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About this book

This brief addresses the design of model predictive control algorithms for performing space rendezvous manoeuvres. It consolidates developments within guidance and control algorithms, with the aim of improving the efficiency, safety, and autonomy of these manoeuvres.

The brief presents several applications of model predictive control to rendezvous manoeuvres, including Ankersen zero-order-hold particular solution1, which provides a realistic thrust profile. It offers new approaches for rendezvous manoeuvres in elliptical orbits, formulating obstacle avoidance constraints, passive safety constraints, and robustness techniques. It also compares finite-horizon and variable-horizon formulations for model predictive control in the context of performance and computational complexity.

Predictive Control for Spacecraft Rendezvous is accessible to academics and students new to the topics of orbital rendezvous and model predictive control, but also presents compelling subject matter for researchers and professionals in the aerospace industry.

Table of Contents

Frontmatter

Chapter 1. Introduction

Abstract
This first chapter is an introduction to the topics treated in the book. It starts by providing some brief historical context and motivation for the development of new rendezvous manoeuvre techniques. The problem to be solved is then introduced within a typical space mission scenario in a Guidance and Control engineering context. A state-of-the-art review for the present topic, namely the application of MPC to rendezvous manoeuvres, is also presented, followed by a brief discussion of the book contributions.
Afonso Botelho, Baltazar Parreira, Paulo N. Rosa, João Miranda Lemos

Chapter 2. Model Predictive Control

Abstract
This chapter introduces the basic concepts of Model Predictive Control (MPC) theory necessary to design the controller in later chapters. With a focus on MPC for linear systems, the design of controllers with different objective functions is covered, and some key methods such as reference tracking are presented while elaborating on implementation details. Experiments with a toy problem are included, showing the effect of tuning the different controller parameters, and adding different control and state constraints, both linear and nonlinear.
Afonso Botelho, Baltazar Parreira, Paulo N. Rosa, João Miranda Lemos

Chapter 3. Relative Orbital Mechanics

Abstract
We introduce relative orbital mechanics concepts in the context of orbital rendezvous and present a derivation of the general dynamic equations of relative motion. A linearization of the equations of motion in the LVLH frame that is valid for circular and elliptical orbits is presented, as well as the derivation of a homogeneous solution, known as the Yamanaka–Ankersen equations. A particular solution is also presented, assuming a zero-order hold discretization, that may be used for rendezvous manoeuvre planning. Simulations of free-drift relative motions between two satellites are included, in the cases of both circular and elliptical target orbits, and the resulting non-intuitive trajectories are explained. We also present simulations with different impulsive manoeuvres, that are typically utilized for performing rendezvous manoeuvres.
Afonso Botelho, Baltazar Parreira, Paulo N. Rosa, João Miranda Lemos

Chapter 4. Rendezvous with Model Predictive Control

Abstract
This chapter applies the concepts presented in the previous ones to design a MPC for generating orbital rendezvous trajectories on board the chaser spacecraft, considering elliptical target orbits. We first present a naive formulation with a state quadratic Lagrangian cost and the receding-horizon strategy and demonstrate through simulation that it is not suitable for this application. This is iteratively improved until we reach two fuel-optimal formulations, known as Finite-Horizon MPC and Variable-Horizon MPCs, where the former has fixed final time and is formulated as a LP, and the latter has free final time and is formulated as a MILP. The passive safety constraint is approached, which makes the problem non-convex, and a new method for efficiently solving it via sequential linear programming is presented. We also cover the topic of robustness to disturbances and perturbations and discuss different techniques for granting robustness, including two contributions in the present work. Finally, we perform several simulations demonstrating the above methods, including in a high-fidelity industrial simulator, with emphasis on illustrating that they may be feasibly implemented in real-time and on-board spacecraft.
Afonso Botelho, Baltazar Parreira, Paulo N. Rosa, João Miranda Lemos

Chapter 5. Conclusions and Future Work

Abstract
The last chapter concludes this book by reiterating the main results of the work, with a more in-detail discussion of its conclusions. It also presents a summary of all the proposed work and open topics mentioned along with the monograph.
Afonso Botelho, Baltazar Parreira, Paulo N. Rosa, João Miranda Lemos
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