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This study presents an innovative approach that utilizes scientific machine learning and two types of enhanced neural networks for modeling a parametric guidance algorithm within the framework of ordinary differential equations to optimize the landing phase of reusable rockets. Our approach addresses various challenges, such as reducing prediction uncertainty, minimizing the need for extensive training data, improving convergence speed, decreasing computational complexity, and enhancing prediction accuracy for unseen data. We developed two distinct enhanced neural network architectures to achieve these objectives: Adaptive (AQResNet) and Rowdy Adaptive (RAQResNet) Quadratic Residual Neural Networks. These architectures exhibited outstanding performance in our simulations. Notably, the RAQResNet model achieved a validation loss approximately 300 times lower than the standard architecture with an equal number of trainable parameters and 50 times lower than the standard architecture with twice the number of trainable parameters. Furthermore, these models require significantly less computational power, enabling real-time computation on modern flight hardware. The inference times of our proposed models were measured in approximately microseconds on a single-board computer. Additionally, we conducted an extensive Monte Carlo analysis that considers a wide range of factors, extending beyond aerodynamic uncertainty, to assess the robustness of our models. The results demonstrate the impressive adaptability of our proposed guidance policy to new conditions and distributions outside the training domain. Overall, this study makes a substantial contribution to the field of reusable rocket landing guidance and establishes a foundation for future advancements.

Optimal Reusable Rocket Landing Guidance: A Cutting-Edge Approach Integrating Scientific Machine Learning and Enhanced Neural Networks