Analytical Safety Bounds for Trajectory Following Controllers in Autonomous Vehicles

A major challenge in autonomous driving is designing control architectures that guarantee safety in all relevant driving scenarios. Given a safe desired reference trajectory for the vehicle, a trajectory following controller has to ensure that the trajectory is followed with a maximally allowed deviation, even in the presence of external disturbances, such as wind gusts or inclined roads. In this paper, a method for computing upper bounds for linear, time invariant single-input-multiple-output systems with state feedback controllers and additive bounded disturbances is proposed. The bounds for the offset between states and the reference are derived analytically based on worst case disturbance sequences. For systems with two states the bounds are strict, while for higher order systems they are conservative. The method is applied to obtain position bounds for lateral trajectory following controllers, and to analyze how different choices of feedback parameters affect safety margins.