涉及任意离散逻辑的多阶段轨迹间接优化
Indirect Optimization of Multi-Phase Trajectories Involving Arbitrary Discrete Logic
AI总结：
本研究针对航空航天飞行器多阶段轨迹中任意离散逻辑触发段转换的问题，提出GRASHS方法，通过逻辑转换与平滑将优化问题简化为两点边值问题，填补了RASHS方法无法处理AND/OR组合逻辑的空白。
摘要：
航空航天飞行器系统的多阶段轨迹包含多个飞行段，其转换可能由连续状态变量、控制和时间中的布尔逻辑触发。当布尔逻辑仅使用状态和/或时间表示时，此类系统被称为自主切换混合系统。之前引入的松弛自主切换混合系统方法（RASHS）旨在简化间接框架中仅使用AND运算表示布尔逻辑的此类系统的轨迹优化过程。本研究实现了涉及任意离散逻辑的情况，新方法被称为广义松弛自主切换混合系统（GRASHS）方法。与RASHS方法类似，GRASHS方法的结果是将最优性必要条件从多点边值问题转换为更易处理的两点边值问题，这通过将任意布尔逻辑转换为析取范式并使用sigmoid和双曲正切函数进行平滑来实现。GRASHS方法通过优化火星进入、下降和着陆轨迹进行演示：当速度低于降落伞展开速度或高度低于降落伞展开高度，且高度高于动力下降启动高度时，降落伞下降段激活，这组条件代表AND和OR逻辑的组合。之前的RASHS方法无法处理此类问题，所提出的GRASHS方法旨在填补这一空白。
英文摘要：
Multi-phase trajectories of aerospace vehicle systems involve multiple flight segments whose transitions may be triggered by boolean logic in continuous state variables, control and time. When the boolean logic is represented using only states and/or time, such systems are termed autonomously switched hybrid systems. The relaxed autonomously switched hybrid system approach (RASHS) was previously introduced to simplify the trajectory optimization process of such systems in the indirect framework when the boolean logic is solely represented using AND operations. This investigation enables cases involving arbitrary discrete logic. The new approach is termed the Generalized Relaxed Autonomously Switched Hybrid System (GRASHS) approach. Similar to the RASHS approach, the outcome of the GRASHS approach is the transformation of the necessary conditions of optimality from a multi-point boundary value problem to a two-point boundary value problem, which is simpler to handle. This is accomplished by converting the arbitrary boolean logic to the disjunctive normal form and applying smoothing using sigmoid and hyperbolic tangent functions. The GRASHS approach is demonstrated by optimizing a Mars entry, descent, and landing trajectory, where the parachute descent segment is active when the velocity is below the parachute deployment velocity or the altitude is below the parachute deployment altitude, and the altitude is above the powered descent initiation altitude. This set of conditions represents a combination of AND and OR logic. The previously introduced RASHS approach is not designed to handle such problems. The proposed GRASHS approach aims to fill this gap.
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