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Arm Astronautica,
Vol. 39, No. 9-12, pp. 977-985, 1996 01997 Microcosm Inc. Published by Elsevier Science Ltd Printed in Great Britain 0149-1970/96 $17.00+0.00
Hans J. Kiinigsmann John Simon
T. Collins Dawson
James R. Wertz Microcosm, Inc., 2377 Crenshaw Blvd, Suite 350, Torrance, CA 90501. E-mail: [email protected]
ABSTRACT Orbit maintenance is a major cost factor for Earth satellites in specialized orbits, such as a repeating ground track, or in formations. While autonomous attitude control is well established, the spacecraft’s orbit is usually uncontrolled or maintained by ground station commands. For small, lower cost satellites, operations costs can be a dominant element of both cost and risk. This implies a need for low-cost autonomous orbit maintenance in order to allow such systems to be economically viable, particularly in today’s constrained budget environment. In addition, if the position of the spacecraft is controlled, it is therefore known in advance. Thus, mission planning can be done as far in advance as desired, without the need for replanning and frequent updating due to unpredictable orbit decay. An interesting characteristic of autonomous orbit maintenance is that it typically requires less software, and less complex software, than does orbit control from the ground. In many cases, an onboard orbit propagator is not needed. 01997 Published by Elsevier Science Ltd. dated. This prediction, planning and replanning represents a significant portion of the operations activity and, therefore, of the operations cost. The critical issue for traditional low Earth orbit maintenance is that only the long term average orbit elements are maintained. The specific position within the orbit, as required for constellation maintenance, is not maintained and future predictions of the satellite position are both difficult and of limited accuracy. In contrast to this appreach, Microcosm has coined the term “controlled orbit” to describe an orbit in which all of the elements, including the true anomaly at any given time, are con-
INTRODUCTION To date, spacecraft in low Earth Orbit (LEO) have been either uncontrolled or loosely controlled by maintaining the average orbital elements. The detailed motion of a spacecraft is affected strongly by varying atmospheric drag and other perturbations, and the positions of the spacecraft at future times can be predicted only by complex orbit propagation software. In any case, this prediction is accurate for only short periods. Scheduling and planning of payload operations, which is especially important for Earth observing satellites, is continually revised and up-
Copyright 0 Microcosm, 1996.Publishedby the IAA with permission. 977
Small Satellites
trolled by frequent small thruster firings. Thus, the satellite is continuously maintained within a pre-specified mathematical box that could, for example, be one component of a low Earth orbit constellation. The position of the satellite at all future times is known to within the size of the box, because the satellite is controlled to be there. The controlled orbit has several interesting characteristics: l
The satellite’s position is known as far in advance as desirable (but can be changed, if, for example, rephasing is needed due to a satellite failure). Propellant usage is minimized. Typically, no on-board gation is required.
orbit propa-
Although the dominant perturbations change, the basic process and algorithms can be used from low Earth orbit to geosynchronous orbit and above.
Generally, we associate tighter control with additional propellant usage. However, for low Earth orbit satellites, the dominant in-track secular perturbation is atmospheric drag. The requirement on the orbit control system is to put back By timing the what drag takes out.
AV executed
or Descending
for Earth Observation
thruster bums correctly, we can put back this Av so as to maintain the in-track position with no additional propellant usage over that required to overcome drag. Since the orbit is continuously being maintained at its highest level, rather than being allowed to decay somewhat and then brought back up, the effect of drag is minimized and the required propellant usage is minimized. Autonomous orbit control is similar to the situation which currently exists for spacecraft attitude control. It is done autonomously, on-board of the spacecraft, and is done with small frequent adjustments. Consequently, there is no need for complex attitude propagation software. Figure 1 shows the employing frequent small bums based ments at a reference
basic control concept application of very on timing measurelocation in the satel-
lite orbit, Av = f(AT). AT is the difference between the actual reference crossactual) and the preing time (Tcrossing,. programmed crossing time (Tcrossing, aef), AT = Tcross~ng, Ref -
Corrective Av bums are applied at the ascending or descending node in direction of instantaneous velocity at that time.
at Node
in direction of instantaneous velocity at that time.
