Method for controlling periodic orbit near collinear Lagrange point

Abstract

The invention provides a control method of a periodic orbit near a collinear Lagrange point. A collinear Lagrangian point belongs to a hyperbolic equilibrium point, and the dynamic characteristic of the collinear Lagrangian point is strongly disturbed by a high-order nonlinear term of a system, so that periodic orbits nearby the collinear Lagrangian point are unstable. Due to the influence of orbit injection errors and external disturbance, the spacecraft cannot meet the precise solution of a periodic orbit all the time, and is constantly away from the Lagrange point under the uncontrolled condition. According to the invention, the idea of the differential correction algorithm is applied to the Hamiltonian structure controller, the control gain is corrected according to the given initial position speed of the spacecraft, and an effective control algorithm is provided to ensure that the spacecraft flies around the controlled period orbit in a bounded manner near the collinear Lagrange point. According to the differential correction algorithm, the initial position speed of the spacecraft does not need to be corrected, and the periodic orbit can be constructed under the condition that the initial position speed of the spacecraft is not required to be high in precision.

Description

technical field [0001] The invention belongs to the field of spacecraft orbit design and control, and relates to a method for controlling periodic orbits near a collinear Lagrangian point. Background technique [0002] There are three collinear Lagrangian points in the circular restricted three-body problem (CR3BP). According to the Lyapunov central theorem, there are a large number of periodic orbital clusters near the collinear Lagrangian points, such as Lyapunov orbital clusters. and Halo orbital clusters. These periodic orbits have advantageous positions and are very suitable for space missions such as relay communication, monitoring and surveillance. [0003] Collinear Lagrangian points belong to hyperbolic equilibrium points, and their dynamic characteristics are strongly disturbed by higher-order nonlinear terms of the system, resulting in unstable periodic orbits around them. In order to obtain the accurate solution of the periodic orbit, the approximate analytical...

AI Technical Summary

Problems solved by technology

Since the above numerical simulation methods all use the initial position and velocity of the spacecraft as the correction amount to complete the numerical iterative correction, when the initial position and velocity of the spacecraft do not meet the periodic orbit conditions, the accuracy of the spacecraft’s orbiting is poor, or deviations occur due to external disturbances, the traditional method Calculated periodic orbits will be invalid

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