With the intensifying space confrontation in geostationary orbit (GEO), the 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. The acquisition of multi-aspect information from non-cooperative targets has thus become a critical component of space security assessment. Close-range spacecraft operations, which employ relative motion configurations such as fly-around, hovering, and drifting flight, provide an effective technical means for approaching and observing targets to obtain multi-aspect payload information. However, existing studies predominantly focus on the control design of a single relative motion configuration, which fails to satisfy the complex mission requirements of multi-aspect observation. The combination of multiple models for observation presents multiple challenges, including smooth switching between modes, fuel optimization, strategy design algorithms, and analysis of payload parameter effects. Therefore, how to coordinately plan a sequential combination of multiple close-range operation models under minimum fuel constraints to efficiently acquire multi-aspect information of non-cooperative targets has become a key bottleneck in enhancing space situational awareness capabilities.
In a recent study published in Space: Science & Technology , the team led by Meng Yunhe from the School of Artificial Intelligence, Sun Yat-sen University, proposed a strategy design method for multi-model combined observation of spacecraft based on sequential coalition game theory. Based on the Clohessy–Wiltshire relative dynamics equations, the study constructs four typical close-range operation models, namely the droplet model, the coplanar fly-around model, the non-coplanar fly-around model, and the drifting flight model, and provides the solution functions for the initial motion states that yield stable relative motion configurations. To achieve smooth switching between models, a waypoint trajectory planning scheme and a multi-impulse maneuver strategy are designed based on the minimum integral squared control theory. On this basis, the sequential coalition game theory is introduced for the first time into the multi-model combined observation problem. By constructing a game tree, the algorithm selects the optimal combination of initial motion points and close-range operation models at each stage under minimum fuel constraints, thereby generating an optimal observation strategy sequence. Furthermore, a statistical analysis of the effective observation time under different observation distances and field-of-view angles is conducted. Simulation results demonstrate that the proposed algorithm can successfully generate a multi-model combined observation strategy sequence under minimum fuel constraints; the effective observation time increases with larger observation distances and field-of-view angles, and reducing the model configuration size also contributes to improved observation performance. This study provides a systematic strategy design method for multi-aspect information acquisition of non-cooperative targets, offering significant engineering reference value for space security assessment and on-orbit situational awareness.
First, this study focuses on the problem of multi-aspect observation strategy design for non-cooperative spacecraft and proposes a multi-model combined observation method based on sequential coalition game theory. As a core strategic resource, the geostationary orbit (GEO) hosts a large number of missile early warning and military communication satellites. In recent years, the U.S. GSSAP (Geosynchronous Space Situational Awareness Program) satellites have conducted close-range observation operations on dozens of on-orbit satellites in the vicinity of GEO, rendering the space security situation increasingly severe. Acquiring multi-aspect payload information of non-cooperative targets to infer their functions and mission statuses is of great significance for space security assessment. Fig. 1 defines the LVLH (Local Vertical–Local Horizontal) coordinate frame, which serves as the basis for describing relative spacecraft motion. Fig. 2 illustrates the observation cameras mounted in the ±y directions of the spacecraft; given the constraints of observation distance and field-of-view angle, the effective observation time is defined as the total duration during which the target can be observed while satisfying the prescribed constraints. Since the observation cameras on the spacecraft are fixedly installed, frequent large-angle attitude maneuvers are time-consuming and consume substantial fuel. By designing a combination sequence of multiple close-range operation models, multi-aspect information acquisition of non-cooperative targets can be achieved with minimum fuel consumption. As shown in Fig. 3, through the sequential combination of the four configurations—namely the droplet model, the coplanar fly-around model, the non-coplanar fly-around model, and the drifting flight model—the observing spacecraft can realize multi-aspect imaging.
Second, the study constructs four typical close-range operation models and designs a sequential coalition game solution algorithm. Based on the Clohessy–Wiltshire relative dynamics equations, the analytical solutions of unforced relative motion are derived, and the solution functions for the initial motion states that yield stable relative motion configurations are provided by designing the relative distance and phase angle parameters. The droplet model, characterized by symmetry and re-visit capability, enables fine observation of the target; the coplanar and non-coplanar fly-around models facilitate fly-around observations in different orbital planes; and the drifting flight model achieves close-range observation through multi-impulse control. To achieve smooth switching between models, a waypoint trajectory planning scheme is designed based on the minimum integral squared control theory. On this basis, the sequential coalition game theory is introduced for the first time into the multi-model combined observation problem. Through game tree search, the optimal combination is selected at each stage under minimum fuel constraints, generating an optimal observation strategy sequence.
Finally, the study validates the effectiveness of the proposed method through simulations and analyzes the influencing factors of effective observation time. Fig. 4 presents the three-dimensional relative trajectories of the four-model combined observation, and Table 3 lists the generated sequential coalition observation strategy set: the first stage selects the initial point and the droplet model, the second stage selects the drifting flight model, and the third and fourth stages sequentially select the coplanar and non-coplanar fly-around models. The simulation results demonstrate that the algorithm can successfully generate the optimal combined observation sequence under minimum fuel constraints. Based on the combined observation strategy, the study conducts a statistical analysis of the effective observation time. As shown in Fig. 5, the combined effects of observation distance and field-of-view angle on effective observation time are comprehensively examined; the results indicate that under the same close-range operation model configuration, increasing the observation distance and field-of-view angle significantly enhances target observability and yields longer effective observation time. Given fixed observation distance and field-of-view angle, reducing the model configuration size also contributes to improved observation performance. This study applies sequential game theory to the multi-model combined observation problem of spacecraft for the first time, providing a systematic strategy design method for multi-aspect information acquisition of non-cooperative targets, which offers significant engineering reference value for space security assessment and on-orbit situational awareness.
Space: Science & Technology
Spacecraft Proximity Operation Model-Based Sequential Coalitional Observation Game Strategy Design
30-Jun-2026