  This paper investigates the application of reachability analysis to the
re-entry problem faced by vehicles entering Earth's atmosphere. The study
delves into the time evolution of reachable sets for the system, particularly
when subject to nonlinear implicit controls, given the potential damage from
the intense heat generated during hypersonic re-entry. Our proposed methodology
leverages zonotopes and constrained zonotopes to ensure compliance with safety
specifications. Furthermore, we utilize Model Predictive Control for detailed
trajectory planning. To substantiate our methodology, we provide detailed
simulations that not only tackle nonlinear re-entry scenarios but also
illustrate trajectory planning using MPC.
