Final Glide-back Envelope Computation for Reusable Launch Vehicle Using Reachability

The main limitation of existing computational tools for continuous system reachability problems is that, due to the exponential growth of the computation with the dimension of the continuous state space, the tools can be applied effectively to relatively low dimensional problems (typically 1-4 dimensions). In this paper we adopt a two time scale approach to extend the use of continuous system reachability tools to six dimensions, thus making them applicable to a number of interesting case studies in the area of aeronautics. To prove the effectiveness of our approach, we apply it in the final glideback envelope computation for safe landing of a small reusable launch vehicle (RLV) in a non-steady atmosphere. The mathematical model of the RLV that is used is a three-degree of freedom (six state) nonlinear point mass model, modified to contain ambient winds and several state constraints for the final approach phase. The results show that it is feasible to do exacting computations with nonlinear continuous dynamics in higher dimensions, if one can exploit additional structure in the model, in our case, the separation into slow and fast dynamics.