Controlled Attitude

1. Overview

1. Functions

  • The ControlledAttitude class provides a perfectly controlled attitude instead of free motion attitude dynamics by numerical propagation.
  • Users can set the attitude as sun pointing, earth pointing, and others for any direction in the spacecraft body frame. Of course, users can select an inertial stabilized attitude.
  • It is useful for power, communication, and orbit analyses with S2E.
  • src/dynamics/attitude/attitude.hpp, .cpp
    • Definition of Attitude base class
  • src/dynamics/attitude/controlled_attitude.hpp, .cpp
    • ControlledAttitude class is defined here.
  • src/dynamics/attitude/initialize_attitude.hpp, .cpp
    • Make an instance of Attitude class.
  • sample_satellite.ini : Initialization file

3. How to use

  • Inside the codes
    • ControlledAttitude class inherits the Attitude class, so other functions can access the ControlledAttitude class by using get functions in the Attitude class.
  • User I/F
    • Firstly, users should set propagate_mode = CONTROLLED at the [ATTITUDE] section in the sample_satellite.ini file.
    • Users can set a target attitude in the initialize file. There are the following setting parameters: main_mode, sub_mode, initial_quaternion_i2t, pointing_t_b, and pointing_sub_t_b.
    • Firstly, users select the control mode by using main_mode and sub_mode. For the control mode.
    • When main_mode is set as INERTIAL_STABILIZE, sub_mode is ignored, and the spacecraft attitude is fixed to the initial_quaternion_i2t value in the simulation.
    • When main_mode is set as HOGE_POINTING modes, the direction of the body-fixed frame defined by pointing_t_b is controlled to point the specific direction of the modes.
      • Ex. 1, the body-fixed +X axis directs to the sun when main_mode = SUN_POINTING and pointing_t_b = [1.0,0.0,0.0].
      • Ex. 2, the body-fixed -Z axis directs to the earth center when main_mode = EARTH_CENTER_POINTING and pointing_t_b = [0.0,0.0,-1.0].
    • sub_mode is only used when users select POINTING modes for main_mode. sub_mode is defined to stop rotation around the pointing direction of main_mode. The selected sub-direction in the body-fixed frame cannot perfectly direct the target direction since the primary target and sub-target usually do not satisfy the vertical relationship.
    • sub_mode cannot be INERTIAL_STABILIZE and the same mode with main_mode.
    • The angle between pointing_t_b and pointing_sub_t_b should be larger than 30 degrees. (90 degrees is recommended)
  • List of attitude control mode
    • INERTIAL_STABILIZE = 0
    • SUN_POINTING = 1
    • EARTH_CENTER_POINTING = 2
    • VELOCITY_DIRECTION_POINTING = 3
    • ORBIT_NORMAL_POINTING = 4
    • orbit normal $n$ is defined as $n=r\times v$, where $r$ is radial direction and $v$ is velocity direction.

2. Explanation of Algorithm

1. Initialize function

1. overview

  • This function initializes the target attitude and confirms that the setting parameters are correct.
  • The parameter checklist
    • Out of range check for both mode definitions.
    • main_mode and sub_mode is not the same
    • The angle between pointing_t_b and pointing_sub_t_b should be larger than 30 degrees.

2. inputs and outputs

  • NA

3. algorithm

  • NA

4. note

  • NA

2. Propagate function

1. overview

  • This is the main function executed in every loop of attitude dynamics calculation.

2. inputs and outputs

  • inputs
    • setting parameters
  • outputs
    • quaternion_i2b

3. algorithm

  • Detail algorithm is described in the next function.

4. note

  • NA

3. CalcTargetDirection

1. overview

  • This function calculates the target direction according to the pointing mode.

2. inputs and outputs

  • inputs
    • control mode
    • orbit class
    • celestial information class
  • outputs
    • the direction of the target object

3. algorithm

  • As written in the code.

4. note

  • NA

3. PointingCtrl

1. overview

  • This function calculates the quaternion_i2b.

2. inputs and outputs

  • inputs
    • the main direction of the target object in ECI frame $t_m^i$
    • the sub direction of the target object in ECI frame $t_s^i$
    • the main controlled direction in the body frame $d_m^b$
    • the sub controlled direction in the body frame $d_s^b$
  • outputs
    • quaternion_i2b

3. algorithm

  • Firstly, the $DCM_{t2i}$, which is the frame transformation from the target frame to the inertial frame, is calculated using $t_m^i$ and $t_s^i$ with CalcDCM.
  • Next, the $DCM_{t2b}$, which is the frame transformation from the target frame to the body-fixed frame, is calculated using $d_m^b$ and $d_s^b$ with CalcDCM.
  • Finally, both DCMs are combined as follows. And quaternion_i2b is calculated from the $DCM_{i2b}$. \[ DCM_{i2b} = DCM_{t2b} \cdot DCM_{t2i}' \]

4. note

  • NA

3. CalcDCM

1. overview

  • This function calculates a DCM from two given directions.
  • The DCM represents the coordinate transform matrix from the new frame defined by the two directions to the original frame.

2. inputs and outputs

  • inputs
    • the main direction in the frame $a$ : $d_m^a$
    • the sub direction in the frame $a$ : $d_s^a$
  • outputs
    • Coordinate transform matrix from the new frame to the original frame $a$

3. algorithm

  • The first basis vector of the new frame is defined as the main direction. \[ e_1=d_m^a \]
  • The second basis vector needs to be direct to the sub direction, but it should be vertical with $e_1$. \[ e_2 = \frac{(e_1\times d_s^a) \times e_1}{|(e_1\times d_s^a) \times e_1|} \]
  • The third basis vector is defined as right-hand coordinate. \[ e_3=\frac{e_1\times e_2}{|e_1\times e_2|} \]

4. note

  • NA

3. note

  • Currently, the ControlledAttitude class does not calculate angular velocity, and it is set as 0. The feature will be implemented in the near future.

3. Results of verifications

1. Inertial stabilize

1. overview

  • To verify the correctness of pointing control

2. conditions for the verification

  • input files
    • default files
  • initial values
    • main_mode = sub_mode = INERTIAL_STABILIZE
    • initial_quaternion_i2b = [0.5,0.5,0.5,0.5]

3. results

  • The inertial stabilize control is succeeded. InertialStabilize

1. Pointing Control

1. overview

  • Several cases described at the bottom were checked to verify the correctness of pointing control.

2. conditions for the verification

  • input files

    • default files

  • cases　　

    casemain modesub modemain_pointing_direction_bsub_pointing_direction_b
    1SunEarth Center[1,0,0][0,1,0]
    2SunEarth Center[0,0,-1][-1,0,0]
    3Earth CenterVelocity[0,-1,0][0,0,1]
    4VelocitySun[0.707,0.707,0][0,0,1]

3. results

  1. Case 1
  • The spacecraft +X axis correctly directs to the sun, and its +Y axis roughly directs to the earth.
Case1
  1. Case 2
  • The spacecraft -Z axis correctly directs to the sun, and its -X axis roughly directs to the earth.
Case2
  1. Case 3
  • The spacecraft -Y axis correctly directs to the earth, and its +Z axis roughly directs to the velocity direction.
Case3
  1. Case 4
  • The spacecraft +XY direction correctly directs to the velocity direction, and its +Z axis roughly directs to the sun.
Case4

4. References

  1. NA