Game tree method plans fuel-minimum inspection sequences around GEO satellites

A team led by Meng Yunhe of the School of Artificial Intelligence at Sun Yat-sen University has proposed a method for planning how a spacecraft can observe a non-cooperative satellite from several aspects in sequence while using the least fuel. The study, published in Space: Science & Technology, applies sequential coalition game theory to the problem, which the authors said had not been done before.

The method treats a close-range inspection as a series of stages. At each stage a game tree search selects the best combination of starting point and relative motion model under a minimum fuel constraint. The output is an ordered observation strategy that chains several motion models together.

Four close-range operation models form the building blocks. The team constructed them from the Clohessy-Wiltshire relative dynamics equations: a droplet model, a coplanar fly-around model, a non-coplanar fly-around model and a drifting flight model. The authors derived the analytical solutions of unforced relative motion and supplied solution functions for the initial motion states that yield stable relative configurations, set through the choice of relative distance and phase angle parameters.

Each model serves a different purpose. The droplet model is symmetric and revisits the target, which allows fine observation. The coplanar and non-coplanar fly-around models circle the target in different orbital planes. The drifting flight model achieves close-range observation through multi-impulse control.

Moving between models is handled separately. The researchers designed a waypoint trajectory planning scheme and a multi-impulse maneuver strategy based on minimum integral squared control theory, intended to give smooth switching from one configuration to the next.

The study describes relative motion in the local vertical, local horizontal (LVLH) coordinate frame. The observing spacecraft carries cameras mounted in the plus and minus y directions. Because the cameras are fixed, frequent large-angle attitude maneuvers would take time and consume substantial fuel. Sequencing several relative motion models lets the spacecraft image the target from multiple aspects without them.

The authors defined effective observation time as the total duration during which the target can be observed while the limits on observation distance and field-of-view angle are satisfied.

In simulation, the algorithm produced a four-stage strategy. The first stage selected the initial point and the droplet model. The second stage selected the drifting flight model. The third and fourth stages selected the coplanar and then the non-coplanar fly-around models. The researchers reported that the algorithm generated the optimal combined observation sequence under the minimum fuel constraint.

A statistical analysis of effective observation time followed. For the same model configuration, a larger observation distance and a larger field-of-view angle significantly improved target observability and lengthened effective observation time. With distance and field of view held fixed, reducing the size of the model configuration also improved observation performance.

The release sets the work against activity in geostationary orbit (GEO), which it describes as a core strategic resource hosting a large number of missile early warning and military communication satellites. It states that U.S. GSSAP (Geosynchronous Space Situational Awareness Program) satellites have conducted hundreds of close-range observation operations on dozens of on-orbit satellites in the vicinity of GEO. According to the release, acquiring multi-aspect payload information on non-cooperative targets, in order to infer their functions and mission status, has become a critical part of space security assessment.

Close-range operations using fly-around, hovering and drifting configurations are an established way to approach and observe such targets. The authors said existing studies mostly address the control design of a single relative motion configuration, which does not meet the needs of multi-aspect observation. Combining several models raises its own problems, including smooth switching between modes, fuel optimization, strategy design algorithms and the effect of payload parameters.

The authors said the result is a systematic strategy design method for multi-aspect information acquisition on non-cooperative targets, with engineering reference value for space security assessment and on-orbit situational awareness.

CONTACT: https://spj.science.org/doi/10.34133/space.0419