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I'm trying to understand a function in a SIMULINK example of a path following UAV simulation. The gist is that, the UAV Waypoint Follower block provides a required heading from a list of waypoints and this heading is converted, by the heading control block, into a Target Roll that is used by the autopilot.fixedWingPathFollowing from the Robotics Blockset The heading control block is the following function: Heading Control This function in the absence of wind evaluates to:

$$ \phi = \text{atan2}(p(\psi_d - \psi)V,g) $$ meaning,

atan2

where, $\phi$ is the target roll, $V$ is the current speed, $\psi$ is current heading, $\psi_d$ is the desired heading and $p$ is the proportional gain "PHeadingAngle".

I'm struggling to understand how that equation works mathematically, and how it transforms a heading to a roll angle.

If possible, I'd also like an explanation for how the function deals with wind. I know that it transforms the heading angle and the speed using the wind speeds but am unsure how that transformation works.

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