Neural Backward Reach-Avoid Tubes with MPC Supervision for High-Dimensional Systems: An Application to Safe Spacecraft Docking
This work addresses safe control for high-dimensional autonomous systems with tight coupling between goal and failure sets, offering a scalable approach to formal reach-avoid guarantees.
The paper proposes a learning-based Backward Reach-Avoid Tube (BRAT) framework for high-dimensional systems, integrating HJ reachability with MPC supervision. Applied to 6D and 13D spacecraft docking, it outperforms existing methods in success rate and computational efficiency.
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.