Onboard trajectory generation for entry vehicles via adaptive multivariate pseudospectral interpolation

One of the most powerful analysis tools to deal with entry-guidance problems is the possibility to formulate them as optimal control problems. Environmental constraints, actuator limits, and strict requirements on the final conditions can be efficiently transcribed, resulting in a discrete, finite-dimension nonlinear programming (NLP) problem. However, NLP problems require a computational power, which often exceeds the vehicle’s onboard capabilities. Moreover, it is important to ensure that the solution can be adapted to the actual flight conditions, which can differ from the nominal scenario. This paper proposes an approach based on an efficient use of multivariate pseudospectral interpolation scheme to generate real-time capable entry guidance solutions. The proposed onboard trajectory generation algorithm is able to deal with wide dispersions at the entry interface, and can improve the lateral performance in cases where the classic bank-reversal logic is not sufficient. The interpolation is applied to subspaces of a database of pre-computed trajectories, which can be efficiently stored onboard. The method is here proposed for initial-conditions variations, but can be applied to every mission parameter, which allows to find a corresponding optimal solution. Results have been generated for SHEFEX-3, an entry demonstrator vehicle, which was planned by the German Aerospace Center. Monte-Carlo simulations show how this approach is applicable, and yields significant improvements both in longitudinal and lateral guidance performance, with an improvement of the dispersion area of about 96%.