Safety and stability analysis of FollowerStopper

In this paper, we demonstrate that the velocity controller, FollowerStopper, is safe and string unstable. FollowerStopper is a controller that is meant to be implemented on an autonomous vehicle or in an adaptive cruise control (ACC) system. Through mathematical proof, simulation in Simulink, and hardware in the loop implementation on a real autonomous vehicle through the Robot Operating System (ROS) and Gazebo, several results are achieved. It is found that an autonomous vehicle controlled by FollowerStopper will never crash. FollowerStopper will dissipate larger traffic waves from human-driven vehicles but will amplify smaller velocity perturbations that are created within the controller. Given the maximum LiDAR range of 81 m, FollowerStopper will never command a velocity greater than 13.69 m/s