For a simulation I want to convert between different kind of set point profiles with one being set points based on steering angles and one being based on circle radius.
I have 2 way points the steering angle the distance driven and now I need to approximate or calculate a circle radius where the arc length equals the distance between the waypoints.
Is this kind of problem solvable or is there no solution but incremental calculations.
Please see the Image i attached as link. I marked the things that I have blue, the things that I need red. Dotted are the things I don't really need.
Edit: Partial Solution Image
Best Answer
Ignoring this “steering angle”, you have two relevant quantities: the distance between points, which is equal to the chord length $c$, and the arc length $a$. You're looking for a radius $r$ and an angle $\theta$ such that
\begin{align*} a &= r\theta \\ c &= 2r\sin\frac\theta2 \end{align*}
This results in a transcendental equation for $\theta$:
$$c\theta=2a\sin\frac\theta2$$
I guess that a numeric solution (perhaps some form of gradient descent) is most likely the best option to solve this. I don't know any special function to solve this equation. Once you have $\theta$, you can compute
$$r=\frac a\theta$$