Minimum time control of the rocket attitude reorientation associated with orbit dynamics

TL;DR

This paper studies the minimal time guidance problem for rocket reorientation considering orbit dynamics, revealing complex control phenomena like chattering and providing numerical methods for optimal solutions.

Contribution

It offers a geometric analysis of extremals in rocket guidance, identifying conditions for chattering and applying this to develop numerical solution techniques.

Findings

Identification of higher-order singular arcs causing chattering.

Application of geometric control theory to rocket guidance.

Development of numerical methods for optimal control solutions.

Abstract

In this paper, we investigate the minimal time problem for the guidance of a rocket, whose motion is described by its attitude kinematics and dynamics but also by its orbit dynamics. Our approach is based on a refined geometric study of the extremals coming from the application of the Pontryagin maximum principle. Our analysis reveals the existence of singular arcs of higher-order in the optimal synthesis, causing the occurrence of a chattering phenomenon, i.e., of an infinite number of switchings when trying to connect bang arcs with a singular arc. We establish a general result for bi-input control-affine systems, providing sufficient conditions under which the chattering phenomenon occurs. We show how this result can be applied to the problem of the guidance of the rocket. Based on this preliminary theoretical analysis, we implement efficient direct and indirect numerical methods, combined with numerical continuation, in order to compute numerically the optimal solutions of the problem.