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A major challenge in autonomous driving is designing control architecturesthat guarantee safety in all relevant driving scenarios. Given a safe desiredreference trajectory for the vehicle, a trajectory following controller has toensure that the trajectory is followed with a maximally allowed deviation, evenin the presence of external disturbances, such as wind gusts or inclined roads.In this paper, a method for computing upper bounds for linear, time invariantsingle-input-multiple-output systems with state feedback controllers andadditive bounded disturbances is proposed. The bounds for the offset betweenstates and the reference are derived analytically based on worst casedisturbance sequences. For systems with two states the bounds are strict, whilefor higher order systems they are conservative. The method is applied to obtainposition bounds for lateral trajectory following controllers, and to analyzehow different choices of feedback parameters affect safety margins.

Analytical Safety Bounds for Trajectory Following Controllers in Autonomous Vehicles