Safety of the Stanley Controller with Curved Lanes and Noisy Perception

The Stanley controller was designed for the DARPA 2005 Grand Challenge and has been widely used in real autonomous vehicles and simulation models. While the original paper presented an analysis of the tracking performance of this controller with straight roads, the analysis for general curved lanes and with perception errors is not available. We utilize Lyapunov theory to give tracking performance guarantees for the Stanley controller. Our analysis can be used for ensuring safety of lane following and provide guidelines for choosing design parameters with respect to velocity, lane curvation, and sensing constraints.