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An improved two-dimensional time-to-collision for articulated vehicles: predicting sideswipe and rear-end collisions
Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering. The Swedish National Road and Transport Research Institute, Linköping, Sweden.ORCID iD: 0009-0000-0356-7799
Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering. The Swedish National Road and Transport Research Institute, Linköping, Sweden.ORCID iD: 0000-0002-7780-7449
Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0001-7349-1937
The Swedish National Road and Transport Research Institute, Linköping, Sweden.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Time-to-collision (TTC) is a widely used measure for predicting rear-end collisions, assuming constant speed and heading for both vehicles in the prediction horizon. However, this conventional formulation cannot detect sideswipe collisions. A two-dimensional extension, TTC2D, has been proposed in the literature to address lateral interactions. However, this formulation assumes both vehicles have the same heading and that their headings remain unchanged during the manoeuvre, in addition to the constant speed and heading assumptions in the prediction horizon. Moreover, its use for articulated vehicles like a tractor-semitrailer remains unclear. This paper proposes three enhanced versions of TTC2D to overcome these limitations. The first incorporates the vehicle heading to account for directional differences. The standard assumption of constant speed and heading in the prediction horizon holds. The second adapts the formulation for articulated vehicles, and the third allows for constant acceleration, relaxing the constant speed assumption in the prediction horizon. All versions are evaluated in simulated cut-in scenarios, covering both sideswipe and rear-end collisions, using the CARLA simulation environment with a tractor-semitrailer model. Results show that the proposed versions predict sideswipe collisions with better accuracy compared to existing TTC2D. They also detect rear-end collisions similar to the existing methods.

Keywords [en]
Time-to-collision, TTC, Two-dimensional time-to-collision, Articulated vehicles, Tractor-semitrailer, Rear-end collision, Sideswipe collision, CARLA
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-219364DOI: 10.48550/arXiv.2507.04184OAI: oai:DiVA.org:liu-219364DiVA, id: diva2:2012711
Note

This a preprint posted 5 July 2025 at preprints.org.

This version is not peer-reviewed.

Available from: 2025-11-10 Created: 2025-11-10 Last updated: 2025-11-10Bibliographically approved
In thesis
1. Performance and Safety Assessment of Articulated Heavy Vehicles using Traffic Data and Simulation
Open this publication in new window or tab >>Performance and Safety Assessment of Articulated Heavy Vehicles using Traffic Data and Simulation
2025 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Recently, the Swedish government permitted five long combination vehicles (LCVs), with a length longer than 25.25 meters but limited to 34.5 meters, along the selected routes in Sweden. LCVs offer potential benefits such as reduced operational costs, improved fuel efficiency, and lower emissions. While simulations have provided insights into the performance of LCVs on the road, they are conducted in idealised conditions that exclude the complexities of real-world traffic. Therefore, the first major focus of this thesis is to investigate the performance of LCVs in real traffic. Two combinations have been studied: the A-double, a tractor hauling two semitrailers with a dolly in between, and the DuoCAT, a truck hauling two center-axle trailers, which is also called C-double.

The analysis is based on Performance-Based Standards (PBS) measures, including rearward amplification (RWA), low-speed swept path (LSSP), high-speed transient offtracking, and high-speed steady-state offtracking. The steering reversal rate is further applied to assess the driver’s cognitive workload during low-speed manoeuvres. The study covers four traffic scenarios: lane changes, roundabout manoeuvring, turning at intersections, and negotiating tight curves. The results show that both vehicle combinations perform within PBS limits in most cases, with a few outliers across the studied scenarios. The A-double exhibits slightly better stability in lane changes, while the DuoCAT demonstrates slightly better manoeuvrability in roundabouts and intersections. Furthermore, the tire-road friction is examined for the A-double in low-speed manoeuvres, showing that it influences the driver’s behaviour but has negligible effects on the performance of the vehicle.

