Ascent Phase Trajectory Optimization for Vehicle with Restricted Space

Abstract

For flight safety, space is often restricted while the vehicle climbs to the target. A general two-dimensional (2-D) vehicle model is unsuitable for ascent when space is restricted because it considers only longitudinal degrees of freedom. Requiring into ascent in three-dimensional (3-D) scenarios as well as into relationships between the 2-D and 3-D trajectories. This paper reports 2-D and 3-D ascent phase minimum time-to-climb and minimum fuel-to-climb problems in different restricted spaces. The Gauss Pseudospectral Method (GPM) is used to transform the trajectory optimization problem into a Nonlinear Program (NLP) problem that can be solved by SNOPT based on a correct initial guess. The results in different restricted spaces illustrate the effect on 2-D and 3-D flight trajectories. Numerical evidence of optimality to trajectories is verified by estimating co-state information and the Hamiltonian.