Lyapunov Based Performance Guarantees for the Potential Field Lane-keeping Assistance System

Active lane-keeping assistance systems hold the potential to save thousands of lives every year, but require an approach that can simultaneously work cooperatively with the driver and provide a guaranteed level of safety. One approach that meets these dual demands is to passively couple the vehicle to the environment using the paradigm of “artificial” potential fields. This paper develops such a controller and demonstrates that with appropriate choice of a preview or look-ahead distance, the lateral and yaw dynamics effectively decouple, enabling a tight energy-based bound on lateral error. Since this control scheme does not attempt to track a desired trajectory, disturbances encountered during normal driving (such as road curvature) will alter the path of the vehicle. However, the energy theoretic framework can be used to develop a Lyapunov-based bound that handles general time-varying disturbances. This technique provides bounds on the lateral motion of the vehicle that are sufficiently tight to use as a design tool. Experimental results verify that this bound, and the system structure itself, work well in practice, providing guaranteed assistance in a cooperative manner.