Trajectory Optimization of Rocket-Propelled Transport Using Pseudospectral and Successive Convexification Methods

Abstract

This paper investigates optimal multiphase trajectory generation for a reusable-launch-vehicle-derived rocket-propelled transport vehicle for ultrafast point-to-point terrestrial transport. The formulation minimizes fuel consumption while enforcing operational limits on dynamic pressure and heat flux, incorporating altitude-dependent atmospheric and aerodynamic models. The problem is transcribed using a pseudospectral method and solved via successive convexification (SCVX), which solves the nonlinear problem through a sequence of convex subproblems. In the three-degrees-of-freedom (DOF) setting, phase-dependent fuel and aerodynamic models are employed, and a free-final-time formulation yields optimal phase-transition times and control histories. The terminal landing phase is evaluated using a six-DOF model to assess landing feasibility. Solutions obtained using our SCVX implementation (solved using CVX) and GPOPS-II show comparable optimality, while SCVX achieves markedly shorter solve times, suggesting potential suitability for sequential in-flight updates. Monte Carlo simulations confirm the robustness of the trajectories and controls. Overall, the results demonstrate the practicality of the proposed approach and provide a foundation for further investigation toward onboard implementation.