Direct trajectory optimization framework for vertical takeoff and vertical landing reusable rockets: case study of two-stage rockets

This study presents a direct trajectory optimization framework for a vertical takeoff and vertical landing (VTVL) reusable rocket with a two-stage structure for a launch mission to simultaneously deliver a payload to the desired orbit and recover the rocket. A two-phase trajectory optimization problem of VTVL reusable rockets is established, with the main features of the flight process. The finite-element collocation approach with Radau collocation is utilized to transcribe the established problem into a nonlinear programming (NLP) problem solved by Interior Point OPTimizer (IPOPT). Novel internal–external-growth initialization strategies are designed to enhance the convergence of solving the NLP problem. The proposed direct trajectory optimization framework is applied to two representative scenarios of VTVL reusable rockets: return to a launch site and return to a drone ship. Simulation results illustrate that the proposed trajectory optimization framework has the adaptability to deal effectively with the complex missions of VTVL reusable rockets.