Takagi-Sugeno Observers: Experimental Application for Vehicle Lateral Dynamics Estimation

Yacine, Zedjiga; Ichalal, Dalil; Ait-Oufroukh, Naïma; Mammar, Saïd; Djennoune, Saïd · 2015 · Crossref

DOI: 10.1109/tcst.2014.2327592

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Summary

This paper addresses the challenge of estimating vehicle lateral dynamics (specifically sideslip angle and lateral velocity) and road curvature for advanced driving assistance systems. These parameters are critical for safety features like electronic stability programs but are often unavailable due to the high cost or technical limitations of direct sensors. The authors aim to overcome the limitations of linear models, which are only valid in normal driving zones, by developing a nonlinear observer capable of handling dangerous driving situations, such as sliding, where tire forces exhibit nonlinear behavior. The methodology employs a Takagi-Sugeno (TS) fuzzy model to represent the nonlinear vehicle lateral dynamics exactly within a compact state space, avoiding information loss. The vehicle model is decomposed into two cascaded subsystems. The second subsystem, relating to vehicle positioning relative to the road, is used to estimate road curvature via an algebraic technique and high-order sliding mode differentiators (HOSMDs). These differentiators provide exact finite-time estimates of the time derivatives of measured signals, such as lateral deviation and heading angle. The first subsystem, describing lateral drift and tire forces, is transformed into a polytopic TS model. A key innovation is the handling of unmeasured premise variables (specifically lateral velocity) by estimating them using the vision system outputs and HOSMDs, thereby converting the TS model into one with measurable premise variables. The observer design ensures exponential convergence of the state estimation error, with stability conditions derived using Lyapunov theory and expressed as linear matrix inequalities. Experimental results using real data validate the proposed approach. The study demonstrates that the observer can accurately estimate lateral velocity, lateral tire forces, and road curvature. The use of HOSMDs allows for the exact recovery of time derivatives, enabling the algebraic estimation of road curvature and the precise determination of premise variables for the TS observer. The results confirm that the method remains effective even when longitudinal velocity varies, a realistic condition often neglected in prior linear model approaches. The significance of this work lies in providing a robust, nonlinear estimation framework that bridges the gap between linear observer designs and complex nonlinear vehicle behaviors. By integrating algebraic techniques with TS fuzzy modeling, the approach offers a practical solution for state estimation in safety-critical driving scenarios without requiring expensive additional sensors. This contributes to the field of control systems by extending linear design tools to nonlinear systems with unknown inputs, enhancing the reliability of vehicle safety systems during extreme maneuvers.

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• lane positioning