Mars entry trajectory planning using robust optimization and uncertainty quantification

Due to the existence of obvious uncertainties within Mars atmospheric entry, design and analysis of the optimal trajectory under uncertainties play a significant role in reducing flight risk and maintaining guidance performance and delivery accuracy. In this paper, using robust optimization strategy and uncertainty quantification technique, we developed an innovative approach for planning the Mars entry trajectory under uncertainties. The main contribution of this work is twofold: one is considering both dynamics parameter uncertainty and initial state uncertainty, and the other is simultaneously focusing on the reliability of constraint satisfaction and insensitivity of performance index towards uncertainties. First, Mars entry trajectory planning problem under uncertainties is formulated as a robust optimization problem. Second, the uncertainty propagation with regard to Mars entry dynamics is derived, and the quantification of objective function and constraints under uncertainties is conducted. Third, the robust trajectory optimization problem is transformed into an equivalent optimal control problem in the expanded higher-dimensional state space by polynomial chaos expansion, and the solution is obtained by the hp-adaptive pseudospectral method. Finally, the effectiveness of the proposed method is verified through two Mars entry optimal trajectory cases. And the obtained optimal trajectories are reliable and evidently robust to uncertainties compared to traditional deterministic optimization and reliability-based optimization.