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首页> 外文期刊>Journal of guidance, control, and dynamics >Lyapunov-Based Guidance for Orbit Transfers and Rendezvous in Levi-Civita Coordinates
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Lyapunov-Based Guidance for Orbit Transfers and Rendezvous in Levi-Civita Coordinates

机译：Levi-Civita坐标中基于Lyapunov的轨道转移和交会指导

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摘要

This paper considers planar orbit transfers and rendezvous problems around a central body using Lyapunov stability theory. The model used is the Levi-Civita transformation of the planar two-body problem. One of the advantages of working in these transformed coordinates is that the solution to the unperturbed equations of motion is that of a simple harmonic oscillator, so the analytical solution is known at all times during coast phases. We design a closed-loop guidance scheme for orbit transfers from any initial elliptical orbit to any final elliptical orbit using a spacecraft with thrust-coast capabilities. A similar procedure is performed to design a control law for rendezvous with any desired target spacecraft. The proposed Lyapunov functions give rise to asymptotically stabilizing control laws. The algorithms designed are robust to initial and final conditions, computationally fast, and no restrictions are imposed on the magnitude of the thrust. The guidance scheme is also effective in a dynamic model where unmodeled perturbations are present.
机译：本文利用李雅普诺夫稳定性理论考虑了围绕中心物体的平面轨道转移和交会问题。所使用的模型是平面两体问题的Levi-Civita变换。在这些变换后的坐标中进行工作的优点之一是，对无扰动运动方程的求解是一个简单的谐波振荡器的解，因此，在惯性运动阶段，解析解始终是已知的。我们设计了一种闭环制导方案，用于使用具有推力滑行能力的航天器将轨道从任何初始椭圆形轨道转移到任何最终椭圆形轨道。执行类似的过程来设计与任何所需目标航天器交会的控制律。提出的Lyapunov函数引起渐近稳定的控制律。设计的算法对初始和最终条件具有鲁棒性，计算速度快，并且对推力的大小没有限制。指导方案在存在未建模扰动的动态模型中也很有效。

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