Analytical Construction of Koopman EDMD Candidate Functions for Optimal Control of Ackermann-Steered Vehicles

Abstract

The path-tracking control performance of an autonomous vehicle (AV) is crucially dependent upon modeling choices and subsequent system-identification updates. Traditionally, automotive engineering has built upon increasing fidelity of white- and gray-box models coupled with system identification. While these models offer explainability, they suffer from modeling inaccuracies, non-linearities, and parameter variation. On the other end, end-to-end black-box methods like behavior cloning and reinforcement learning provide increased adaptability but at the expense of explainability, generalizability, and the sim2real gap. In this regard, hybrid data-driven techniques like Koopman Extended Dynamic Mode Decomposition (KEDMD) can achieve linear embedding of non-linear dynamics through a selection of “lifting functions”. However, the success of this method is primarily predicated on the choice of lifting function(s) and optimization parameters. In this study, we present an analytical approach to construct these lifting functions using the iterative Lie bracket vector fields considering holonomic and non-holonomic constraints on the configuration manifold of our Ackermann-steered autonomous mobile robot. The prediction and control capabilities of the obtained linear KEDMD model are showcased using trajectory tracking of standard vehicle dynamics maneuvers and along a closed-loop racetrack.