An hp-Legendre Pseudospectral Convex Method for 6-Degree-of-Freedom Powered Landing Problem

Abstract

This paper presents a fast trajectory optimization method combining the hp-Legendre pseudospectral method and convex optimization for the 6-Degree-of-Freedom rocket-powered landing problem. To accelerate calculations, this paper combines the Legendre pseudospectral method with a linearization method for convexification, and an hp method that can divide the mesh is introduced to reduce the computational workload. In terms of accuracy, a trust region update strategy that can control the solution process is presented to approximate the original problem iteratively. Convergence analysis is provided as evidence, substantiating that any solution produced by the hp-Legendre pseudospectral convex method is not only feasible but potentially optimal for the original problem. The effectiveness of the proposed method is demonstrated by numerical experiments. When compared, the proposed method achieves higher calculation accuracy in solving the 6-Degree-of-Freedom rocket-powered landing trajectory problem, while taking into account rocket attitude control.