I have the problem that I want to steer a 4 wheel robot. It should move on a straight line, and for turning to go on a circle with a defined radius, as in this picture:
The problem I have is that if I move on a straight line and then enter the circle, the curvature suddenly changes which would lead to a sudden steering angle change for the robot. I tried using a cubic spline interpolation, which makes the curvature continuous, but there is still a lot of change in curvature during a small amount of time (in practice still leading to a sudden steering angle change). Is there a way to approximate this to go smoothly into such a curve?
Edit: Is there an interpolation that would have continuously increasing curvature?
I think this wiki article about Harmonic Drives might be helpful:
https://en.wikipedia.org/wiki/Harmonic_drive
There are also many publications on the topic of Circular Splines that you should search for.