Pure Pursuit Path Tracking
Pure pursuit is a simple, popular way to follow a path. The robot picks a point on the path a fixed distance ahead, called the look-ahead point, and steers along the arc that would reach it. Then it picks a new point and does it again.
The steering rule
If the look-ahead point is at distance \(L_d\) and angle \(\alpha\) from the robot's heading, the arc through it has curvature
$$\kappa = \frac{2\sin\alpha}{L_d} \qquad \omega = v\,\kappa$$
What to notice
A short look-ahead hugs the path tightly but wobbles and can overshoot at speed. A long look-ahead is smooth but cuts corners, since it aims at points far around the bend. The usual practice is to grow the look-ahead with speed. Pure pursuit is used widely, from early self-driving research to the Regulated Pure Pursuit controller in ROS 2 Nav2.