Set-Based Reachability for Low-Thrust Spacecraft in Two-Body and Cislunar Dynamical Systems

Abstract

This paper investigates the application of zonotope-based reachability analysis to low-thrust spacecraft in both two-body and cislunar environments. Reachable sets are generated under two-body and circular restricted three-body (CR3BP) dynamics using set-based methods that approximate nonlinear systems via Taylor expansions. A state-dependent coefficient (SDC) parameterization is also explored to represent nonlinear dynamics in a pseudo-linear form, enabling efficient matrix based propagation of reachable sets. Applications include Earth-Mars transfer and cislunar scenarios such as L1 and L2 Halo orbits and Near Rectilinear Halo Orbits (NRHOs). The resulting reachable sets are used for safe trajectory generation and tracking, with comparisons drawn between model predictive control (MPC) and LQR-based station-keeping. The proposed approach provides a scalable framework for analyzing spacecraft behavior under complex dynamics and control constraints.