The operations of a satellite formation require an active orbit control. Firstly, the formation has to be established from some initial configuration (formation acquisition) and secondly, the formation has to be kept in a predefined control window to counteract the differential perturbations, acting on the two spacecraft (formation keeping). The control of a satellite formation is efficiently performed by activating appropriate on-board thrusters. There are basically three different ways to control formations in space
A ground-based control is primarily restricted to formations with a large separation and control window. A typical example is the GRACE formation with a nominal separation of 200 km and a control window of about 50 km. As consequence, a sparse control is fully sufficient, which calls for formation keeping maneuvers every few weeks. Avoiding the complexity of onboard autonomous systems, such maneuver schedules are more efficiently executed by the satellite operations center.
Ground-in-the-loop control of formation flight might be necessary, when high safety requirements have to be met, e.g. when a docking takes place involving manned missions, such as of the Shuttle docking to the International Space Station (ISS). Since an extended ground-link involves communication over dedicated relay satellites, such links are very costly and not appropriate for the considered scenario.
A fully autonomous space-borne control of a formation is adequate when close formations (separation distances < 1 km) with tight control windows are considered. For example in case of satellite mode drops, caused by sensor problems, impulses of the actuator system may be activated, which cause a rapid change of the relative motion of the formation, which might no longer be counteracted by the operations center, especially with a limited ground station complement. Considering for example a differential velocity of 1 cm/s, a 10 m control window may be violated within 15 mins.
Although an operational autonomous formation keeping for close satellite formations has, so far, not been performed, the feasibility of autonomous close formation flight is, e.g. demonstrated by the Progress cargo carrier, which is designed to dock automatically with the ISS.
Demonstration of Autonomous Formation Flying
To study the feasibility of autonomous formation flying, a closed-loop system for the demonstration of autonomous satellite formation flying technologies using hardware-in-the-loop has been developed.
When GPS receivers are employed as navigation sensors on satellites, the terrestrial GPS signals may no longer be used, since they do not show the dynamic characteristics of a receiver moving at about 7600 m/s. Hence, a so-called GPS signal simulator has to be employed, which allows a realistic generation of GPS high-frequency signals as received by a GPS receiver in space through a detailed and complex definition of a suitable scenario .
Making use of a GPS signal simulator with a dual radio frequency outlet, the developed system includes two GPS space receivers as well as a powerful onboard navigation processor dedicated to the GPS-based guidance, navigation, and control of a satellite formation in real-time. The formation flying scenario aimed at the autonomous transition of a Low Earth Orbit satellite formation from an initial along-track separation of 800 m to a target distance of 100 m. Assuming a low-thrust Pulsed Plasma Thruster (PPT), a typical control accuracy of about 3 m has been achieved which proves the applicability of autonomous formation flying techniques to formations of satellites as close as 30 m.
Out of the many possible control theories which are applicable to the problem of formation control, Lyapunov's direct method (second method) appears as a feasible approach to the problem of relative motion control. Here, the control drives the system dynamics along a direction opposite to the gradient of a specific Lyapunov function in such a way, that the current state approaches and finally reaches the terminal state conditions.
Although Lyapunov's method is necessarily neither time-optimal nor fuel-optimal, it provides globally asymptotically stable solutions to linear and non-linear systems. As the computation of the feedback control requires only a moderate computational effort, it is especially suited for real-time and onboard applications. Furthermore, large matrices as in predictive control strategies are avoided since the involved matrix/vector dimensions are just of the size of the state of the dynamical system.
The adopted formation control algorithm requires the absolute current and target state of the formation as input. While the absolute current state vector of the spacecraft is readily available from its GPS position and velocity fixes, the derivation of an appropriate target state is part of the guidance problem of formation flying. Although this problem might be solved by numerically integrating a reference trajectory, this approach is inefficient since it requires a high computational effort on the navigation processor. Furthermore it is not flexible, since the guidance is defined with respect to a fixed trajectory.
In general, guidance of a formation may well be separated into guidance with respect to the absolute orbit of one of the spacecraft and guidance with respect to the relative formation geometry. Scientific or technological objectives of a formation flying mission are in fact in many cases only related to the relative formation geometry.
Thus, for a formation separated in along-track direction with spacecraft 1 preceding spacecraft 2 and a positive target separation of DL, the target elements for the first spacecraft are the current elements of the second spacecraft, except for the mean anomaly, which is offset by the target separation divided by the semi-major axis.
This guidance approach based on the relative formation geometry has the following characteristics:
In the conducted demonstration, this approach has been extended to allow both spacecraft to be active and control the formation in parallel. Although not fuel optimal, this concept allows for a completely autonomous and dynamic acquisition of the final formation geometry. Even if one spacecraft's thruster system should fail, no ground intervention would be required to achieve the target relative formation geometry in this case.
Gill E., Naasz B., Ebinuma T.;First Results from a Hardware-in-the-Loop Demonstration of Closed-Loop Autonomous Formation Flying;26th Annual AAS Guidance and Control Conference, 5-9 Feb. 2003, Breckenridge, Colorado (2003).
Leung S., Gill E., Montenbruck O., Montenegro S.;A Navigation Processor for Flexible Real-Time Formation Flying Applications;International Symposium Formation Flying Mission & Technologies, 29-31 October 2002, Toulouse, France (2002).