73208 - Spacecraft Attitude Dynamics and Control

Learning outcomes

During the course, the student learns how to model and analyze the attitude dynamics of a spacecraft, and the principles which drive the design of an attitude determination and control subsystem. In particular, in the first part of the course the student acquires the fundamentals of attitude representation and dynamics. In the second part, he/she learns the algorithms and sensors which are employed for estimating the attitude, together with the algorithms and actuators for its control.

Course contents

Elements of attitude dynamics

• Attitude Parameterization with respect to an inertial reference frame: direction cosine matrix, Euler axis and angle, quaternions, Euler angles;
• Spacecraft attitude propagation:
  • Kinematic Equations in terms of direction cosine matrix, quaternions and Euler angles;
  • Dynamic Equations: Euler rigid body equations.
• Description of various external torques:
  • Disturbance torque: Gravity gradient, Aerodynamic Torque, Solar Radiation Pressure Torque, Residual magnetic dipole Torque;
  • Control torque: Momentum/Reaction Wheels torque (modification to Euler's Equations); Magnetic Control Torque; Thrusters Control Torque.
• Analytic solution to the attitude dynamics of the torque-free rigid body motion; special solution for axismmetric bodies. Integrals of motion and physical meaning of their equations; description of the attitude motion of an axisymmetric body.

Elements of attitude determination

• Sensors for attitude determination:

Sun sensors, magnetometers, Earth sensors, Star trackers, gyros.

• Deterministic Methods:

-Spin stabilized spacecraft:
Type and number of measurements necessary for spin axis determination; angular measurements; geometric solution.

-Three-axes stabilized spacecraft:
Type and number of measurements required; unit vectors measures in body axes.

• TRIAD method for Direction Cosine Matrix estimation.
• Quaternion and DCM-SVD solutions to Wahba's problem.

• Recursive Methods (estimation filters):
  • Linear Estimation of a state vector;
  • Introduction to recursive methods;
  • The Kalman Filter: equations and practical design aspects;
  • Fading memory Morrison Filter.

Elements of attitude control

• Passive Control:

- Spin Stabilization;

- Gravity Gradient Stabilization;

• Active Control:

- Momentum/Reaction Wheels control;

- On-Off Control: jet thrusters;

- Magnetic control.

• Introduction to the stability and control of nonlinear dynamic systems.

Readings/Bibliography

Course notes distributed by the lecturer

Recommended further readings:

1. James R. Wertz, "Spacecraft Attitude, Dynamics and Control, ISBN: 978-90-277-1204-2, Springer, 1978".
2. F. Landis Markley and John L. Crassidis, "Fundamentals of Spacecraft Attitude Determination and Control", ISBN 978-1-4939-0802-8 Springer, 2014.

Teaching methods

Lectures are mostly held by the course teacher. In lecturing hours the subjects are presented by the lecturer, including the explicit demonstration of all mathematical formulas introduced and to the presentation of the methods to solve the problems given in the practicing hours. The proposed exercises require the use of pocket calculators for the solution of the mathematical end engineering problems given by the lecturer.

Assessment methods

The examination usually constists of three questions on various subjects. In the course of the examination, the student ability to resolve new problems or at least to set up the correct resolutive strategy, will be assessed. The assessment of such ability has a fundamental weight in the attribution of the final marks. The student must perform well in at least two of the three questions placed by the lecturer in order to pass the examination.

Teaching tools

LCD projector, overhead projector and PC are used in addition to the blackboard

Office hours

See the website of Dario Modenini