MARS ENTRY TRAJECTORY ROBUST OPTIMIZATION BASED ON EVIDENCE UNDER EPISTEMIC UNCERTAINTY

The epistemic uncertainties caused by lack of knowledge in atmosphere, aerodynamic coefficient and entry state make the entry process challenging, since they not only result in the deviation of preplanned trajectory, but also may lead to non-satisfaction of path constraints. In this paper, a robust epistemic uncertainty optimization (REUO) method based on evidence is proposed to solve the Mars entry trajectory optimization problem under epistemic uncertainty. The belief and plausibility from Dempster-Shafer theory of evidence are employed to quantify the evidence level of trajectory terminal deviation in REUO objective function. In addition, the maximal and minimal trajectory performances within each focal element (FE) are used to evaluate the evidence level. Therefore, the two-level nested robust optimization model is formulated. Besides, to solve the path constraint violation problem under uncertainties, the constraint design based on extreme case is considered in the robust optimization model. The random set theory is used to analyze the epistemic uncertainty propagation in stochastic entry dynamics. The original averaging discretization method (ADM) is modified to adapt to boundary points of the interval-based epistemic uncertainties and is used to discretize the uncertainty space into FEs with associated Basic Probability Assignments (BPAs). To improve the computational efficiency of the two-loop optimization resulted by the two-level nested optimization model, the polynomial chaos expansion (PCE) is employed into the inner-loop optimization to obtain the approximate analytic function of trajectory performance under uncertainties. Thereafter, the inner-loop optimization 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 optimal trajectory performance under epistemic uncertainties.