orbit becomes
controlled with application of small AV at regular interval
Earth Equatorial
time is compared reference
with a desired time)
Uncontrolled Orbit due to drag; period shrinks
Figure 1: Orbit Control Concept
Small Satellites for Earth Observation
The use of autonomous orbit maintenance has several secondary characteristics that are, nonetheless, important in further reducing the cost and risk relative to traditional orbit maintenance. Autonomous orbit maintenance uses a much larger number of much smaller burns. To have reasonable thruster efficiency, the thrusters themselves must be much smaller than those traditionally used for orbit control. Thruster firings are ordinarily the single largest disturbance torque seen by the spacecraft (typically by a very wide margin). By going to smaller thrusters, we are reducing the weight of the reaction control system and substantially reducing the maximum disturbance torques, thus reducing the control complexity and control authority. It may even be possible to do the thruster firings while the payload is operating with only the normal attitude control system. Another key characteristic is failure modes. Failures in traditional rocket engine firings have the potential for being disastrous for the spacecraft, although this is less of a problem for orbit maintenance than for orbit transfer. If a thruster fails to fire in autonomous orbit maintenance, the effect is likely to be so small as to be undetectable until the spacecraft begins to drift slowly out of its assigned box. There is ample time to analyze the failure and execute a recovery plan (assuming that the failure itself can be fixed), with an insignificant loss of propellant. So long as there is an external limiter on the time that the thrusters can tire, autonomous orbit control is an inherently “fail safe” process. Autonomy in attitude control is well established, because for most LEO satellites autonomous attitude control is considered essential. Compared to autonomous orbit control, attitude control involves much higher risks. A failure of the attitude control system can result in a wrong orientation or a tumbling spacecraft, while a failure of the orbit control system would
cause the satellite’s orbit to decay very slowly. The principal roadblock to introducing the orbit control technology is simply tradition. Orbit control has always been done from the ground and new programs do not want to risk change for what is perceived as a marginal benefit for that flight.
To simulate the autonomous orbit controller, the control algorithms have been incorporated into the High Precision Orbit Propagator (HPOP), developed by Microcosm. NASA’s forthcoming Small Satellite Technology Initiative (SSTI) Lewis mission has been chosen as an example. Figure 2 compares the motions of a controlled and an uncontrolled spacecraft relative to a “drag-free” spacecraft for a period of 2 days. The position error of the orbit control is defined as the motion relative to a drag-free satellite. The scales of the axes are very different in figure 2; the cross-track axis has been enlarged by a factor of 3500, the radial error axis by a factor of 175 compared to the in-track axis. The motion of the uncontrolled satellite relative to the drag-free satellite resembles an insect wing and reaches a maximum in-track distance of 70 km in 2 days. The comparably small circles around the origin of the coordinate system represent the position error of the controlled spacecraft, which is shown on a larger scale in figure 3. The satellite moves within a “control cylinder” (representing the box mentioned above), and thrust is applied to move the spacecraft from the back to the front of this cylinder. The corrective impulses increase the radial and cross-track errors, but a long term analysis shows that this does not affect stability. The maximum in-track error is 2.7 km, cross-track and radial errors remain much smaller during this short simulation.
Small Satellites
for Earth Observation

In-Track [km]
Figure 2: Relative Motion of Uncontrolled and Controlled Spacecraft Relative to a Drag-Free Satellite (530 km Altitude, Sun-synchronous Circular Orbit). See text for explanation. 0.25 j 0.24

’ -0.5




In-Track [km]
Figure (Zoom
3: Relative from Figure
Motion 2)
Small Satellites for Earth Observation
A measure for the performance of the orbit controller is the time delay, or “time late”, AT at the ascending node, shown in figure 4 for a 1 year simulation. It should be noted that a comparably large deadband of +/- 0.25 s has been used for the
simulation shown in this figure. The histogram in figure 5 shows the error distribution, indicating a bias error of -0.15 s . This error could be canceled by adding a bias to the measurement data or shifting the controller’s dead band.
Time Late at Ascending

(c) Microcosm. 50
200 Time PJays)
Figure 4: AT (Time delay at the node crossing) Hl%g,mn 0,Tlme-Lats C-Or
Figure 5: Histogram of Time Late at the Ascending Node for a 1 Year Simulation The standard deviation of CT= -0.16 s corresponds to an in-track position error of less than 1.3 km, the maximum error of -0.5 s to 3.8 km. These data depend on the individual spacecraft configuration, the orbital altitude and the controller gains.
