Proposal for improving Pure Pursuit documentation

[Barth1777]

[Barth1777]

Hi,

I have been studying the Pure Pursuit implementation from PythonRobotics as part of a robotics trajectory-tracking project.

While working on it, I wrote a short derivation of the Frenet-frame dynamics used in path tracking, together with some geometric explanations and diagrams for Pure Pursuit (lateral error, heading error, curvature derivation, etc.).

Before adapting everything into a more GitHub-friendly format, I wanted to ask whether this kind of concise pedagogical mathematical documentation could be of interest for the project.

The goal would not be to add heavy theory, but rather short explanations directly connected to the existing implementation and simulations.

Thanks!

[Barth1777]

been completely clear in my initial message. My idea was not really to document one specific function such as calculate_steering_angle, but rather to add some explanation about the geometry behind Pure Pursuit itself. What I had in mind was something along the lines of a short document introducing the main geometric ideas: the Frenet frame attached to the reference path, the lookahead point, the angle alpha, the lookahead distance, the pursuit circle, and how this construction leads to the relation kappa = 2 sin(alpha) / Ld.
I also added some diagrams, because I think this algorithm is much easier to understand visually than only from the code.
While working on this for a personal robotics project, I went a bit further and also studied some convergence properties in simple cases, such as straight-line tracking, circular-path tracking, and curvature saturation. I understand that this part may be too detailed or outside the scope of PythonRobotics, but it gives an idea of the direction I was exploring.
I attached the draft document I wrote, not as something I expect to be merged as-is, but simply to make my proposal more concrete. If this kind of material seems useful, I would be happy to make a much shorter ad more GitHub-friendly version focused only on the geometric intuition behind the existing Pure Pursuit implementation.

PS : The attached document is currently written in French, as it was originally developed for a personal project. If the general direction seems useful, I would be happy to prepare an English and GitHub-oriented version.

Analyse mathématique de pure pursuit.pdf

[AtsushiSakai]

PR is welcome