Curve recontruction using Velocity and Curvature

Question

This might be a duplicate question, but I didn't get the conclusive answer in them.

I have the vehicle data i.e., velocity (m/s), yaw rate(in radians), sampling times, with these two I calculated the curvature of the road using the equation - curvature = YawRate/velocity.

mSec Speed YawRate(with offset 500) Velocity

22 113 513 31.38888889

53 113 513 31.38888889

84 113 513 31.38888889

115 113 513 31.38888889

915 110 510 30.55555556

946 110 510 30.55555556

978 110 510 30.55555556

24 109 510 30.27777778

56 109 510 30.27777778

87 109 511 30.27777778

118 109 511 30.27777778

Now I want to plot the road curvature on an image of the road. I have the equation for curvature,

Curvature = YawRate/Velocity)

(something like showing the trail of the vehicle). **Remember-I have to plot this trajectory on an image. How can I do it?

P:S at high speeds steering angle is not significant. so ruling out steering angle as input.

Answer 1

What you want to plot are the known positions of the vehicle across time.

From the available data set we can infer that the polar coordinates are given by the steering angle (which seems to be absolute - deduct a quarter turn) and the instantaneous radius of curvature.

Convert from polar to Cartesian.

Without better information, you have to assume that the instantaneous center of rotation is fixed.