11/96HJK 350
for a 12 Months Simulation Acc”ma”ed D&a “*bxlty 0‘TOtal “s!QCly
Figure 6: Delta-V Burns During a 5 Day Period Figure 6 shows how the controller corrects the in-track error. For 3-4 successive orbits, the thruster is activated to cancel the aerodynamics drag effect, followed by a longer period of no activity during which the satellite drifts from the front to the back of the stationkeeping box. Each individual correction has a delta-v of approximately 0.025 m/s, and the average control velocity required per
Small Satellites for Earth Observation
month is little more than 2 m/s with slight variations caused by varying solar flux levels.
Possible applications are: l
Correction of the nodal drift rate after separation from launcher.
Constellation maintenance, keeping satellites within one plane and separating the orbital planes sufficiently to avoid collisions.
North-South stationkeeping synchronous satellites.
As could be seen in figure 2 and 3, the cross-track error is typically orders of magnitude smaller than the in-track error. Since radial and in-track error are coupled, cross-track is the remaining component to be controlled for fY_tll orbit control. The cross-track error is determined by comparing the longitude measured at the ascending node to a pre-determined longitude. It is then corrected by adjusting the orbital inclination to a new nodal drift rate, computed by the cross-track controller. The thruster fire perpendicular to the velocity at the ascending or descending node. Orbit plane changes require a much larger amount of Av than the intrack control, but due to the small error the time constants are large. Some missions might not require cross-track control at all, while other missions could require it more the in-track control.
of geo-
For an example, we assumed a slightly wrong inclination of the orbit after the satellite has been separated from the launcher. The initial inclination would cause the orbit to drift slightly faster than desired for a sun-synchronous orbit. Figure 7 shows the change in inclination over a period of 15 days, until the desired nodal drift rate is established. This demonstrates the long time constants of the controller and the system. Since inclination changes require much fuel, the key element is to avoid any overshoot during the correction.
Inclination During Crosstrack Control
1 Time [min]
2.5 x lo4
Figure 7: Inclination Change due to Cross-Track Control during 15 Days
Small Satellites for Earth Observation
most applications. Very tight control would require constant thruster burns and, therefore, a large amount of extra fuel.
The above described orbit control system, especially the in-track controller, may be used onboard two or more independent spacecraft to maintain a small constellation. This application is of particular interest to Earth observing satellites, e.g. if a second satellite is added to an already orbiting spacecraft, or constellations that take advantage of the long baseline between instruments. The distance between the two spacecraft is not tightly controlled, because it is not be required in
Our example uses a large spacecraft, followed by a small spacecraft at 10 seconds distance in a sun-synchronous orbit and at 530 km altitude. The relative motion is shown in figure 5, which has some similarity to Figure 3. Both spacecraft use the same algorithm to control independently their individual orbits, and due to the high precision their relative motion always maintains a safe distance between them.
-0.005 -0.01
’ -78


In-Track [km]
Figure 8: Relative Motion of 2 Satellites of a Small Constellation Since both orbit controllers work independently, we call this control mode absolute stationkeeping, rather than relative stationkeeping. Relative stationkeeping is the maintenance of a spacecraft’s position with respect to other spacecraft within the constellation. Intuitively, relative stationkeeping appears compelling. However, it implies the need for a large, distributed computing resource in the con-
stellation in order to maintain this ‘constellation-wide’ approach. In addition, relative stationkeeping requires the same or more propellant as absolute stationkeeping. The greatest advantage of the Microcosm approach to constellation maintenance is its inherent simplicity: It tightly controls each spacecraft to stay within its predefined box. Then, assuming each box is
Small Satellites for Earth Observation
correctly designed, a constellation of two spacecraft, twenty spacecraft or two hundred spacecraft all can use the same approach with the same minimal computing power. This negates the major obstacle faced by advocates of inter-constellation control: constellation-wide control would perform very differently for a partially completed and a fully completed constellation of a large number of satellites. Another serious drawback to the constellation-wide control approach is the scenario where a spacecraft that has gone awry still reports to the remainder of the constellation that it is functioning perfectly and it is at x,y, z, when really it is at a, b, c. The possibility then can occur that the constellation pulls itself to destruction trying to reconcile the errant spacecraft with the fully functioning remainder. Under Microcosm’s plan each spacecraft’s position is controlled onboard the craft and independently of all other craft, resulting in a very robust system.
