Safe Operating Limits of Vehicle Dynamics under Parameter Uncertainty using Koopman Spectrum

Abstract Ground vehicles operate under different driving conditions, which requires the analysis of varying parameter values. It is essential to ensure the vehicle's safe operation under all these conditions of the parameter variation. In this paper, we investigate the safe operating limits of a ground vehicle by performing the reachability analysis for varying parameters using the Koopman-spectrum approach. The reachable set is computed using the Koopman principal eigenfunctions obtained from a convex optimization formulation for different values of the parameter. We consider the two degrees-of-freedom non-linear quarter car model to simulate the vehicle's dynamics. Based on the obtained reachable sets, we provide the mean and variance computation framework with parametric uncertainty. The results show that the reachable set for each value provides valuable information regarding the safe operating limits of the vehicle and can assist in developing safe driving strategies.