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<p>The growing demand for enhancements in vehicle driving safety has prompted extensive investigations into vehicle stability. Much of the work to estimate the stability region has been pursued using the Lyapunov-based approaches. In this paper, we have proposed a new non-Lyapunov-based perspective for analyzing the stability boundary of the lateral dynamics of the vehicle based on the Koopman theory. The stability boundary of the vehicle dynamics is obtained using the spectral analysis of the Koopman operator. The stability boundary is characterized using the stable manifold of an unstable equilibrium point on the stability boundary. The stable manifold is obtained as a zero-level curve of the Koopman principal eigenfunction corresponding to the unstable eigenvalue. We use the path integral formula to compute the Koopman principal eigenfunction. Further, the simulation results have been provided to obtain the lateral stability boundary for the two-degree-of-freedom planar nonlinear vehicle model. We have also discussed the effect of vehicle model parameters on characterizing the stability boundary.</p>

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Identifying lateral stability regions in vehicle dynamics: a Koopman spectral approach

  • 期刊论文

  • 发表日期：

    2025年1月14日

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  • Alok Kumar,
  • Bhagyashree Umathe,
  • Umesh Vaidya,
  • Atul Kelkar

摘要

The growing demand for enhancements in vehicle driving safety has prompted extensive investigations into vehicle stability. Much of the work to estimate the stability region has been pursued using the Lyapunov-based approaches. In this paper, we have proposed a new non-Lyapunov-based perspective for analyzing the stability boundary of the lateral dynamics of the vehicle based on the Koopman theory. The stability boundary of the vehicle dynamics is obtained using the spectral analysis of the Koopman operator. The stability boundary is characterized using the stable manifold of an unstable equilibrium point on the stability boundary. The stable manifold is obtained as a zero-level curve of the Koopman principal eigenfunction corresponding to the unstable eigenvalue. We use the path integral formula to compute the Koopman principal eigenfunction. Further, the simulation results have been provided to obtain the lateral stability boundary for the two-degree-of-freedom planar nonlinear vehicle model. We have also discussed the effect of vehicle model parameters on characterizing the stability boundary.