Neural Backward Reach-Avoid Tubes with MPC Supervision for High-Dimensional Systems: An Application to Safe Spacecraft Docking

• URL: http://arxiv.org/abs/2605.02021v1
• Date: Sun, 03 May 2026 19:00:06 GMT
• Title: Neural Backward Reach-Avoid Tubes with MPC Supervision for High-Dimensional Systems: An Application to Safe Spacecraft Docking
• Abstract summary: Hamilton-Jacobi (HJ) reachability provides formal reach-avoid guarantees, but classical solvers are limited to low-dimensional systems.<n>We propose a learning-based Backward Reach-Avoid Tube (BRAT) framework that tightly integrates HJ structure with MPC-based supervision.<n>We evaluate the proposed method on a 6D planar docking problem against grid-based ground truth and then scale to the full 13D system.
• Score: 6.387263468033964
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Autonomous spacecraft docking requires control policies that simultaneously ensure collision avoidance and target reachability under coupled, high-dimensional translational-rotational dynamics. Hamilton-Jacobi (HJ) reachability provides formal reach-avoid guarantees, but classical solvers are limited to low-dimensional systems. Learning-based approaches have begun to scale HJ analysis, yet they struggle in reach-avoid settings, especially where goal and failure sets are tightly coupled, as in docking. We propose a learning-based Backward Reach-Avoid Tube (BRAT) framework that addresses this challenge by tightly integrating HJ structure with MPC-based supervision. In the offline phase, we train a neural approximation of the HJ value function using PDE-based losses augmented with curriculum-driven MPC supervision, which provides informative value targets and stabilizes training in regions where purely PDE-based methods fail. In the online phase, the learned value function is deployed through two real-time controllers: (i) a value gradient-driven controller, and (ii) a value-function-augmented terminal MPC that explicitly enforces reachability at the horizon. We evaluate the proposed method on a 6D planar docking problem against grid-based ground truth and then scale to the full 13D system. Across both settings, our approach outperforms existing methods in success rate and computational efficiency.

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