Models and methodology for optimal trajectory generation in safety-critical road–vehicle manoeuvres
DOI: 10.1080/00423114.2014.939094
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Summary
This paper addresses the challenge of generating optimal vehicle trajectories for safety-critical maneuvers, aiming to improve active safety systems like Electronic Stability Control (ESC). The authors note that current systems lag behind the performance of professional drivers and that finding the right balance between vehicle models, optimization criteria, and computational tools is difficult. The study focuses on time-optimal trajectory generation to understand at-the-limit vehicle behavior, providing insights for future driver-assistance systems that mimic expert driving techniques. The methodology employs a platform combining state-of-the-art nonlinear optimization tools with various established vehicle chassis and tire models. The researchers evaluated three specific time-critical scenarios: a 90-degree turn, a hairpin turn, and a double lane-change maneuver. They tested six different combinations of chassis and tire models to analyze the impact of model complexity on results. The chassis models included a complex double-track (DT) model with roll and pitch dynamics, a single-track (ST) model with pitch dynamics, and a simplified ST model neglecting roll and pitch. Tire modeling utilized the Pacejka Magic Formula, with attention to how different parameterizations affect force generation under aggressive conditions. The optimization problem was formulated as a minimum-time control problem subject to physical constraints on inputs and states, including wheel dynamics for drive and brake torques. The results demonstrate that the choice of tire model has a fundamental influence on the resulting control inputs, particularly in aggressive maneuvering where tires operate near their limits. The study found that certain combinations of chassis and tire models yield inherently different behaviors, highlighting the sensitivity of optimal solutions to modeling assumptions. However, key variables relevant to safety systems, such as yaw moment and body-slip angle, remained similar across several model configurations during aggressive maneuvers. This suggests that while detailed dynamics affect specific control signals, the overall vehicle stability metrics may be robust to certain simplifications. The analysis also revealed that simplified models, while computationally cheaper, can sometimes produce nonphysical behavior or numerical instability when pushed to their limits by optimization algorithms. The significance of this work lies in its comprehensive comparison of modeling trade-offs for optimal control applications. The authors conclude that while complex models are necessary for accurate control input determination, simpler models may suffice for capturing essential safety-relevant variables like yaw moment. This provides a basis for designing efficient onboard systems that balance computational demand with accuracy. The study underscores the importance of proper tire modeling in optimization contexts, as standard simulation models may fail or behave unpredictably when used for time-optimal control. Ultimately, the research offers a validated platform and methodological guidelines for developing future active safety systems that can achieve performance closer to that of professional drivers.
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| Stage | Outcome | Tool | Model | Prompt | Attempts | Completed |
|---|---|---|---|---|---|---|
| discover | success | OpenAlex-citations | — | — | 1 | 2026-06-18 |
| archive | success | unpaywall | — | — | 2 | 2026-06-25 |
| extract | success | cached | — | — | 2 | 2026-06-26 |
| clean | success | clean | — | — | 1 | 2026-06-19 |
| chunk | success | chunk | — | — | 1 | 2026-06-19 |
| embed | success | embed | Qwen/Qwen3-Embedding-8B | — | 1 | 2026-06-19 |
| promote | success | — | — | — | 1 | 2026-06-18 |
| summarize | success | llm | qwen3.6-27b-prismaquant | summ-v5 | 1 | 2026-06-26 |
| tag | success | vector_similarity | — | — | 6 | 2026-06-19 |
| verify | success | — | — | — | 1 | 2026-06-26 |
Summary generated by qwen3.6-27b-prismaquant on 2026-06-26; verification: verified.
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- Theoretical Contribution: computational model