Mars entry trajectory robust optimization based on evidence under epistemic uncertainty

The epistemic uncertainties caused by insufficient knowledge of the atmosphere, aerodynamic coefficient, and entry state render the entry process challenging, as they not only result in the deviation of the preplanned trajectory, but also may lead to the nonsatisfaction of path constraints. Herein, a robust epistemic uncertainty optimization (REUO) method based on evidence is proposed to solve the Mars entry trajectory optimization problem under epistemic uncertainty. A two-loop nested robust optimization (RO) model is formulated, in which the outer-loop optimization searches the optimal control while the inner-loop optimization calculates the extremal trajectory performances within each focal element (FE) to evaluate the evidence level. To solve the path constraint violation problem under uncertainties, the constraint design based on limitation bounds is considered in the RO model. The polynomial chaos expansion (PCE) is employed to obtain the approximate analytic function of the trajectory performance under uncertainties. Thereafter, the optimization based on ordinary stochastic entry dynamics in the inner loop is replaced by a simple parameter optimization of the analytic functions, which can be readily and rapidly solved. The REUO method is tested in a specific Mars entry mission. The simulation results show that the proposed method can identify the most robust solutions with the optimal trajectory performance under epistemic uncertainties.