Tensor modeling of zero-sum games for competitive and cooperative formation flying

In the last decade, space has finally emerged as an independent domain for defense and security. Since then, applications aimed at monitoring or interfering with other spacecraft in close proximity, including space surveillance and in-orbit servicing, have been attracting growing interest. As the number of spacecraft involved grows, the need to implement guidance and control laws capable of ensuring an adequate degree of autonomy and safety emerges. The proposed method models satellite interactions as zero-sum differential games where each spacecraft optimizes its control strategy considering the others. Using tensor algebra, the framework extends to multiple satellites and achieves coordinated, collision-free behavior through Nash equilibrium solutions verified through numerical simulations.