Reachable and Controllable Sets for Planetary Entry and Landing

Understanding the envelope of entry trajectories that a given planetary lander is capable of flying can be an important aid for mission analysis and design. Two characteristics of this envelope are considered: 1) the set of states reachable from a given entry state and 2) the set of entry states controllable to a given final state. Precise definitions of these sets are given and methods for computing them are presented. To illustrate their use, the sets are employed to characterize the performance of two vehicle configurations, a low lift-to-drag-ratio capsule and a mid lift-to-drag-ratio ellipsled, for Mars entry. Roles for the sets in evaluating entry trajectory planning algorithms, choosing a nominal entry state, and planning skip entries are described.