Machine learning-based quasi-optimal feedback control for a propellantless re-entry

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Atmospheric re-entry includes all the activities ensuring the safety of individuals and ground assets, with potential implications for the controlled landing of humans and payloads on planetary surfaces. A robust system for controlled re-entry is imperative for space missions requiring the retrieval of samples. Initially developed for large vehicles, the re-entry technologies evolved to encompass compact capsules capable of retrieving small satellites on Earth, driven by the increasing interest in SmallSats. In this context, the current work proposes an aerodynamic-based approach to ensure an optimal controlled re-entry up to a desired target point in terms of altitude, latitude, and longitude. Furthermore, a novel closed-loop feedback control system based on Deep Neural Networks (DNNs) is proposed to face the unpredictable perturbations that can affect the re-entry. The aerodynamic force modulation can be accomplished by changing the aerodynamic angles. After an initial passive descent, a subsequent phase starts, during which active control is performed to ensure precise targeting. Formulated as a single-stage optimal control problem, the algorithm focuses on this second phase, exploiting the angle of attack and the bank angle as control variables to reach the desired target point in the minimum time. A set of 750 optimal control trajectories is generated to constitute the training set for the DNN. The successful outcome of the optimal control algorithm and the closed-loop feedback controller is demonstrated by different Monte Carlo analyses. The proposed work offers a noteworthy alternative for real applications, allowing propellantless devices to perform a safe and controlled re-entry.