Libration Point Spacecraft Body Coordinate System (Libration Point Spacecraft Body Coordinate System)

Author: 天疆说
Reference: 钱霙婧(2014)《地月空间拟周期轨道上航天器自主导航与轨道保持研究》
Website: https://cislunarspace.cn

Definition

The Libration Point Spacecraft Body Coordinate System ( $\mathcal{O}_b - X_b Y_b Z_b$ ) is a body-fixed coordinate system with its origin at the spacecraft center of mass, used to describe spacecraft attitude and sensor installation directions. In 钱霙婧 (2014)'s research, the body coordinate system is defined as the principal axes of inertia coordinate system, with $X_b$ as the roll axis, $Y_b$ as the pitch axis, and $Z_b$ as the yaw axis.

Coordinate Axis Definition

Axis	Name	Direction	Description
$X_b$	Roll axis	Along a characteristic axis of the spacecraft	Describes rotation about the longitudinal axis
$Y_b$	Pitch axis	Along another characteristic axis of the spacecraft	Describes rotation about the transverse axis
$Z_b$	Yaw axis	Along the third characteristic axis of the spacecraft	Describes rotation about the vertical axis

The three axes $X_b$ , $Y_b$ , and $Z_b$ form a right-handed Cartesian coordinate system.

Relationship with Sensor Measurement Coordinate System

钱霙婧 (2014) assumed that the sensor measurement coordinate system coincides with the libration point spacecraft body coordinate system, with installation errors considered separately. This means:

Sensor measurement axes align with body coordinate axes
Angle measurements in observation equations are directly processed in the body system
In actual engineering, sensor installation error compensation needs to be considered

Observation Equation

In autonomous navigation systems, sensor measurement angle information needs to be transformed to the inertial coordinate system:

\mathbf{y}_{\text{measured}} = \mathbf{R}_{b \to i} \cdot \mathbf{y}_{\text{body}}

Where $\mathbf{R}_{b \to i}$ is the attitude transformation matrix from body to inertial coordinates.

Attitude Determination

Star sensor measures star direction projection in the body coordinate system; combined with attitude control system attitude information, observation equations can be established for state estimation.

Attitude Control Terminology

Terminology	English	Description
Roll	Roll	Rotation about $X_b$ axis
Pitch	Pitch	Rotation about $Y_b$ axis
Yaw	Yaw	Rotation about $Z_b$ axis

References

钱霙婧. 地月空间拟周期轨道上航天器自主导航与轨道保持研究[D]. 哈尔滨工业大学, 2014.