Ignition Point Reachability for Aerodynamically-Controlled Reusable Launch Vehicles

TL;DR

The paper addresses ignition-point reachability for aerodynamically controlled reusable launch vehicles by projecting a high-dimensional reachability set onto a low-dimensional ignition space and sampling it with sequential convex programming-based trajectory optimization. It combines a detailed 5DoF axisymmetric vehicle model—including environmental effects, axisymmetric aerodynamics with a smooth lift formulation, and fin-based actuators—with two-phase aerodynamic/propulsive descent constraints and a defect-hull reachability algorithm. The approach yields a reachable ignition polytope through iterative trajectory optimizations, demonstrated on a Kerbal Space Program-based scenario, while noting computational challenges and non-guaranteed over/under-approximations. The work highlights practical potential for planning and safety analyses and points to improvements in sparse computation, SCP algorithms, and GPU acceleration for faster, broader applicability.

Abstract

We describe a successive convex programming (Sequential Convex Programming (SCP)) based approach for estimate the set of points where a 5-degree of freedom (5-DoF) reusable launch vehicle (RLV) returning to a landing site can transition from aerodynamic to propulsive descent. Determining the set of feasible ignition points that a RLV can use and then safely land is important for mission planning and range safety. However, past trajectory optimization approaches for RLVs consider substantially simplified versions of the vehicle dynamics. Furthermore, prior reachability analysis methods either do not extend to the full constraint set needed for an RLV or are too beset by the curse of dimensionality to handle the full 5-DoF dynamics. To solve this problem, we describe an algorithm that approximates the projection of a high dimensional reachable set onto a low dimensional space. Instead of computing all parts of the reachable space, we only calculate reachability in the projected space of interest by using repeated trajectory optimization to sample the reachable polytope in the reduced space. The optimization can take into account initial and terminal constraints as well as state and control constraints. We show that our algorithm is able to compute the projection of a reachable set into a low dimensional space by calculating the feasible ignition points for a two-phase aerodynamic/propulsive RLV landing trajectory, while also demonstrating the aerodynamic divert enabled by our body and fin actuator model.

Figures (19)

• Figure 1: Schematic representation of two-phase aerodynamic descent guidance.
• Figure 2: Vehicle dynamics
• Figure 3: Modified vs. unmodified lift predictions at mach 0.9.
• Figure 4: Relative lift force error vs. original lookup table at mach 0.9.
• Figure 5: Fin control constraints and drag polar coupling.