Piecewise affine state feedback controller for lane departure avoidance

Benine-Neto, Andre; Mammar, Said · 2011 · Crossref

DOI: 10.1109/ivs.2011.5940496

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Summary

This paper addresses the design of a Lane Keeping Assistance System (LKAS) for passenger vehicles, specifically targeting the challenge of maintaining vehicle stability when tire forces are saturated. Lane departure accidents are often caused by driver fatigue or inattention, and existing control strategies frequently rely on linear tire models that fail to account for the nonlinear behavior of tires under high lateral acceleration. The authors propose a Piecewise Affine (PWA) state feedback controller that approximates the nonlinear lateral tire forces across their entire operating domain, thereby enhancing safety during aggressive maneuvers or on degraded road surfaces. The methodology employs a nonlinear bicycle vehicle model that considers lateral translational and yaw motions, utilizing the Pacejka "magic formula" to describe tire forces. To handle the nonlinearities, the authors approximate the front tire forces using a PWA function divided into three regions based on the sideslip angle, while assuming a linear approximation for the rear tires. The control synthesis is formulated as a Bilinear Matrix Inequality (BMI) optimization problem. This problem is solved using the V-K method, an iterative procedure that transforms the BMI into solvable Linear Matrix Inequalities (LMI). The objective is to simultaneously determine the state feedback gains and a Piecewise Quadratic Lyapunov (PWQL) function that ensures the stability of the closed-loop system. The design incorporates a first-order actuator model to ensure control input continuity and uses ellipsoidal cell descriptions to relax constraints during the Lyapunov function search. Simulation results demonstrate the effectiveness of the proposed PWA controller compared to a controller designed solely for linear tire behavior. The study highlights that the PWA approach provides improved performance, particularly under conditions of degraded road adhesion where tire saturation is more likely to occur. By accounting for the full domain of tire forces, the controller maintains stability and lane-keeping accuracy even when the vehicle operates near the limits of tire grip. The simulations validate that the PWA approximation, despite its simplicity, captures sufficient nonlinear dynamics to outperform linear controllers in critical scenarios. The significance of this work lies in its contribution to the development of robust LKAS systems that remain effective under extreme driving conditions. By successfully applying PWA control synthesis to vehicle lateral dynamics, the paper provides a viable method for handling nonlinear tire characteristics without the computational complexity of more advanced strategies like Model Predictive Control. The findings suggest that PWA-based controllers can enhance vehicle safety by preventing loss of control during lane departure avoidance maneuvers, offering a practical solution for next-generation driver assistance systems.

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Topics

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• lane positioning
• steering pattern