New Method Optimizes Low-Thrust Trajectory Reachability Analysis

This paper introduces a dual formulation of the reachability problem for low-thrust spacecraft trajectory optimization. Instead of computing reachable sets directly, the method determines, for fixed transfer time and boundary conditions, the maximum allowable initial mass (or, for solar sails, a scalar sail-strength parameter) that permits a successful transfer. A target is reachable if the spacecraft's initial mass does not exceed this threshold. This reformulation reduces reachability assessment to a scalar optimization problem for each target, producing a smooth scalar field that encodes equivalent feasibility information to classical reachable sets. The authors develop indirect maximum-initial-mass (MIM) formulations for both electric low-thrust and solar-sail dynamics and show how they can serve as efficient reachability oracles. Building on this formulation, they construct data-driven surrogate models to approximate the MIM-based reachability indicator, using fully connected neural networks and residual networks. The resulting surrogates enable rapid reachability evaluation while preserving the numerical advantages of the dual formulation, offering a practical tool for preliminary mission design and feasibility assessment. This approach addresses the computational limitations of classical reachability analysis, particularly for high-dimensional systems or strongly nonlinear dynamics encountered in cislunar environments or solar sail missions.

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