This article presents an approach to address the problem of localisation within the autonomous driving framework. In particular, this work takes advantage of the properties of polytopic Linear Parameter Varying (LPV) systems and set-based methodologies applied to Kalman filters to precisely locate both a set of landmarks and the vehicle itself. Using these techniques, we present an alternative approach to localisation algorithms that relies on the use of zonotopes to provide a guaranteed estimation of the states of the vehicle and its surroundings, which does not depend on any assumption of the noise nature other than its limits. LPV theory is used to model the dynamics of the vehicle and implement both an LPV-model predictive controller and a Zonotopic Kalman filter that allow localisation and navigation of the robot. The control and estimation scheme is validated in simulation using the Robotic Operating System (ROS) framework, where its effectiveness is demonstrated.
Keywords: LPV modelling; autonomous driving; interval methods; optimal estimation.