Reference Frame Definitions

Inertial Lab Reference Frame

The inertial lab frame $\mathcal{F}_I = \lbrace \vec{\mathcal{I}}_x \ \ \vec{\mathcal{I}}_y \ \ \vec{\mathcal{I}}_z \rbrace^\top$ is used by the PhaseSpace system to output the inertial states of the platforms during experiments. Similarly, the entire experimental datalogging system uses the same reference frame to output the platform states, velocities, command forces, etc.

The inertial lab frame is defined as follows: The origin is defined at the back left corner of the table (see the below diagram) nearest to the windows of the laboratory. The $x$-direction is defined along the long-side of the table, with the $+x$-direction pointing from the back left corner to the front left corner of the table (nearest to the air compressor). The $y$-direction is defined along the short-side of the table, with the $+y$-direction pointing from the back left corner to the back right corner of the table. The $+z$-direction completes the triad and points toward the ceiling (this is typically not used in any capacity, but is defined nonetheless in the PhaseSpace system).

Body-Fixed Reference Frame

The body frame $\mathcal{F}_B = \lbrace \vec{\mathcal{B}}_x \ \ \vec{\mathcal{B}}_y \ \ \vec{\mathcal{B}}_z \rbrace^\top$ of a platform is defined as follows: The origin is defined at the center of mass of the platform. The front face where you can access the onboard computer (the Jetson Xavier NX, for the current configuration) is the $+x$-axis, $\vec{\mathcal{B}}_x$. For the chaser platform, the vision sensor suite points in the $+x$-direction. This is directly opposite the control panel, i.e., the control panel is in the $-x$-direction. The face with the pressure gauges (and docking interface, in the case of the chaser and target) are in the $+y$-axis, $\vec{\mathcal{B}}_y$. Directly upward through the top of the platform is the $+z$-axis, $\vec{\mathcal{B}}_z$.

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