A lane keeping system for a vehicle sets a safe zone in which the driver can drive the vehicle. If the system determines that the driver is at risk of leaving the safe zone, the system takes a corrective action, such as notifying the driver or applying a steering correction to the vehicle. The system adjusts the width of the safe zone depending on the driver's capability to stay within the safe zone. A lane centering system may be capable of autonomously steering the vehicle to remain within a lane. The lane centering system may include a controller that determines a target path for the vehicle depending on certain parameters. The controller may model each of the lane delimiters in a simplified form. This facilitates the determination of one of the target paths (the centerline of the lane). The simplified form may be a 3rd order polynomial equation.