Lobatto IIIA Collocation Method

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

An implicit Runge-Kutta collocation method for solving boundary value problems. It satisfies state equations and boundary conditions simultaneously at each collocation point, converting optimal control problems into nonlinear algebraic systems. Unlike shooting methods, it requires state and co-state values at all sample points as initial guesses, enabling direct use of full-field periodic orbit or invariant manifold data.

Application Value

在Lobatto IIIA配点法的设计与分析中，可用于优化转移方案，减少燃料消耗 为航天器的精确控制提供理论依据，确保任务执行的可靠性 描述系统状态随时间的变化规律，是轨道预报的基础。

References

• Du et al., 2023, Two trajectory configurations for the low-thrust transfer between northern and southern halo orbits