Satellite formation control for cooperative observation around the rotating China Space Station

With the long-term on-orbit operation of the China Space Station, using nanosatellite swarms for cooperative observation of its external structures has become an important technical direction for enhancing in‑orbit monitoring capabilities. However, the space station itself has a non‑spherical complex geometry (e.g., protruding structures such as modules and docking ports) and may perform attitude maneuvers (e.g., sun‑pointing) during orbital flight, making it a dynamic obstacle with both intricate shape and rotational motion relative to the nanosatellites. Traditional artificial potential field obstacle avoidance methods mostly simplify obstacles as spheres or ellipsoids, which cannot accurately characterize the composite geometric features of the space station, and usually ignore the obstacle's own rotational motion. This leads to difficulties in constructing the repulsive potential field, limited maneuvering space, and, more critically, a lack of rigorous theoretical proof to guarantee closed-loop system stability and collision avoidance. Therefore, developing a nanosatellite formation control method that can handle rotating non‑spherical obstacles while providing strict stability guarantees is of significant theoretical importance and engineering value for ensuring safe fly-around and efficient cooperative observation in the vicinity of the space station.

Recently, a study published in Space: Science & Technology by the team of Dang Zhaohui from the School of Astronautics, Northwestern Polytechnical University, proposed a nanosatellite swarm formation control method for cooperative observation of the rotating China Space Station. The study first established a space‑station‑centered inertial coordinate system, derived the open-loop dynamics model of the nanosatellite swarm, and provided the transformation relationships between the state and control variables in the inertial frame, the local-vertical-local-horizontal (LVLH) frame, and the body‑fixed frame. Using the three-dimensional elliptical parametric equations and the analytical solutions of relative motion, a near-natural-fly-around formation configuration was defined in the LVLH frame, and the formation parameters that satisfy both obstacle avoidance and observation coverage requirements were optimized through exhaustive search. On this basis, incorporating the composite repulsive potential function for the space station previously proposed by the team, a tracking control law incorporating attractive potential from the target, damping, inter-satellite repulsion, and obstacle repulsion was designed in the body-fixed frame. By constructing a Lyapunov function and adjustable damping coefficient rules, the stability and collision‑avoidance performance of the closed‑loop system were rigorously proven. Simulation results under two scenarios—inertial pointing and attitude maneuvering of the space station—demonstrated that the proposed control law enables the nanosatellite swarm to safely converge to the desired formation configuration while effectively avoiding collisions with the space station. In contrast, classical methods based on ellipsoidal envelope failed to mitigate collision risks. Furthermore, during attitude maneuvers of the space station, the swarm maintained obstacle avoidance and stable formation tracking, validating the method's adaptability to rotating composite obstacles. This study provides a theoretically rigorous and engineering‑feasible solution for safe nanosatellite formation control in environments with rotating composite obstacles, offering significant application value for enhancing China's external cooperative observation capabilities of the space station.

First, the authors established a dynamic model and coordinate transformation framework for nanosatellite swarm cooperative observation, targeting the China Space Station (CSS) as a non-spherical, rotating complex obstacle. As shown in Fig. 1, the nanosatellites are required to form a fly-around formation near the space station to continuously observe key areas such as module connection zones. Since the space station itself consists of protruding structures including modules and docking ports, and may perform attitude maneuvers in orbit, traditional methods that simplify obstacles as spheres or ellipsoids cannot accurately describe the collision-avoidance boundaries. To address this, the study defined four coordinate systems: the Earth-centered inertial frame, the space-station-centered inertial frame, the LVLH (local-vertical-local-horizontal) frame, and the space-station body-fixed frame. By deriving the transformation relationships of state variables, natural accelerations, and control accelerations among these coordinate systems, the kinematic foundation was laid for subsequent formation control and obstacle avoidance analysis in the body‑fixed frame. In particular, when the space station orbit is approximately circular and unperturbed, the transformation matrix from the LVLH frame to the inertial frame can be expressed analytically. This part of the work resolves the key issue of describing nanosatellite relative motion under a moving base, enabling the target formation configuration to be intuitively expressed in the body‑fixed frame and facilitating the imposition of obstacle‑avoidance and observation constraints.

Second, the authors designed a near-natural three-dimensional elliptical fly-around formation based on the periodic solutions of the Clohessy-Wiltshire (CW) equations, and optimized the formation parameters through exhaustive search to meet both observation coverage and obstacle avoidance requirements. Since the periodic solutions correspond to natural relative trajectories under zero control, formations based on them can significantly reduce fuel consumption during long-duration flight. The formation configuration was described using a three-dimensional elliptical parametric equation, whose parameters correspond one-to-one to the amplitudes and phases of the CW solution. To quantify the observation effect on the space station's connection segments, the study selected 14 sampling points and defined the cost function as the average number of invisible points, then performed exhaustive computations under different parameter combinations. Fig. 2 presents the distribution of the cost function for different radial and normal amplitude parameter values, where the minimum corresponds to a higher observation coverage rate. After further fixing the normal amplitude to zero, Fig. 3 shows the variation of the cost function with radial amplitude and phase, and ultimately a set of formation parameters was selected that satisfies the constraints of minimum inter-satellite distance and minimum satellite-station distance. Verification confirmed that the target formation maintains a minimum distance from the space station surface well beyond the collision-detection threshold over the orbital period, and that inter-satellite distances also meet safety requirements, thus ensuring that the target state itself lies within the collision-free region and providing a feasible target for subsequent tracking control.

Finally, the authors designed a tracking control law with obstacle avoidance capability and closed-loop Lyapunov stability, and validated its effectiveness through simulations under two typical scenarios. The control law is implemented in the space-station body-fixed frame and includes target acceleration compensation, natural dynamics compensation, an attractive potential term, an adjustable damping term, an inter-satellite repulsion term, and an obstacle repulsion term based on a composite geometric repulsive potential. The damping coefficient is adaptively adjusted according to real‑time states to eliminate the influence of uncertain terms on stability. Rigorous theoretical proofs demonstrate that the control law ensures Lyapunov stability of the system and that the distance between each nanosatellite and the space station surface remains strictly positive, fundamentally avoiding collisions. In Case 1 (space station in inertial pointing attitude), as shown in Fig. 4, the nanosatellite swarm gradually converges from an initial circular formation to the designed elliptical fly-around orbit, maintaining a safe distance throughout the process; Fig. 5 shows that, if the traditional ellipsoidal envelope potential field is used, collisions may occur. Fig. 6 presents the variation of the number of visible observation points over time, and the full-coverage time ratio during the steady-state phase meets the design expectations. In Case 2, where the space station undergoes a transient attitude maneuver, Fig. 7 demonstrates that the proposed control law can still guide the swarm to safely track the target formation, verifying its adaptability to rotating obstacles. The paper also presents Monte Carlo simulation statistics for multiple performance metrics, showing that the final position errors, control magnitudes, and velocity increments are all within acceptable ranges. This study provides a theoretically rigorous and engineering-feasible control solution for safe cooperative observation of nanosatellites in the complex environment of the space station.