Data-driven identification of vehicle dynamics using Koopman operator

Abstract

This paper presents the results of identification of vehicle dynamics using the Koopman operator. The basic idea is to transform the state space of a nonlinear system (a car in our case) to a higher-dimensional space, using so-called basis functions, where the system dynamics is linear. The selection of basis functions is crucial and there is no general approach on how to select them, this paper gives some discussion on this topic. Two distinct approaches for selecting the basis functions are presented. The first approach, based on Extended Dynamic Mode Decomposition, relies heavily on expert basis selection and is completely data-driven. The second approach utilizes the knowledge of the nonlinear dynamics, which is used to construct eigenfunctions of the Koopman operator which are known by definition to evolve linearly along the nonlinear system trajectory. The eigenfunctions are then used as basis functions for prediction. Each approach is presented with a numerical example and discussion on the feasibility of the approach for a nonlinear vehicle system.

Dynamic Modeling of Bucket-Soil Interactions Using Koopman-DFL Lifting Linearization for Model Predictive Contouring Control of Autonomous Excavators

“…This was observed to be caused by the regressed model often being dynamically unstable. This is an issue which has been observed by prior works [31], [32]. The observables determined through DFL appear to be more robust to obtaining a model from data than higher order models when using a pure L2 regression.…”

Model Predictive Control of a Vehicle using Koopman Operator

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This paper continues in the work from Cibulka et al (2019) where a nonlinear vehicle model was approximated in a purely data-driven manner by a linear predictor of higher order, namely the Koopman operator. The vehicle system typically features a lot of nonlinearities such as rigid-body dynamics, coordinate system transformations and most importantly the tire.

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“…The Koopman operator, an increasingly popular tool for global linearization and analysis of nonlinear dynamics (Mezić (2005), Korda and Mezić (2019) , Korda and Mezić (2018), Mezić and Banaszuk (2004)), is used in this work to approximate the vehicle nonlinear dynamics in order to achieve a linear representation of the system in a predefined subspace of the state space. This paper continues in the work from Cibulka et al (2019), where different methods for global linearization of the single-track model were used. The most promising method (described in detail in Korda and Mezić (2019)) is used for approximation of autonomous and controlled behaviour of the nonlinear vehicle system by a highdimensional linear system.…”

“…The vehicle model derived in Cibulka et al (2019) will be reviewed here. The model is depicted in Fig.…”

“…Areas with large |v y | and low |v x | (car sliding sideways) contain more points because the vehicle leaves this area of state-space rather quickly, resulting in sparse data coverage. See Cibulka et al (2019) for more details.…”