Vehicle lane keeping control based on piecewise affine regions

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

DOI: 10.1109/itsc.2011.6082817

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Summary

This paper addresses the challenge of designing robust lane-keeping assistance systems (LKAS) that remain effective during demanding maneuvers where tire forces enter the nonlinear saturation region. Traditional control strategies often rely on linear vehicle models, which fail to capture the complex dynamics of tire-road interactions at high lateral accelerations, potentially leading to loss of control. The authors propose a control strategy based on Piecewise Affine (PWA) modeling to approximate these nonlinear tire forces, specifically parametrizing the system dynamics with respect to the vehicle yaw rate. This parametrization is chosen because yaw rate is a low-cost, measurable variable, avoiding the need for expensive sensors or complex estimation algorithms required to measure tire sideslip angles directly. The methodology employs a simplified single-track vehicle model combined with the Pacejka tire model to represent lateral dynamics. The nonlinear tire forces are approximated using PWA functions, partitioning the state space into three regions based on yaw rate thresholds derived from steady-state analysis. To ensure zero lateral offset despite road curvature disturbances, the authors design a Piecewise Linear Proportional Double-Integral Derivative (P IIDi) controller. The controller switches between different gain sets depending on the current operating region. Stability of the closed-loop system is rigorously proven using a continuous piecewise quadratic Lyapunov function, formulated as a convex optimization problem involving Linear Matrix Inequalities (LMI). Controller gains are tuned using numerical optimization to meet specific performance criteria regarding rise time, settling time, and overshoot. Simulation results were conducted using a standard CarSim D-Class vehicle model at a speed of 30.6 m/s, comparing the proposed PWA controller against a linear-only controller. The tests included sudden lateral force and yaw moment disturbances, as well as demanding lane-change maneuvers reaching lateral accelerations of 8.9 m/s² on both dry and wet pavements. The results demonstrate that the PWA controller significantly improves vehicle stability and lane-keeping performance. Specifically, when subjected to strong disturbances that push the vehicle into the nonlinear region, the PWA controller reduced the lateral offset overshoot by approximately 50% compared to the linear controller. Additionally, the PWA strategy prevented excessive increases in tire sideslip angles by adjusting the control input appropriately as the yaw rate exited the linear region, thereby maintaining better traction and control during critical maneuvers. The significance of this work lies in its practical approach to handling nonlinear vehicle dynamics without requiring complex state estimation. By leveraging yaw rate as a scheduling variable, the proposed control scheme offers a computationally efficient and robust solution for LKAS. The study confirms that accounting for tire force nonlinearity through PWA modeling and switching control strategies enhances safety and performance in scenarios where traditional linear controllers are insufficient, such as emergency avoidance maneuvers or driving on low-friction surfaces. This approach provides a viable pathway for implementing advanced driver assistance systems that are effective across the complete domain of tire forces.

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Topics

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• lane positioning
• steering pattern