Purpose: The purpose of this paper is to present a method to achieve small satellite formation keeping operations by using the differential lift and drag to control the drift caused by J2 perturbation in circular or near-circular low earth orbits (LEOs). Design/methodology/approach: Each spacecraft is equipped with five large flat plates, which can be controlled to generate differential accelerations. The aerodynamic lift and drag acting on a flat plate is calculated by the kinetic theory. To maintain the formation within tracking error bounds in the presence of J2 perturbation, a nonlinear Lyapunov-based feedback control law is designed. Findings: Simulation results demonstrate that the proposed method is efficient for the satellite formation keeping and better accuracy advantage in comparison with classical approaches via the fixed maximum differential aerodynamic acceleration. Research limitations/implications: Because the aerodynamic force will reduce drastically as the orbital altitude increases, the formation keeping control strategy for small satellites presented in this paper should be limited to the scenarios when satellites are in LEO. Practical implications: The formation keeping control method in this paper can be applied to solve satellite formation keeping problem for small satellites in LEO. Originality/value: This paper proposes a Lyapunov control strategy for satellite formation keeping considering both lift and drag forces, and simulation results show better performance with high accuracy under J2 perturbation.

For continuous-discrete filtering with unpredictable approximation errors, by proposing the novel stochastic feedback scheme, this note elaborates a closed-loop adaptive Kalman filter for nonlinear continuous-discrete systems. In conventional filters, unknown approximation errors might arise due to the integration/discretization and linearization of continuous model, and ruin the optimality of Kalman theory. As the main contribution of this note, the stochastic feedback based covariance adaption scheme does not require the approximation steps; instead, the posteriori sequence is mined as a feedback to adapt the priori error covariance, so that the unpredictable errors and costly calculations can be reduced or controlled in the novel closed-loop filtering structure. The new approach's advantages in computational cost, adaptability, and accuracy have been demonstrated by the numerical simulations.

The optimal satellite-formation collision-avoidance maneuver problem is investigated in terms of relative eccentricity and inclination vectors (E/I vectors) in relative E/I vectors plane. Using the relative E/I vectors theory and under the relative inclination vector unchanged assumption, first, the fuel-optimal collision-avoidance maneuver problem to maneuver the final target configuration with predefined passive safety parameters using minimal fuel is transferred to the geometrical problem to find the shortest distance from the initial point determined by the current relative eccentricity vector to the hyperbolic curve, which is determined by a predefined passive safety parameter in the relative E/I vectors plane. This case is solved using the Newton interaction method. Second, the optimal collision-avoidance maneuver problem to maneuver the final target configuration having maximum passive safety parameter under limiting fuel constraint is interpreted as the geometrical problem to find the opti...

It's important for China's Land Observing Satellite-1 to run in a repeat ground-track orbit with almost constant altitude over the same geographical area, so the satellite can have a high-precision deformation monitoring capability. The strong continuity of reference trajectory and high computational efficiency of the algorithm are required in the satellite orbit design stage. To fulfill those requirements, we first propose a fast orbit design method based on objective dimensionality reduction and decoupling optimization, which makes the satellites drift naturally without additional propellant consumption. Besides, a completely different convergence standard for the orbit design is introduced, which greatly reduces the complexity of the optimization process by decreasing the optimization objective dimension. Meanwhile, an optimal strategy keeping the argument of latitude constant is proposed, which reduces the coupling characteristics among optimization objectives. In addition, the optimization model of the repeat ground-track orbit is established. Then the steepest descent method is introduced to solve this optimization problem. Simulation results in the high-order gravity force reveal that the position accuracy and velocity accuracy of the reference trajectory are up to millimeters and centimeters per second respectively. The calculation efficiency of our method is about 56 times faster than that of the NSGA-II method.