Direct Collocation Methods for Hypersonic Trajectory Optimization by the Process of Continuation

An algorithm was created to optimize trajectories of hypersonic glide vehicles with selected cost functions by applying the process of continuation to direct orthogonal collocation methods. The trajectory was optimized to maximize the range of launch position given a fixed terminal location. The process of continuation was used to address the complexity of the model whereby less complex solutions were used to seed increasing complex modeling in an iterative fashion. The hypersonic glide vehicle system dynamics were modeled with three-dimensional, three degree of freedom equations of motion assuming no thrust and a non-rotating Earth for the states defined as vehicle radial position, latitude, longitude, speed, flight path angle, and heading angle. The control for the system was placed on the bank angle of the vehicle. The results presented here are the foundational stages of ongoing research. Use of the continuation method enabled rapid generation of optimized trajectories. Differences noted between iterations of the continuation process showed the evolution of vehicle trajectories based on the problem formulations. The continuation method was demonstrated as an effective tool for optimization.