Specification for StarSensor class

1. Overview

1. functions

• StarSensor class simulates a star sensor.
• The StarSensor class calculates and returns the observed quaternions and error flags.

2. files

• star_sensor.cpp, star_sensor.hpp : Definitions and declarations of the class
• star_sensor.ini : Initialization file
• plot_star_sensor.py: An example of a Python script to plot star sensor output

3. how to use

• Set the parameters in star_sensor.ini.
• Create an instance by using the initialization function InitStarSensor
• Use Get* function to get quaternion information.

2. Explanation of Algorithm

1. Update

• TBW

2. Judgement

1. EarthJudgement

• Calculate the angle $\theta_{ce}$ between the earth's center direction $\boldsymbol{r_{sc}}$ and the earth's edge direction $\boldsymbol{r_{se}}$. $R_e$ is the earth's radius.
• Calculate the angle $\theta_{es}$ between the sight direction $\boldsymbol{r_{sight}}$ and the earth's edge direction $\boldsymbol{r_{se}}$.
• Judge the STT error flag by comparing $\theta_{es}$ with the earth forbidden angle $\theta_{efa}$. If $\theta_{es} > \theta_{efa}$, the earth is completely outside the earth forbidden angle.

$$\begin{align} \theta_{ce} = \arctan{\left(\frac{|\boldsymbol{r_{se}}|}{R_e}\right)}\\ \theta_{cs} = \arccos{(\boldsymbol{r_{se}}*\boldsymbol{r_{sight}})}\\ \theta_{es} = \theta_{ce} - \theta_{cs} \tag{1} \end{align}$$

3. Results of verifications

1. verification of Earth judgement

1. overview

• Check that Earth judgement is performed correctly

2. conditions for the verification

• PropStepSec: 0.001
• StepTimeSec: 0.1
• EndTimeSec: 200
• Initial position [m] : [4.2164140100E+07,0,0]
• Initial velocity [m/s] : [0,3.074661E+03,0]
• ControlledAttitude
  • main mode = EARTH_CENTER_POINTING: the pointing direction is determined by each case
  • sub mode = SUN_POINTING: [0,0,1]
• STT quaternion from body frame to component frame: [0,0,0,1]
• Earth forbidden half-angle: 10deg
• The angle between the earth's center and edge direction: 8.6deg

3. results

• The angle between pointing direction and earth center = 15deg
  • STT flag is always 1, since the angle $\theta_{es}$ between the sight direction and the earth's edge direction is 15 - 8.6 = 6.4deg < 10deg.

• The angle between pointing direction and earth center = 20deg
  • STT flag is always 0, since the angle $\theta_{es}$ between the sight direction and the earth's edge direction is 20 - 8.6 = 11.4deg > 10deg.

• The angle between pointing direction and earth center = 30deg
  • STT flag is always 0, since the angle $\theta_{es}$ between the sight direction and the earth's edge direction is 30 - 8.6 = 21.4deg > 10deg.

• The output result obtained by the default initial settings.
  • The figure is generated by the Python script.