Optimal Control of Endo-Atmospheric Launch Vehicle Systems: Geometric and Computational Issues

TL;DR

This paper presents a geometric and computational approach for optimal guidance of endo-atmospheric launch vehicles, addressing singularities and initialization challenges to improve accuracy and efficiency in missile interception scenarios.

Contribution

It introduces a local chart representation to eliminate Euler singularities and combines indirect methods with homotopies for better shooting method initialization.

Findings

Effective handling of Euler singularities in guidance problems

High-accuracy solutions achieved through combined indirect methods and homotopies

Numerical simulations demonstrate efficiency in missile interception scenarios

Abstract

In this paper we develop a geometric analysis and a numerical algorithm, based on indirect methods, to solve optimal guidance of endo-atmospheric launch vehicle systems under mixed control-state constraints. Two main difficulties are addressed. First, we tackle the presence of Euler singularities by introducing a representation of the configuration manifold in appropriate local charts. In these local coordinates, not only the problem is free from Euler singularities but also it can be recast as an optimal control problem with only pure control constraints. The second issue concerns the initialization of the shooting method. We introduce a strategy which combines indirect methods with homotopies, thus providing high accuracy. We illustrate the efficiency of our approach by numerical simulations on missile interception problems under challenging scenarios.