The objective of this paper is to present an approximation-based strategy for solving the problem of nonlinear trajectory optimization with the consideration of probabilistic constraints. The proposed method defines a smooth and differentiable function to replace probabilistic constraints by the deterministic ones, thereby converting the chance-constrained trajectory optimization model into a parametric nonlinear programming model. In addition, it is proved that the approximation function and the corresponding approximation set will converge to that of the original problem. Furthermore, the optimal solution of the approximated model is ensured to converge to the optimal solution of the original problem. Numerical results, obtained from a new chance-constrained space vehicle trajectory optimization model and a 3-D unmanned vehicle trajectory smoothing problem, verify the feasibility and effectiveness of the proposed approach. Comparative studies were also carried out to show the proposed design can yield good performance and outperform other typical chance-constrained optimization techniques investigated in this paper.

中文翻译：

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在存在概率约束的情况下解决弹道优化问题。

本文的目的是提出一种基于近似的策略，该算法考虑了概率约束来解决非线性轨迹优化问题。该方法定义了一个光滑且可微的函数，用确定性约束代替概率约束，从而将机会约束的轨迹优化模型转换为参数非线性规划模型。另外，证明了逼近函数和相应的逼近集合将收敛于原始问题的逼近函数。此外，确保近似模型的最优解收敛到原始问题的最优解。数值结果 从新的机会受限的空间飞行器轨迹优化模型和3-D无人飞行器轨迹平滑问题中获得的数据，验证了该方法的可行性和有效性。还进行了比较研究，以表明所提出的设计可以产生良好的性能，并且胜过本文研究的其他典型的机会受限的优化技术。