Nonlinearity-Kept Picard–Newton’s Method-Based Ascending Trajectory Planning for Single-Stage-to-Orbit Aerospace Plane With Combined-Cycle Propulsion

This article addresses the problem of ascending trajectory planning for single-stage-to-orbit aerospace planes equipped with combined-cycle propulsion. By utilizing a nonlinearity-kept reformulation, the Picard approximation introduces a mapping between inputs and states, facilitating decoupling at each step. This means that the convex subproblems do not include the hard boundary constraints of the dynamics, allowing for nonlinearities. The trajectory is divided into distinct phases, using sequential convex programming and Newton’s method to address the specialties and control objectives involved. The characteristics associated with combined-cycle propulsion are handled by incorporating a relatively realistic model. The parameters of mode transition points are optimized along with the trajectory, and a climb/descent maneuver is introduced by minimizing the duration to address the potential risks associated with drag-thrust mismatches. Numerical simulations illustrate its effectiveness and comparative advantages, while Monte Carlo simulations assess its robustness in terms of performance indexes, convergence, and the endpoint errors.