With the increasing complexity of space missions, traditional Keplerian models no longer satisfy the precision requirements for spacecraft orbital calculations in modern deep space exploration and lunar transfer missions. Unlike J₂ perturbations, third-body perturbations induce long-period oscillations in orbital eccentricity and inclination, resulting in significant nonlinear changes in long-term orbital evolution that present challenges for deriving analytical solutions. This paper proposes an analytical method for spacecraft orbit propagation under third-body perturbations, which divides the calculation into long-term and periodic components. The long-period terms are determined by solving the mean orbital dynamics using elliptical integrals, while the periodic terms are computed using von Zeipel theory. The proposed method enables the analytical computation of satellite orbital states at arbitrary epochs. This method accounts for the perturbing body’s orbital eccentricity and inclination, making it applicable to all scenarios, including both circulating and librating orbit types. The effectiveness of the proposed method is verified through numerical simulations. This analytical propagation method provides robust support for orbital optimization and autonomous control in deep space exploration missions.

This study investigated the problems of non-cooperative target recognition and relative motion estimation during spacecraft rendezvous maneuvers. A structure integrating an Inertial Measurement Unit (IMU) and a visual camera was presented. The angular velocity output of the IMU was used to calculate the motion trajectories of star points in multiple image frames, which can highlight the motion of non-cooperative targets with respect to the image background to improve the probability of target recognition. To solve the problem of target misidentification caused by new star points entering the field of view, a target-tracking link based on IMU prediction was introduced to track the position of the target in the image. Furthermore, a measurement model was constructed using the line-of-sight vector generated from target recognition, and the relative motion state was estimated using a Huber-based non-linear filter. Semi-physical and numerical simulations were performed to evaluate the effectiveness and efficiency of the proposed method.

The distributed prescribed-time orbit containment control for the satellite cluster flight with multiple dynamic leaders is investigated. The directed information communication topology between followers is taken into account in the overall paper. When the satellite mass is assumed to be constant, a distributed prescribed-time orbit containment controller is, firstly, presented to drive the followers into the dynamic convex hull produced by multiple leaders. Then, the parameter uncertainty is considered, and a prescribed-time sliding mode estimator is introduced to estimate the desired velocity of each follower. Based on the estimated state, a novel distributed adaptive prescribed-time orbit containment control scheme is proposed. The Lyapunov stability theory is utilized to prove the prescribed-time stability of the closed-loop system. Finally, several numerical simulations and comparison of different control methods are provided to verify the effectiveness and superiority of the proposed control method.

This paper addresses a coordinated control problem for Spacecraft Formation Flying (SFF). The distributed followers are required to track and synchronize with the leader spacecraft. By using the feature points in the two-dimensional image space, an integrated 6-degree-of-freedom dynamic model is formulated for spacecraft relative motion. Without sophisticated three-dimensional reconstruction, image features are directly utilized for the controller design. The proposed image-based controller can drive the follower spacecraft in the desired configuration with respect to the leader when the real-time captured images match their reference counterparts. To improve the precision of the formation configuration, the proposed controller employs a coordinated term to reduce the relative distance errors between followers. The uncertainties in the system dynamics are handled by integrating the adaptive technique into the controller, which increases the robustness of the SFF system. The closed-loop system stability is analyzed using the Lyapunov method and algebraic graph theory. A numerical simulation for a given SFF scenario is performed to evaluate the performance of the controller.