Review of Advanced Trajectory Optimization Methods

When encountering atmospheric or exo-atmospheric spacecraft flight, a well-designed trajectory is essential for making the flight stable and enhancing the guidance and control of the vehicle. Much research has focused on how to design suitable spacecraft trajectories available for various mission profiles. To optimize the flight trajectory, researchers have designed numerous useful tools successfully. Nevertheless, it is only in the last five years that the interest in how to plan flight trajectories and consider numerous mission goals and different model errors/uncertainties simultaneously has grown greatly. Note that for various practical guidance, navigation and control systems for spacecraft, during the trajectory planning process, the frequent consideration of multiple performance indices and various forms of uncertainty is necessary. Consequently, the multi-objective spacecraft trajectory optimization methods and stochastic spacecraft trajectory optimization algorithms are successfully proposed with the help of the requirements mentioned above. The core aim of this chapter is to provide a wide overview of current developments in numerical multi-objective trajectory optimization algorithms and stochastic trajectory planning approaches for spacecraft flight operations. First, we will briefly describe the process of how the problem is formulated mathematically. Then several optimization strategies for addressing spacecraft trajectory planning problems, such as gradient-based methods, convexification-based methods, and evolutionary/metaheuristic methods, are discussed. Besides, we will overview the formulation process of the multi-objective spacecraft trajectory optimization problem, as well as multiple types of multi-objective optimization algorithms. The significant features, for example, the merits and demerits of the newly-proposed multi-objective approaches, are summarized. Furthermore, we will pay some attention to the extension of the original deterministic problem to a stochastic form. To handle the stochastic trajectory planning formulation, several robust optimization algorithms are also outlined. Additionally, applications of the optimized trajectory proposed recently will be especially focused on. Finally, we will draw some conclusions and discuss further research about strategies for multi-objective and stochastic trajectory optimization.