Reliable Modeling for Safe Navigation of Intelligent Vehicles: Analysis of First and Second Order Set-membership TTC

Developing high fidelity models to compute the Time-To-Collision (TTC) between vehicles is addressed in this work. A TTC interval value is over-approximated while considering several uncertainties via interval analysis. Furthermore, to decrease modeling inaccuracy, a novel second-order set-membership TTC formalization is introduced by solving a polynomial equation with interval coefficients. This latter is derived from vehicles' motion equations. Hence, an approach based on correlation analysis is exploited to improve the uncertainty evaluation. The simulation results applied on an adaptive cruise control system of both high/low-order TTC formalizations prove that the low-order model inaccuracy is compensated. Thanks to interval analysis and correlation characterization, a great balance between modeling accuracy and simplicity is reached.