The main objective of the course is to study and design the dynamics and control of attitude and trajectory of autonomous and semi-autonomous space vehicles. The problems related to modeling and control will be addressed, introducing the mathematical tools required to design and solve the problems under analysis. The study of orbital maneuvers, proximity flight and rendezvous and docking maneuvers is part of the course objectives.

• Ability to use mathematical tools to model and control space systems, including complex ones, with an understanding of flight determination and control problems. • Understand the issues related to orbital flight and satellite dynamics, focusing on rendezvous and docking maneuvers. • Acquire the ability to simulate rendezvous and docking maneuvers using design tools commonly employed in industrial environments (MATLAB, Simulink).

The student should have basic knowledge of Space Flight Mechanics. In addition, the student should have knowledge of computer science, geometry, and programming.

• Historical background, examples, and classifications of reference vehicles and missions (definition of the technical context). • Introduction to proximity maneuvers (orbital maneuvers, proximity flight, rendezvous and docking): reference frames and orbital parameters. • Review of rigid body dynamics: attitude representation (Euler angles and quaternions). Euler’s equation and its generalized form. Hill’s equations for circular orbits in inertial and local reference frames. Torque free motion of spinning bodies in the absence of external torques. • The space environment and its effects on translational and attitude dynamics. Disturbance forces and torques. The problem of attitude motion stability and control (active and passive stabilization, dual-spin satellites, dissipation effects, orbital stabilization). • Review of basic control concepts (definition of open- and closed-loop systems, time-response analysis). Overview of control algorithms and their implementation (hardware and software), ranging from classical (robust) control laws to variable-structure control laws (sliding mode control). • Orbital proximity operations and docking maneuvers (orbital maneuvers, proximity flight, rendezvous and docking). Analysis of maneuver types and guidance algorithms. Types of actuators. Analysis of the components of an orbital simulator. • Introduction to the problem of position and attitude determination: sensors and algorithms. Experimental systems and industrial software and hardware-in-the-loop simulators. Limits of validity of the rigid-body assumption for space vehicles: “flexible” satellites and robotic arms. In addition to the theoretical lectures, the student will also carry out practical exercises on the following topics: • Exercise 0: Rigid body dynamics with quaternions. Introduction to Hill’s Equations • Exercise 1: Attitude dynamics (single-axis) – Feedback control with pole placement. PWPF modulation for thruster-type actuators. • Exercise 2: Attitude dynamics (3-axes) – Implementation of an LQR controller with Reaction Wheel (RW) actuators. • Exercise 3: Position dynamics (Hill’s Equations) – Free drift + Hohmann maneuver in open-loop. Implementation of a Sliding Mode Controller (SMC) to track the trajectory. Moreover, an orbital flight simulator for a 6 degree of freedom spacecraft will be designed and implemented.

Given its practical and application-oriented nature, the course is well suited to the development of exercises related to the topics covered, with particular emphasis on the development of an orbital simulator. Practical sessions will therefore constitute an important part of the course. In addition, a brief introduction to automatic control systems will be provided in the first part of the course, in order to give all students a basic understanding of the subject.

De Ruiter et.al., "Spacecraft Dynamics and Control: An Introduction", Wiley, 2013. Fehse, "Automated Rendezvous and Docking of Spacecraft", Cambridge Aerospace Series, 2003. Markeley et.al., "Fundamentals of Spacecraft Attitude Determination and Control", Springer, 2014.

Slides; Libro di testo; Esercizi;

Modalita di esame: Prova scritta (in aula); Prova orale obbligatoria; Elaborato scritto individuale; Elaborato progettuale in gruppo;

Exam: Written test; Compulsory oral exam; Individual essay; Group project;

... The exam includes the following parts: • Preparation of a report related to the practical exercises carried out during the course (3 points) and to the design of an orbital simulator for rendezvous and docking maneuvers (7 points). This document must be submitted in its COMPLETE form at least two days before the exam session scheduled for the written test. The evaluation of the produced work will be individual (maximum 10/30). The software may be developed in groups of 3–4 students, but the report must be prepared individually. • The evaluation of the theoretical part of the course is divided into two parts: (1) a written test consisting of 6 questions: 2 descriptive questions and 4 theoretical questions (maximum 16/30); (2) an oral examination in which both the course topics and the written-test questions will be discussed. The discussion of the practical exercises also contributes to the final evaluation (maximum 6/30). The oral examination is mandatory even if the sum of the written test and the report evaluation exceeds 18/30. To be admitted to the oral examination, the student must obtain at least 10/16 in the written test.

Gli studenti e le studentesse con disabilita o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unita Special Needs, al fine di permettere al/la docente la declinazione piu idonea in riferimento alla specifica tipologia di esame.