Analytical Safety Bounds for Trajectory Following Controllers in Autonomous Vehicles

TL;DR

This paper introduces an analytical method to compute safety bounds for trajectory following controllers in autonomous vehicles, accounting for disturbances and aiding in safety assurance.

Contribution

It presents a novel analytical approach to derive safety bounds for linear systems with disturbances, specifically applied to autonomous vehicle trajectory controllers.

Findings

Bounds are strict for two-state systems, conservative for higher orders.

The method helps analyze how feedback parameters influence safety margins.

Position bounds for lateral controllers are effectively obtained.

Abstract

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.