Space and astronautical engineering

1. Space missions: an overview - Main mission categories - Landers, Rovers, Atmospheric Probes and Craft - Missions for planetary exploration: fly-by spacecraft and orbiters - Fundamental of space system engineering. Mission phases and main milestone reviews. 2. Dynamical systems and orbit determination: - Introductory concepts - Linearization of the equations of motion and observation equations - The least squares solution - Equations of linearized dynamics: state transition matrix, properties and examples (lunar free return trajectories) - Statistical significance of the least square solution: covariance matrix and its propagation - Weighted least squares solutions - Least squares solution with a priori information - A priori information as additional observations. Minimum variance estimator. Minimum variance estimator with a priori information. - Sequential estimation: Kalman filter and Extended Kalman Filter. - Comparison of batch and sequential estimation. - The fly-by problem and the uncertainty ellipsoid - Square root methods. Householder transformation. Square Root Estimation Filter. 3. Attitude determination and control: - The TRIAD algorithm - The Wahba problem. Quest algorithm. - Stars and stellar types - Star sensors, Earth sensors, Sun sensors - Fiber optics gyros, hemispherical resonator gyros - Farrenkopf error model - Attitude errors: APE, AME, RPE - A reminder on quaternions and their properties - Attitude control: introduction - The linearized Euler equations and gravity gradient stabilization. The case of a space tether - Analysis of a LTI system with Laplace transform. - One axis bang-bang control and PID control of a spacecraft under impulsive and constant disturbances - One axis proportional-derivative (PD) control - Wheel desaturation maneuvers. Space state analysis of triaxial satellite in circular orbit - Stability of triaxial satellite: Laplace domain analysis - Pitch dynamics of a triaxial satellite in earth orbit under constant external torque - Dynamics of a triaxial satellite under gravity gradient and constant disturbances in the roll and yaw axes - Attitude control with magneto-torquers. Pitch control of a satellite in circular orbit. - Full RWA control system - Case study: attitude control of Cassini during Enceladus fly-by 4. Observables for orbit determination and radio-metric systems: - Introduction to space telecommunications, parabolic antennas (prime focus, Cassegrain). A simple model for the antenna gain. Link budget. Coherent demodulation. - Beam waveguide antennas. Architecture and functions of a ground station. - Mathematical model of the spacecraft signal. Signal tracking via a PLL. Doppler measurements. Range and angular measurements (Delta-Differential One-Way Ranging). 5. Time, clocks and reference frames: - Time scales and relativity of simultaneity, concepts of special relativity, the Schwarzschild metric. - Dynamic and kinematic definition of reference frames: WGS84 and ITRF 6. Relativity and Global Satellite Navigation Systems: - Basic principles of Global Navigation Satellite Systems (GNSS). - Time, relativity and GNSS

The knowledge of the equations governing the attitude dynamics of a space platform is required. The knowledge of the concepts addressed in the courses on Space Flight Mechanics and Control Systems is highly recommended.

Tapley, Schutz, Born: Statistical Orbit Determination, Elsevier (2004) Sidi: Spacecraft Dynamics and Control, Cambridge (1997) Transparencies and additional material will be distributed during the course through the teacher's web site (http://radioscience.dima.uniroma1.it).

The course entails lecturing for eight hours per week. Some lectures will offer demonstrations of numerical codes for the solution of simple orbit determination and attitude control problems. Two or three homeworks will be proposed during the course. The problems, to be solved within 4-5 days, require the writing of a simple numerical code, in any programming language (e.g. Matlab). Their solution, although not mandatory, is highly recommended for its learning value. Those students who will pass two homeworks will access the oral exam without going through the multiple choice test (MCT - see "Evaluation" section). The teacher will offer also a challenge, to be solved in similar ways. The winners will benefit of increased marks at the exam (up to 3 additional points).

The teacher expects the student to attend lessons regularly

The evaluation is made up by 2-3 home tests (not mandatory), a multiple choice test (in some cases - see below), and an oral exam. For students who successfully passed the home tests, the examination consists in a standard Q&A interview of approximately 30 min. For the students who did not pass the home tests, the examination is an in-depth oral test of variable duration on all topics addressed in the course. All students who DID NOT pass the home tests are required to take a quick multiple choice test prior to the oral exam. The test duration is 20 minutes, for 15 questions. On the basis of the outcome, students will be notified if they are admitted to the oral exam and the maximum attainable score. They will then decide whether or not to take the oral exam. The details on the threshold for admission and the algorithm to compute the maximum attainable mark are available at the teacher's web site: http://radioscience.dima.uniroma1.it/docenti/index.php?lan=en

The course entails lecturing for eight hours per week. Some lectures will offer demonstrations of numerical codes for the solution of simple orbit determination and attitude control problems. Two or three homeworks will be proposed during the course. The problems, to be solved within 4-5 days, require the writing of a simple numerical code, in any programming language (e.g. Matlab). Their solution, although not mandatory, is highly recommended for its learning value. Those students who will pass two homeworks will access the oral exam without going through the multiple choice test (MCT - see "Evaluation" section). The teacher will offer also a challenge, to be solved in similar ways. The winners will benefit of increased marks at the exam (up to 3 additional points).