CONCLUSIONS The performance of an autonomous orbit controller onboard a LEO spacecraft has been simulated with a high precision orbit propagator. The results show a small position error and, for constellations, only a small relative motion between two or more spacecraft. Long term stability has been verified by 12 month simulation runs, which also showed that autonomous orbit control, if the thrust level is small enough, saves fuel compared to traditional ground station orbit control. The merits of autonomous orbit control as an experiment and an emergent technology are: l
As has been noted, future operators of large constellations are presented with the formidable task of attempting to intimately control numerous spacecraft relative to each other. Traditional approaches to the orbit maintenance will lead to huge investments in time, manpower and,
hence, money. Microcosm’s approach to constellation maintenance frees operators to handle situations that need human intervention rather than those timeconsuming, mundane, tasks that traditional operations’ schemes presently endure. The fact that the routine is removed from the operations team’s schedule allows that time to better assigned to longterm planning and system evolution and upgrade. l
The major reductions in routine operations and scheduling leads directly to large reductions in operations costs. These savings are brought about through the fact that there is no more “mothering” of spacecraft by standing armies of operators. This fact is particularly pertinent the larger the constellation becomes, and the greater the effect of these reductions. l
Lower risk
Historically, more spacecraft problems and failures are the result of operations and communications errors than any other source. If one examines for a moment a process that today is deemed commonplace on spacecraft, that of on-board attitude determination and control, then one soon realizes that attitude control could be done from the ground, yet we still trust the spacecraft with this task. What would happen if the on-board attitude system were to fail? The spacecraft could soon lose its orientation with respect to the Sun, losing power generation capability from its solar arrays, and rapidly draining its batteries. Alternatively, the spacecraft could point a delicate instrument directly into the Sun’s glare thus destroying the instrument. These scenarios however, rarely happen. We have faith in the ability of the autonomous onboard systems to manage things, even though a spacecraft is always perilously close to a catastrophic end should the system fail. Let us now similarly examine the analogous full orbit control system. Assuming, the system is performing correctly, what
Small Satellites for Earth Observation
happens if we now strike it down such that it fires the thrusters in the wrong way altogether. The thrusters would be chosen so as to be efficient even when the spacecraft might thrust every orbit. This contrasts sharply with the traditionally sized orbit control thruster which needs to raise the orbit every month in a comparably larger maneuver - hence a much larger thruster is needed to accomplish the maneuver in a time commensurate with not disturbing the normal on-orbit payload activities. Given that the autonomous orbit control system has reached a point where it is doing the exact opposite of what it is meant to be doing, what would be the worst outcome? Firing the thruster every orbit, or every n orbits, even in the wrong direction would cause a small drift from the nominal position - not a large deleterious maneuver as might occur if a traditional system were to tire in the wrong direction. The failure mode is therefore ‘soft’ and not analogous to the attitude control system’s failure mode which is decidedly ‘hard’. Orbit control, once proven in simulation, represents an experiment with few risks. Those risks that are incurred are those of challenging the traditional approach rather than technical, mission-ending risks,
REFERENCES 1. Hosken, R, Wertz, J.: “Microcosm Autonomous Navigation System OnOrbit Operation”, 18th AAS Guidance and Control Conference (AAS 95-074), ’ United States Air Force, Air Force Systems Command, Phillips Laboratory (PL), K&land AFB, New Mexico 87 117-6008 * U.S. Patent No. $528,502 issued June 18, 1996. Patent allowed in Europe.
Keystone, Colorado, 1995 2. Wertz, J: “Implementing Autonomous Orbit Control”, AAS, 1996 3. Wertz, J., Larson, W: Space Mission Analysis and Design, 2”d ed., Kluwer Academic Publishers, 1992 4. Glickman, R: TIDE: “The TimedDestination Approach to Constellation Formationkeeping”, AAS, 1994

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