Optimal Nonlinear Feedback Guidance for Reentry Vehicles

Abstract

It is well-known that onboard, real-time, optimal trajectory generation for reusable launch vehicles can substantially increase safety while reducing cost. Arguably, this is one of the most challenging problems in optimal control theory. In recent years, pseudospectral (PS) methods have shown considerable promise in solving such problems. In this paper, we investigate the utility of a PS guidance algorithm for solving this problem. Based on the X-33, a generic vehicle model is constructed for analysis. It is shown that the PS guidance algorithm is capable of compensating for large uncertainties and disturbances that include greater than Category 5-level hurricane-force wind gusts (Hurricane Katrina was Cat 4). A single algorithm is used to guide the vehicle from its entry condition to a final approach corridor of about 2000 ft away from the landing site. Despite that much research is still necessary, results so far suggest that PS guidance methods can enhance safety considerably. Computational times for unoptimized codes range from about a second to 10 seconds under a MATLAB environment running on legacy computer hardware. This suggests that real-time trajectory reshaping, and even abort guidance, are well within the reach of modern methods and existing computational capabilities.