Path following control for a reversing general 2-trailer system

TL;DR

This paper develops a Linear Quadratic controller for a 2-trailer system with off-axle hitching, enabling reliable path following in reverse despite disturbances and model errors, with proven stability around planned paths.

Contribution

It introduces a novel LQ controller design for a general 2-trailer system with off-axle hitching, ensuring stability over a set of planned paths in backward motion.

Findings

Controller stabilizes the 2-trailer system in reverse

A single quadratic Lyapunov function guarantees stability

Convex optimization computes the Lyapunov function

Abstract

In order to meet the requirements for autonomous systems in real world applications, reliable path following controllers have to be designed to execute planned paths despite the existence of disturbances and model errors. In this paper we propose a Linear Quadratic controller for stabilizing a 2-trailer system with possible off-axle hitching around preplanned paths in backward motion. The controller design is based on a kinematic model of a general 2-trailer system including the possibility for off-axle hitching. Closed-loop stability is proved around a set of paths, typically chosen to represent the possible output from the path planner, using theory from linear differential inclusions. Using convex optimization tools a single quadratic Lyapunov function is computed for the entire set of paths.