Piecewise affine output feedback controller for vehicle lane keeping

Benine-Neto, A.; Mammar, S. · 2012 · Crossref

DOI: 10.1109/acc.2012.6314735

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Summary

This paper presents the design and simulation of a piecewise affine (PWA) output-feedback controller for a vehicle lane-keeping assistance system (LKAS). The research addresses the challenge of maintaining vehicle stability during extreme dynamic maneuvers where lateral tire forces become nonlinear and saturated. While previous approaches often relied on state feedback requiring unavailable sensors like the vehicle sideslip angle, this work develops an output-feedback controller that utilizes only measurable states: yaw rate, lateral displacement, and steering angle. The motivation is to create a robust control system capable of operating across the entire domain of tire forces, ensuring safety even when the vehicle approaches loss of control. The methodology begins with a nonlinear bicycle model of the vehicle, incorporating lateral translational and yaw motions. The nonlinear lateral tire forces, described by the Pacejka magic formula, are approximated using PWA functions partitioned by the front tire sideslip angle. To facilitate output feedback, an estimator is integrated to reconstruct the unmeasured sideslip angle from available sensor data. The control synthesis is formulated as a Bilinear Matrix Inequality (BMI) optimization problem. This non-convex problem is solved using the V-K method, which iteratively transforms the BMI into two Linear Matrix Inequality (LMI) problems. This approach simultaneously determines the PWA regulator and estimator gains alongside a Piecewise Quadratic Lyapunov (PWQL) function, ensuring the stability of the closed-loop system. The design also accounts for actuator dynamics by modeling the steering angle as a first-order system. Simulation tests were conducted on a nonlinear vehicle model to validate the controller's performance. The results demonstrate that the proposed LKAS successfully executes the standard ISO-3888-2 transient maneuver, a rigorous test for lane-keeping capabilities. The controller effectively manages the transition between linear and nonlinear tire force regions, maintaining stability and keeping the vehicle within the lane despite significant lateral solicitations. The use of degenerated ellipsoids to describe the PWA regions allowed for efficient handling of the stability constraints. The significance of this work lies in its practical applicability to autonomous driving systems. By relying on output feedback rather than full state feedback, the controller avoids the need for expensive or unavailable sensors, making it viable for commercial vehicles. The successful application of the V-K method to solve the BMI problem provides a computationally efficient framework for designing stable PWA controllers for complex nonlinear systems. This approach offers a robust solution for lane-keeping assistance that remains effective under extreme driving conditions, contributing to the development of safer autonomous vehicle technologies.

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Topics

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• lane positioning
• steering pattern