1. Vehicle Specs and Model Details

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Shuttle Geometry

An orthographic, wireframe view of the shuttle is shown below:

Each image is centered on the shuttle's center of mass, and each grid square is 1 $\text{m}^{2}$. The two coordinate frames visible in each image represent the positions of the cameras on the shuttle, and their reference frames are identical to the shuttle body-fixed frame. More information on the cameras can be found in the Cameras section below.

The shuttle mass properties (expressed in its body-fixed frame) are as follows:

Quantity	Value	Units	Description
Mass	3388.7	kg	The total mass of the shuttle; this is treated as a constant value that does not change with fuel use.
Center of Mass	$\left[ 0 \quad 0 \quad 0 \right]$	m	The shuttle's center of mass defines its body-fixed frame.
Inertia Tensor	$I_{xx} = 3025.8$, $I_{xy} = -171.7$, $I_{xz} = 461.7$, $I_{yy} = 5927.5$, $I_{yz} = 313.6$, and $I_{zz} = 6756.0$	$\text{kg m}^{2}$	The inertia tensor of the shuttle; this is also treated as a constant.

Shuttle and Spacecraft States

The shuttle position, velocity, orientation, and angular velocity can all be obtained directly from the Space Teams PRO simulation. This data can be treated as the "truth" and there is no need to filter it. If it helps, you can also treat the data as if it came from a very high-quality inertial measurement unit (IMU) with imperceptible bias and noise. Example code for obtaining these states is provided.

The interplanetary spacecraft does not move with respect to Phobos, and hovers roughly a kilometer above the surface. Its exact coordinates can be obtained in a similar manner to the shuttle states, and example code for this is provided as well.

Debris Field States

Every object within the debris field starts the simulation with a random initial position, velocity, orientation, and angular velocity. While these states cannot be obtained directly at any point during the simulation, the shuttle's radar can obtain estimates for some of these states (see below).

Space Environment

The competition environment is characterized by the concurrent gravitational pulls of Phobos and Mars. The motion of every object in the simulation—excluding the interplanetary spacecraft—is affected by the combined gravitational field of the two bodies. Gravity from the Sun, Deimos (Mars' other moon), and other planets/moons/asteroids is not included. Additionally, solar radiation pressure (SRP) is not modeled.

Reference Frames

All object states are integrated in the Phobos-fixed reference frame. Since Phobos has a relatively slow rotation period, and since the simulation run time should not exceed several minutes, this reference frame can be treated as inertial. Some states are also provided in the shuttle body-fixed reference frame (e.g., radar outputs). See below for more details.

Radar

The shuttle's radar accumulates measurements of position, range rate, and diameter for the N nearest pieces of debris. The data is provided in a $3\times3$ matrix of radar outputs $R$ for each piece of debris, as shown below:

$$R = \begin{bmatrix} x & y & z \\ r_{c} & v_{r} & d \\ \Delta t & 0 & 0 \end{bmatrix}$$

Any zeros in the matrix represent components that are not used. Each actual term is defined as follows:

Component	Description	Estimate Standard Deviation
$\left[ x \quad y \quad z \right]$	The object's center of mass with respect to the shuttle, expressed in the Phobos-fixed reference frame	2 meters
$r_{c}$	The distance from the shuttle to the closest point on the object	2 meters
$v_{r}$	The range rate of the object with respect to the shuttle (i.e., the object's speed along the direction away from the shuttle)	0.02 meters per second
$d$	The average diameter of the object	5% of the object's true diameter
$\Delta t$	The measurement time since the start of the simulation	Perfect timekeeping (no error)

Cameras

The shuttle has two cameras that can be used to obtain images of the surrounding environment in real time. The camera specifications are listed below:

Camera	Position (meters, shuttle body-fixed frame)	Yaw Limits (degrees, shuttle body-fixed frame)	Pitch Limits (degrees, shuttle body-fixed frame)
Top Camera	$\left[ 1.27 \quad 0 \quad 0.9 \right]$	$\left[ -89, 89 \right]$	$\left[ -50, 0 \right]$
Bottom Camera	$\left[ 1.675 \quad 0 \quad -1.025 \right]$	$\left[ -89, 89 \right]$	$\left[ 0, 50 \right]$

The yaw and pitch of each camera is defined in the body-fixed frame of the shuttle. When a yaw ($\psi$) or pitch ($\theta$) is commanded, the camera's orientation is set as a body-to-camera transformation matrix that is generated from a 3-2-1 Euler angle sequence (with zero roll) as follows:

$$T_{body}^{cam} = \begin{bmatrix} \cos{(\theta)} & 0 & -\sin{(\theta)} \\ 0 & 1 & 0 \\ \sin{(\theta)} & 0 & \cos{(\theta)} \end{bmatrix}\cdot\begin{bmatrix} \cos{(\psi)} & \sin{(\psi)} & 0 \\ -\sin{(\psi)} & \cos{(\psi)} & 0 \\ 0 & 0 & 1 \end{bmatrix}$$

This means that a positive yaw will turn the camera to the left, and a positive pitch will turn the camera down (which is why the top camera is limited to negative pitches and the bottom camera is limited to positive ones).