PCE-Based Robust Trajectory Optimization of Launch Vehicles via Adaptive Sample and Truncation

Abstract

To reduce the sensitivity of trajectory to uncertainty, this paper concerns the robust trajectory optimization of the solid ascent launch vehicles with the uncertainty of aerodynamic parameters and engine mass flow. Due to the strong nonlinearity and fast time-varying characteristics, the traditional robust trajectory optimization method based on polynomial chaos expansion (PCE) has slow convergence speed and large prediction errors. To overcome these difficulties, an improved robust optimization algorithm based on sample updating and adaptive truncated PCE (UAPCE) is put forward. Compared with the conventional PCE optimization methods, our contributions mainly focus on three aspects: First, to optimize the standard deviation of the terminal trajectory under uncertainty conditions, the original state is sampled and expanded by PCE, and the statistical characteristics of the original state, constraints, and indicators are described by the expanded state. Second, in order to promote the convergence speed of PCE, the sampling points are updated automatically by the proposed sample updating method in the pseudo-spectral optimization of the expanded state. Finally, the adaptive polynomial truncation method is creatively proposed to break through the fitting accuracy limit of the conventional PCE method under the same computation complexity. Through Monte Carlo simulations, the proposed UAPCE greatly reduces the standard deviation of the terminal state compared with the nonrobust optimization, demonstrating strong robustness to the uncertainty. Simultaneously, the UAPCE method has better convergence speed and prediction accuracy compared with the traditional PCE method.