1. Space missions: an overview - Main mission categories - Landers, Rovers, Atmospheric Probes and Craft - Missions for planetary exploration: fly-by spacecraft and orbiters - Fundamental of space system engineering. Mission phases and main milestone reviews. 2. Dynamical systems and orbit determination: - Introductory concepts - Linearization of the equations of motion and observation equations - The least squares solution - Equations of linearized dynamics: state transition matrix, properties and examples (lunar free return trajectories) - Statistical significance of the least square solution: covariance matrix and its propagation - Weighted least squares solutions - Least squares solution with a priori information - A priori information as additional observations. Minimum variance estimator. Minimum variance estimator with a priori information. - Sequential estimation: Kalman filter and Extended Kalman Filter. - Comparison of batch and sequential estimation. - The fly-by problem and the uncertainty ellipsoid - Square root methods. Householder transformation. Square Root Estimation Filter. 3. Attitude determination and control: - The TRIAD algorithm - The Wahba problem. Quest algorithm. - Stars and stellar types - Star sensors, Earth sensors, Sun sensors - Fiber optics gyros, hemispherical resonator gyros - Farrenkopf error model - Attitude errors: APE, AME, RPE - A reminder on quaternions and their properties - Attitude control: introduction - The linearized Euler equations and gravity gradient stabilization. The case of a space tether - Analysis of a LTI system with Laplace transform. - One axis bang-bang control and PID control of a spacecraft under impulsive and constant disturbances - One axis proportional-derivative (PD) control - Wheel desaturation maneuvers. Space state analysis of triaxial satellite in circular orbit - Stability of triaxial satellite: Laplace domain analysis - Pitch dynamics of a triaxial satellite in earth orbit under constant external torque - Dynamics of a triaxial satellite under gravity gradient and constant disturbances in the roll and yaw axes - Attitude control with magneto-torquers. Pitch control of a satellite in circular orbit. - Full RWA control system - Case study: attitude control of Cassini during Enceladus fly-by 4. Observables for orbit determination and radio-metric systems: - Introduction to space telecommunications, parabolic antennas (prime focus, Cassegrain). A simple model for the antenna gain. Link budget. Coherent demodulation. - Beam waveguide antennas. Architecture and functions of a ground station. - Mathematical model of the spacecraft signal. Signal tracking via a PLL. Doppler measurements. Range and angular measurements (Delta-Differential One-Way Ranging). 5. Time, clocks and reference frames: - Time scales and relativity of simultaneity, concepts of special relativity, the Schwarzschild metric. - Dynamic and kinematic definition of reference frames: WGS84 and ITRF 6. Relativity and Global Satellite Navigation Systems: - Basic principles of Global Navigation Satellite Systems (GNSS). - Time, relativity and GNSS

The knowledge of the equations governing the attitude dynamics of a space platform is required. The knowledge of the concepts addressed in the courses on Space Flight Mechanics and Control Systems is highly recommended.

Tapley, Schutz, Born: Statistical Orbit Determination, Elsevier (2004) Sidi: Spacecraft Dynamics and Control, Cambridge (1997) Transparencies and additional material will be distributed during the course through the teacher's web site (http://radioscience.dima.uniroma1.it).

The course entails lecturing for eight hours per week. Some lectures will offer demonstrations of numerical codes for the solution of simple orbit determination and attitude control problems. Two or three homeworks will be proposed during the course. The problems, to be solved within 4-5 days, require the writing of a simple numerical code, in any programming language (e.g. Matlab). Their solution, although not mandatory, is highly recommended for its learning value. Those students who will pass two homeworks will access the oral exam without going through the multiple choice test (MCT - see "Evaluation" section). The teacher will offer also a challenge, to be solved in similar ways. The winners will benefit of increased marks at the exam (up to 3 additional points).

The teacher expects the student to attend lessons regularly

The evaluation is made up by 2-3 home tests (not mandatory), a multiple choice test (in some cases - see below), and an oral exam. For students who successfully passed the home tests, the examination consists in a standard Q&A interview of approximately 30 min. For the students who did not pass the home tests, the examination is an in-depth oral test of variable duration on all topics addressed in the course. All students who DID NOT pass the home tests are required to take a quick multiple choice test prior to the oral exam. The test duration is 20 minutes, for 15 questions. On the basis of the outcome, students will be notified if they are admitted to the oral exam and the maximum attainable score. They will then decide whether or not to take the oral exam. The details on the threshold for admission and the algorithm to compute the maximum attainable mark are available at the teacher's web site: http://radioscience.dima.uniroma1.it/docenti/index.php?lan=en

The course entails lecturing for eight hours per week. Some lectures will offer demonstrations of numerical codes for the solution of simple orbit determination and attitude control problems. Two or three homeworks will be proposed during the course. The problems, to be solved within 4-5 days, require the writing of a simple numerical code, in any programming language (e.g. Matlab). Their solution, although not mandatory, is highly recommended for its learning value. Those students who will pass two homeworks will access the oral exam without going through the multiple choice test (MCT - see "Evaluation" section). The teacher will offer also a challenge, to be solved in similar ways. The winners will benefit of increased marks at the exam (up to 3 additional points).