Abstract Equipping a spacecraft with multiple solar-powered electric engines (of the same or different types) compounds the task of optimal trajectory design due to presence of both real-valued inputs (power input to each engine in addition to the direction of thrust vector) and discrete variables (number of active engines). Each engine can be switched on/off independently and “optimal” operating power of each engine depends on the available solar power, which depends on the distance from the Sun. Application of the Composite Smooth Control (CSC) framework to a heliocentric fuel-optimal trajectory optimization from the Earth to the comet 67P/Churyumov-Gerasimenko is demonstrated, which presents a new approach to deal with multiple-engine problems. Operation of engine clusters with 4, 6, 10 and even 20 engines of the same type can be optimized. Moreover, engine clusters with different/mixed electric engines are considered with either 2, 3 or 4 different types of engines. Remarkably, the CSC framework allows us 1) to reduce the original multi-point boundary-value problem to a two-point boundary-value problem (TPBVP), and 2) to solve the resulting TPBVPs using a single-shooting solution scheme and with a random initialization of the missing costates. While the approach we present is a continuous neighbor of the discontinuous extremals, we show that the discontinuous necessary conditions are satisfied in the asymptotic limit. We believe this is the first indirect method to accommodate a multi-mode control of this level of complexity with realistic engine performance curves. The results are interesting and promising for dealing with a large family of such challenging multi-mode optimal control problems.

中文翻译：

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具有多种推进系统运行模式的最优轨迹设计的新方法，第 2 部分

摘要 由于存在两个实值输入（除了推力矢量的方向，每个发动机的功率输入），为航天器配备多个太阳能电动发动机（相同或不同类型）使优化轨迹设计的任务复杂化。和离散变量（活动引擎的数量）。每个引擎都可以独立打开/关闭，每个引擎的“最佳”运行功率取决于可用的太阳能，这取决于与太阳的距离。展示了复合平滑控制 (CSC) 框架在从地球到彗星 67P/Churyumov-Gerasimenko 的日心燃料优化轨迹优化中的应用，这提出了一种处理多发动机问题的新方法。可以优化具有 4、6、10 甚至 20 个相同类型发动机的发动机组的运行。此外，具有不同/混合电动发动机的发动机组被视为具有 2、3 或 4 种不同类型的发动机。值得注意的是，CSC 框架允许我们 1) 将原始的多点边值问题简化为两点边值问题 (TPBVP)，以及 2) 使用单次射击解决方案和缺失的协同作用的随机初始化。虽然我们提出的方法是不连续极值的连续邻居，但我们表明在渐近极限中满足不连续必要条件。我们相信这是第一种通过真实的发动机性能曲线来适应这种复杂程度的多模式控制的间接方法。