Multiphase Return Trajectory Optimization Based on Hybrid Algorithm

Yi Yang,Ying Nan

doi:10.1155/2016/6257050

Abstract

A hybrid trajectory optimization method consisting of Gauss pseudospectral method (GPM) and natural computation algorithm has been developed and utilized to solve multiphase return trajectory optimization problem, where a phase is defined as a subinterval in which the right-hand side of the differential equation is continuous. GPM converts the optimal control problem to a nonlinear programming problem (NLP), which helps to improve calculation accuracy and speed of natural computation algorithm. Through numerical simulations, it is found that the multiphase optimal control problem could be solved perfectly.

Highlights

Return trajectory, as an important part of satellite recovery mission, is flight trajectory of spacecraft from its working orbit to required reentry point
In this paper, we proposed a hybrid algorithm to combine the advantages of these two methods, where Gauss pseudospectral method (GPM) is adopted to transform the original optimal control problem into a nonlinear programming problem (NLP), and solve this NLP based on natural computation algorithm (NCA)
As the discretization process discussed above, the original multiphase continuous optimal control problem is transformed into a discrete NLP successfully, which could be solved by natural computation algorithm (NCA) later

Summary

Introduction

As an important part of satellite recovery mission, is flight trajectory of spacecraft from its working orbit to required reentry point. Indirect methods [1,2,3,4] transform the trajectory optimization problem into a two-point boundary value problem based on Pontryagin minimum principle and boundary condition. GPM transforms the original optimal control problem into a nonlinear programming problem (NLP) at the discrete points subject to continuous state equality and inequality constraints. The NLP is usually solved by sequential quadratic programming method (SQP), but SQP falls into local optimal solution and is highly dependent on initial values, which make it hard to obtain global optimal solution. In this paper, we proposed a hybrid algorithm to combine the advantages of these two methods, where GPM is adopted to transform the original optimal control problem into a nonlinear programming problem (NLP), and solve this NLP based on natural computation algorithm (NCA)

Problem Formulation

Description of Hybrid Algorithm

Numerical Simulation and Analysis

Conclusion