Planar tilting maneuver of a spacecraft: singular arcs in the minimum time problem and chattering

TL;DR

This paper investigates the minimum time planar tilting maneuver of a spacecraft, focusing on the occurrence of chattering phenomena and providing conditions for optimal control solutions without chattering.

Contribution

It proves the existence of optimal chattering arcs at singular junctions and offers sub-optimal strategies replacing chattering with finite switchings.

Findings

Existence of chattering arcs at singular junctions.

Conditions for bang-bang solutions without chattering.

Numerical simulations demonstrating control strategies.

Abstract

In this paper, we study the minimum time planar tilting maneuver of a spacecraft, from the theoretical as well as from the numerical point of view, with a particular focus on the chattering phenomenon. We prove that there exist optimal chattering arcs when a singular junction occurs. Our study is based on the Pontryagin Maximum Principle and on results by M.I. Zelikin and V.F. Borisov. We give sufficient conditions on the initial values under which the optimal solutions do not contain any singular arc, and are bang-bang with a finite number of switchings. Moreover, we implement sub-optimal strategies by replacing the chattering control with a fixed number of piecewise constant controls. Numerical simulations illustrate our results.