systems). 
Limited t ypes of  l aunch vehicle c apabilities a nd s pacecraft bus  de signs gi ve a n uppe r 
bound t o t he m ass a nd volume of  o rbital s pacecraft. F or i nstance, t he s tatic l aunch 
envelope ins ide the launch vehicle f airing limits the v olume of a s pacecraft. Increased 
modularity o f s ystems a llows f or a  l arger va riation in pa yloads, s ensors, a nd 
configurations. This research will be based on homogenous spacecraft, including similar 
sensors, control system and actuators. However, dissimilar size and shape spacecraft may 
be considered as long as the dynamics of each spacecraft is properly modeled. Exploring 
the varying pe rturbations d ynamics of  multiple he terogeneous s pacecraft is be yond t he 
scope of  this work. I n t his research, a ll c ommanded spacecraft a re a ssumed to use t he 
same basic navigation scheme and be  equipped w ith sensors and actuators which of fer 
the same level of precision. 
2. Orbiting Spacecraft Mission Phases 
The m ultiple s pacecraft na vigation a lgorithm us ed de pends on t he ph ase of  
spacecraft op erations. I n or der t o d istinguish between pha ses of  s pacecraft ope rations 
based on physical proximity, it is helpful to adapt some terminology from missile 
engineering. In missile interception, four fundamental stages of flight have been defined. 
These s tages a re c ommonly referred t o a s l aunch, midcourse, terminal, a nd endgame 
stages of flight. They can be extended in spacecraft phase proximity operations, referred 
to as launch, midcourse, rendezvous, and docking. Here are the four spacecraft proximity 
phases: 
1. Launch phase e nds a fter the s atellite s eparates f rom t he launch vehicle 
upper s tage (booster) a nd i t i s i n ope rational or bit. All l arge orbital m aneuvers a re 
performed during the launch phase. 
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2. M idcourse pha se be gins w hen t he spacecraft h as be en stabilized into its 
operational or bit a nd it c an pe rform s tation k eeping. Small o rbital corrections may b e 
performed during this midcourse phase. 
3. R endezvous, or  terminal, pha se i s t he w hen t he spacecraft c onverges t o a  
common point in its operational orbit. This rendezvous phase begins when the spacecraft 
receives its rendezvous command to translate toward a point in space. This space may be 
occupied by another spacecraft or be an empty space which the spacecraft will move into 
and oc cupy. If a group of s pacecraft are c ommanded to rendezvous t o empty s paces 
relative to each other they will form a spacecraft formation. On the other hand, if a group 
of s pacecraft are c onverging on  t he s ame location i n space t hey are c onverging for 
docking. 
4. Docking, or endgame, phase begins when spacecraft on-board proximity sensor 
acquire the target location/vehicle. Spacecraft docking is a very precise maneuver, since 
uncertainties in guidance and attitude need to be corrected quickly and effectively during 
this engagement scenario. 
3. Multiple Spacecraft Groups 
Before addressing the navigation of multiple spacecraft, it is useful to define the  
differences be tween c onstellations, f ormations, a nd swarms/clusters. C onstellations a re 
groups of spacecrafts in relative motion, or orbit(s), but their positions and attitudes are 
not dynamically coupled in any way. This means that a change in position or velocity of 
one spacecraft does not impact the others. For instance, the GPS constellation is made up 
of at least 24 satellites with four satellites in six different GEO planes. Each 
satellite i s m aintained i n its or bit i ndependently via gr ound c ommanding. 
Maintaining t he or bital pos ition of  t he s pacecraft, r eferred t o a s s tation ke eping, is 
required due to several perturbation influences (e.g., Sun and Moon gravitational f ields, 
variations in Earth's gravitational f ield, a erodynamic dr ag). C onstellations a re us ually 
maintained via centralized ground control. 
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Formations a re g roups of spacecrafts which are d ynamically coupled through a  
control la w. The motion of  one  s pacecraft c an gi ve relative s tate i nformation a bout a t 
least one other spacecraft. Formation flight control of multiple small spacecraft is the task 
of maintaining the spatial formation, via control of the motion of the individual spacecraft 
in or der to maintain t he o verall f ormation shape. The control law typically uses t he 
position a nd velocity of one  spacecraft t o command another s pacecraft. The l ead 
spacecraft moves a long a  c ommanded p ath and t he f ollowing spacecraft(s) maintain a 
relative position, attitude, and velocity w ith respect to the leader. This i s a c ommon 
concept in leader/follower tracking schemes, where the relative motion is like a flock of 
geese i n f light. Collisions a re generally a voided t hrough s trict c ontrol of  t he f ollowing 
spacecraft's motion. For spacecraft formation control a virtual structure control approach 
is c ommonly u sed. In s pacecraft o rbital terms, t he lead spacecraft i s r eferred to as t he 
“Target” and the t racking spacecraft i s called the “Chaser.” The ta rget motion may be  
represented by an i maginary spacecraft. The idea of  a n i maginary target leads better 
understanding of a swarm/cluster. 
A swarm/cluster is a group of spacecrafts that move in concert with one another, 
but without strict control of relative positions, attitudes, or velocities. In the idea of a bee 
swarm, an outside observer can see the relatively smooth motion of an entire swarm but 
can not  determine the s pecific r elationship be tween a ny two spacecrafts. Think of  the 
center of  the swarm as an imaginary target and a ll of  the spacecrafts a s Chasers which 
only stay w ithin a  s pecific r ange. A  t ight s warm w ould be  r epresented b y a  s mall 
acceptable d istance bet ween the Target a nd Chasers. However, the s pecific pos ition, 
attitude, and velocity of e ach Chaser s pacecraft a re not  c entrally c ontrolled. Each 
spacecraft autonomously manages its own motion and is only influence by its range from 
the target and the need not to collide with other spacecrafts. 
The de sire i s to of fer a control a lgorithm which br idges the g ap be tween s ingle 
cost op timal fuel t rajectory tracking o f r igid formation and t he emergent be havior of  
swarms. U sing A PF ba sed c ontrol, a llows for i ncorporation o f c ollision a voidance 
directly into the close proximity control algorithm. The goal position of each spacecraft is 
explicit and the gener al spacecraft path will be in the p redictable d irection of t he goa l. 
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The obstacle po tential functions can be  defined and used to de termine navigation pa ths 
which are robust enough to allow for both convergence and collision avoidance.