Piecewise affine control for lane departure avoidance
DOI: 10.1080/00423114.2013.783220
archive: archived pipeline: cataloged verified
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Summary
This paper addresses the design of a lane departure avoidance system capable of operating during demanding maneuvers where lateral vehicle dynamics are significant and tire forces may approach saturation. While existing Lane Keeping Assistance Systems (LKAS) typically function under weak lateral solicitation, this work aims to enhance safety by handling the nonlinear behavior of lateral tire forces, particularly in degraded road adhesion conditions. The authors propose a control strategy that integrates exteroceptive sensor data (from a video camera) with yaw rate control to prevent unintended lane departures. The methodology employs Piecewise Affine (PWA) state feedback and output feedback controllers to approximate the nonlinear Pacejka tire model. The vehicle dynamics are modeled using a simplified single-track bicycle model, expanded to include lateral displacement, yaw angle error, and steering column dynamics. The nonlinear tire forces are approximated by PWA functions partitioned based on front and rear tire sideslip angles. Controller synthesis is achieved by searching for a piecewise quadratic Lyapunov function, formulated as a Bilinear Matrix Inequalities (BMI) problem. To ensure practical applicability, an observer-regulator structure is introduced to avoid reliance on sensors not standard in commercial vehicles. The stability of the system is verified through bifurcation analysis, which demonstrates that the PWA model accurately captures the stability regions of the nonlinear model across varying road adhesion levels (dry, wet, and icy asphalt). Experimental tests were conducted on a prototype vehicle equipped with a DC-motor for steering torque actuation. The results demonstrate the performance of both the PWA state feedback and output feedback controllers during lane departure avoidance maneuvers on degraded adherence conditions. The controllers successfully maintained vehicle stability and lane position despite the nonlinearities and reduced friction, validating the effectiveness of the PWA approach in handling strong lateral solicitations. The significance of this work lies in its ability to extend the operational domain of LKAS beyond low-lateral-acceleration scenarios. By explicitly accounting for tire force saturation and nonlinear dynamics through PWA control, the system offers improved safety margins in emergency situations or poor road conditions. The study confirms that PWA systems can approximate nonlinearities with arbitrary precision, providing a robust framework for automated driving tasks that require stability guarantees across the complete domain of tire forces.
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| Stage | Outcome | Tool | Model | Prompt | Attempts | Completed |
|---|---|---|---|---|---|---|
| discover | success | Crossref | — | — | 1 | 2026-06-25 |
| archive | success | unpaywall | — | — | 2 | 2026-06-26 |
| extract | success | cached | — | — | 2 | 2026-06-26 |
| clean | success | clean | — | — | 1 | 2026-06-26 |
| chunk | success | chunk | — | — | 1 | 2026-06-26 |
| embed | success | embed | Qwen/Qwen3-Embedding-8B | — | 1 | 2026-06-26 |
| enrich | success | openalex | — | — | 1 | 2026-06-26 |
| promote | success | — | — | — | 1 | 2026-06-25 |
| summarize | success | llm | qwen3.6-27b-prismaquant | summ-v5 | 1 | 2026-06-26 |
| tag | success | vector_similarity | — | — | 6 | 2026-06-26 |
| verify | success | — | — | — | 1 | 2026-06-26 |
Summary generated by qwen3.6-27b-prismaquant on 2026-06-26; verification: verified.
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