Abstract—

The problem of an optimal spatial turn on a fixed time interval is considered for a quaternion-based model of a spacecraft. It is required to transfer a spacecraft from the specified initial state to the desired final position, provided that the control is bounded. As an example, cases are considered, when the objective functional has a sense of minimizing the fuel consumption or expenses for control. The desired control is found using Pontryagin’s maximum principle and the quasilinearization technique. The method of separation of phase and conjugate variables is proposed to solve the resulting two-point boundary-value problem (TPBVP). The use of an analytical approach for solving the TPBVP allows one to increase the calculation accuracy and to reduce computation time.

中文翻译：

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变量分离方法及其在航天器最佳转弯问题中的应用

摘要—

对于基于四元数的航天器模型，考虑了在固定时间间隔上实现最佳空间转向的问题。只要控制装置是有界的，就需要将航天器从指定的初始状态转移到所需的最终位置。作为示例，考虑了当目标功能具有最小化燃料消耗或控制费用的感觉的情况。使用Pontryagin的最大原理和拟线性化技术可以找到所需的控制。提出了分离相位和共轭变量的方法，以解决由此产生的两点边值问题。使用解析方法来解决TPBVP可以提高计算精度并减少计算时间。