Robust Trajectory Optimization for Aerogravity-Assist With Dynamic Uncertainty by Riemann–Stieltjes Integral Expansion

Abstract

Aerogravity-assist (AGA) flybys of planets are influenced by many uncertain model parameters. Current research has found that optimal AGA trajectories obtained from deterministic optimization models exhibit less robustness. Under the influence of model parameter uncertainties, the trajectories diverge significantly, rendering the flyby infeasible. This article proposes a robust trajectory optimization method for AGA. This method converts the stochastic ordinary differential equations (ODEs) with dynamic uncertainty into a set of expanded deterministic ODEs by expanding the dynamic dimension. Based on the Riemann–Stieltjes integral theory, a nonclassical trajectory optimization model considering uncertain parameters is established. Inspired by the idea of unscented transform, a points selection strategy is proposed. Based on it, the integral functions in the model are further discretized to construct a standard trajectory optimization model suitable for the pseudospectral method. We conducted simulation analysis in the Mars AGA scenario and obtained the optimization results under the uncertainty of atmospheric density and area-to-mass ratio. Monte Carlo simulation shows that the proposed method is suitable for the robust trajectory optimization problem under multidimensional uncertain parameters, and effectively improves the robustness of the AGA trajectory while retaining the optimization characteristics.