Multidisciplinary Design Optimization for a Reusable Launch Vehicle using Multiple-Phase Pseudospectral Optimization

Multidisciplinary Design Optimization (MDO) entails combining all variable components into a single composite optimized system. The Reusable Launch Vehicle (RLV) concept includes multiple components to achieve a common objective. The separate components include a flyback booster and an expendable upper stage; however, these two components must operate in three regimes. There is an adjoined ascent phase, and separated orbital and return to landing site phases. Previous works have addressed these as branching trajectories. The branches have been handled separately, then an outer feedback loop was required to work towards a holistic system optimization. A Design Structure Matrix can be used to construct the system from its parts. This has also been called a distributed approach since its focus is on the pieces rather than a non-distributed approach which simultaneously optimizes the whole. This paper will demonstrate how to construct the problem to optimize the design of the entire system. Each phase, or component, has the freedom to have a unique set of equations of motion, mass properties, and state constraints or limitations. Furthermore, this construct using phases allows for discontinuities which accurately models launch vehicle staging dynamics, specifically the near-instantaneous change in mass. The formulation of an MDO problem into a multiple-phase dynamic optimization problem allows the use of established solution techniques using pseudospectral optimization methods. This direct optimization technique uses linkage constraints to enforce state and optimization parameter continuity between phases, or allows for discontinuities where applicable. The independent phases, linked together, allow for a common cost or objective function to be optimized. A common objective function across all elements of the design is the enabling feature to optimize the whole system. An RLV demonstrates this multiplephase optimization solution technique.