To address the high-efficiency orbit calculation problem of spacecraft, this paper reviews research on integral correction methods. First, a variety of integral correction methods based on different principles are systematically introduced within a unified notation framework, and a classification comparison is conducted. Then, focusing on the advantages of these methods in large-step and parallel computation, the research progress in parameter optimization and parallel acceleration is summarized. Subsequently, the unique superiority of integral correction methods is elaborated by typical applications such as spacecraft orbit design, high-precision orbit propagation, and spacecraft guidance. Finally, combining the methods’ characteristics and the orbit calculation requirements, the development trends and directions worth studying are analyzed and proposed.

To establish the optimal reference trajectory for a near-space vehicle under free terminal time, a time-optimal model predictive static programming method is proposed with adaptive fish swarm optimization. First, the model predictive static programming method is developed by incorporating neighboring terms and trust region, enabling rapid generation of precise optimal solutions. Next, an adaptive fish swarm optimization technique is employed to identify a sub-optimal solution, while a momentum gradient descent method with learning rate decay ensures the convergence to the global optimal solution. To validate the feasibility and accuracy of the proposed method, a near-space vehicle example is analyzed and simulated during its glide phase. The simulation results demonstrate that the proposed method aligns with theoretical derivations and outperforms existing methods in terms of convergence speed and accuracy. Therefore, the proposed method offers significant practical value for solving the fast trajectory optimization problem in near-space vehicle applications.

To achieve precise control of terminal states for near-space vehicles under underactuated conditions, it is necessary to overcome the limitations of onboard computational capability and develop a highly precise and efficient trajectory optimization framework in computational guidance. If the number of discretization points is too low, existing Newton-type trajectory optimization methods by deviation dynamic equations (Model Predictive Static Programming) have large terminal control errors. Motivated by current quasi-spectral Newton method, a quasi-spectral optimization method is proposed by actual dynamic equations. Unlike existing methods that update the optimization coefficient indirectly, this method updates the optimization coefficient directly. Additionally, it is proven that this method is a Newton optimization method, and it is clearly shown that when damping mechanism is not considered, this method suffers from poor robustness during multiple iterations. To address the poor robustness and low control accuracy in typical Newton methods, an adaptive trajectory optimization method is proposed with fuzzy control. This method avoids the divergence problem commonly encountered in damping-free methods with sensitive initial values, thereby enhancing both robustness and accuracy. Simulation results show that the proposed method achieves faster dynamic trajectory optimization than existing methods under identical conditions.

A servicing spacecraft installed with compliant flexible rod has recently emerged as an innovative solution for efficiently detumbling satellite. However, the undesired vibrations of the flexible rod are easily excited by the contact process, bringing detrimental effects for the accurate and safe operations. Besides, the contact-induced strong disturbance makes most of the existing controllers difficult to achieve guaranteed transient and steady-state performances. To conquer the above problems, a novel Nonlinear Energy Sink with Active Varying Stiffness (NES-AVS) device is proposed to significantly reduce the vibrations, wherein the AVS is realized by a small steel plate with the compression force adjusted by a piezoelectric actuator. Moreover, a composite prescribed performance detumbling controller is designed based on the fast non-singular terminal sliding mode control technique. A performance function is adopted to constrain the tracking errors to meet the prescribed dynamic properties, and an adaptive law is incorporated into the control framework to effectively reject the disturbance. Extensive simulations are conducted to demonstrate the effectiveness of the proposed NES-AVS device and controller.