All-At-Once formulation integrating pseudo-spectral optimal control for launch vehicle design and uncertainty quantification

Launch vehicle design is a multidisciplinary process involving different disciplines such as aerodynamics, structure, propulsion and trajectory. This latter is a key discipline in the design process as it is used to assess the overall performance of the vehicle by solving of an optimal control problem involving a system of nonlinear ordinary differential equations. Usual Multidisciplinary Design Optimization methods for launch vehicle design consider the trajectory design discipline as an auxiliary embedded optimization problem to find the optimal trajectory control. In this paper, a multidisciplinary approach is proposed relying on an All-At-Once formulation by using Gauss–Lobatto collocation technique to solve the optimal control problem. The problem is solved using a gradient-based optimizer. Furthermore, based on this framework, an uncertainty quantification technique using post-optimality analysis is derived to perform sensitivity analysis. This allows to analyze the influence of modeling uncertainty on the optimal launch vehicle performance in the early design phases. The efficiency of the proposed approach is illustrated on the optimization and uncertainty quantification of a representative Two-Stage-To-Orbit launch vehicle design problem.