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ADCS Review – Attitude Determination

ADCS Review – Attitude Determination. Prof. Der-Ming Ma, Ph.D. Dept. of Aerospace Engineering Tamkang University. Contents. Attitude Determination and Control Subsystem (ADCS) Function Spacecraft Coordinate Systems Spacecraft Attitude Definition Quaternions

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ADCS Review – Attitude Determination

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  1. ADCS Review – Attitude Determination Prof. Der-Ming Ma, Ph.D. Dept. of Aerospace Engineering Tamkang University

  2. Contents • Attitude Determination and Control Subsystem (ADCS) Function • Spacecraft Coordinate Systems • Spacecraft Attitude Definition • Quaternions • Assignment – Attitude Dynamics Simulation Attitude Determination

  3. ADCS Function • The ADCS stabilizes the spacecraft and orients it in desired directions during the mission despite the external disturbance torques acting on it: • To stabilize spacecraft after launcher separation • To point solar array to the Sun • To point payload (camera, antenna, and scientific instrument etc.) to desired direction • To perform spacecraft attitude maneuver for orbit maneuver and payloads operation • This requires that the spacecraft determine its attitude, using sensors, and control it, using actuators. Attitude Determination

  4. X-axis Z-axis Yaw: rotation around Z-axis Pitch: rotation around Y-axis Y-axis Roll: rotation around X-axis X-axis Y-axis 2. Euler Angle Definition Z-axis (Nadir direction) 1. Spacecraft (ROCSAT-2) Coordinate System Spacecraft Coordinate Systems- Spacecraft Body Coordinate System Attitude Determination

  5. Spacecraft Coordinate Systems (Cont.) - Earth Centered Inertial (ECI) Coordinate System ZECI: the rotation axis of the Earth ECI is a inertial fixed coordinate system Attitude Determination

  6. x z Earth x z z x z x Spacecraft Coordinate Systems (Cont.) - Local Vertical Local Horizontal (LVLH) Coordinate System LVLH is not a inertial fixed coordinate system Attitude Determination

  7. Spacecraft Attitude Definition • Spacecraft Attitude: the orientation of the body coordinate with respect to the ECI (or LVLH) coordinate system • Euler angle representation: • [   y ] : rotate y angle around Z-axis, then rotate  angle around Y-axis, finally  angle around X-axis Attitude Determination

  8. Euler Angles - • Yaw angle - It is measured in the horizontal plane and is the angle between the xf and x1 axes. • Pitch angle - It is measured in the vertical plane and is the angle between the x1 and x2 (or xb) axes. • Roll angle - It is measured in the plane which is perpendicular to the xbaxes and is the angle between the y2 and yb axes. • The Euler angles are limited to the ranges Attitude Determination

  9. Referring to the definitions of , , and , we obtain the following equations: Attitude Determination

  10. Performing the indicated matrix multiplication, we obtain the following result: Attitude Determination

  11. The angular velocity is Attitude Determination

  12. The relationship between the angular velocities in body frame and the Euler rates can be determined as The equations can be solved for the Euler rates in terms of the body angular velocities and is given by By integrating the above equations, one can determine the Euler angles. Attitude Determination

  13. Quaternions • The quaternion is a four-element vector q = [q1q2q3q4]T that can be partitioned as where eis a unit vector and z is a positive rotation about e. If the quaternion q represents the rotational transformation from reference frame a to reference frame b, then frame a is aligned with frame b when frame a is rotated by z radians about e. Note that q has The normality property that ||q||=1. Attitude Determination

  14. The rotation matrix from a frame to b frame, in terms of quaternion is Attitude Determination

  15. Initialization of quaternions from a known direction cosine matrix is Attitude Determination

  16. The Euler angles can be obtained from the of quaternion Attitude Determination

  17. Quaternion derivatives or Attitude Determination

  18. Assignment – Attitude Dynamics Simulation • Consider a rectangular box of 10cm X 14 cm X 20cm as shown in the figure with uniformly distributed mass of 2 Kg. The box has an initial angular velocity of 0.3 rad/sec and 0.05 rad/sec in the positive y and z directions, respectively. The center of mass of the box moves along a 10 m radius orbit with 0.3 rad/sec orbital speed. Neglect gravity effect and any external force or torqu • Draw the attitude and the center of mass trajectories of the box for 10 seconds. • Do as much as you can to show the continuous motion of the box at least for 10 seconds. (You may design an animation routine motion or use on-the-shelf software for the motion) Attitude Determination

  19. Attitude Determination

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