In the thesis, an alternative approach is investigated that combines low-cost GPS and IMU instead of high-precision sensors to analyse the performance of an LCV. The performance measures, RWA and LSSP, obtained using sensor fusion of GPS/IMU are compared against those obtained from high-precision sensors. The results show a rather good agreement between the two sensor setups in most cases; however, further investigation is needed to improve the LSSP estimates. In addition, a method is presented that employs a computer vision-based approach using data from a forward-facing camera to estimate the relative positions of surrounding vehicles. This method is employed to study lane changes of an A-double, providing insights into its interactions with the surrounding traffic.

The second major focus of the thesis is the simulation-based assessment of collision risk for articulated heavy vehicles. CARLA is used as a simulation environment for this purpose. Since models of articulated vehicles, including LCVs, do not exist in CARLA vehicle libraries, a tractor–semitrailer model is developed as a first step, building upon existing studies. The modelled tractor-semitrailer is used to evaluate the efficacy of an improved two-dimensional time-to-collision (TTC) measure for articulated vehicles, proposed in this thesis. Unlike conventional TTC, which primarily addresses rear-end collisions, the results show that the pro-posed formulation captures both rear-end and sideswipe collision risks, making it more suitable for multi-unit vehicles.

Overall, the thesis enhances the understanding of the behaviour of articulated heavy vehicles, specifically LCVs in real traffic, and proposes frameworks to support future performance and safety studies related to these vehicles.

Abstract [sv]

Nyligen tillät svenska regeringen 5 typer av fordonståg vars längd överstiger 25.25 meter men inte 34.5 meter (LCV) att trafikera utvalda rutter i Sverige. Långa fordonståg erbjuder fördelar såsom lägre driftkostnader, bättre bränsleeffektivitet och minskade utsläpp. Även om simuleringar ger värdefulla insikter om prestanda så bygger de på idealiserade förhållanden och tar inte hänsyn till egenskaper hos verklig trafik. Därför är det första huvudsakliga fokuset i denna avhandling att undersöka prestandan hos LCV i verklig trafik. Två kombinationer har studerats: A-dubbel, en dragbil som drar två påhängsvagnar med en dolly emellan, samt Duo-kärra, en lastbil som drar två släpvagnar med centrerade axlar (kärror), även kallad C-dubbel.

Analysen baseras på Performance-Based Standards (PBS)-mått, inklusive bakåtförstärkning samt svept bana i låg fart (LSSP), och spåravvikelse vid höga hastigheter. Styrreverseringshastighet används dessutom för att bedöma förarens arbetsbelastning vid lågfartsmanövrar. Studien omfattar fyra trafikscenarier: filbyten, manövrering i rondeller, svängar i korsningar samt körning i snäva kurvor. Resultaten visar att båda fordonskombinationerna generellt presterar inom PBS-gränserna men med vissa avvikelser. A-dubbeln uppvisar något bättre stabilitet vid filbyten medan C-dubbel uppvisar något bättre manövrerbarhet i rondeller och korsningar. Däck-väggrepp undersöks vidare för A-dubbeln vid lågfartsmanövrer och resultaten visar att det påverkar förarens beteende men har försumbar effekt på fordonets prestanda.

I avhandlingen undersöks också en analysmetod som kombinerar lågkostnads-GPS och IMU istället för dyra högprecisionssensorer, där de prestandamått som erhålls genom signalbehandling av dessa billigare sensorer jämförs med de som erhålls från högprecisionssensorer. Resultaten visar god överensstämmelse mellan de två sensorsystemen, men ytterligare undersökning krävs för att förbättra LSSP-uppskattningarna. Dessutom presenteras en kamerabaserad metod med en framåtriktad kamera för att uppskatta de relativa positionerna för omgivande fordon. Denna metod tillämpas för att studera filbyten hos ett A-dubbelfordon och analysera dess interaktion med den omgivande trafiken.

Avhandlingens andra huvudsakliga fokus är den simuleringsbaserade bedömningen av kollisionsrisk för tunga fordonskombinationer där simuleringsmiljön CARLA används. Eftersom modeller av tunga fordonskombinationer, inklusive LCV, inte finns i CARLA:s fordonsbibliotek, har en modell av en dragbil med påhängsvagn utvecklats som ett första steg. Den modellerade dragbil-påhängsvagn-kombinationen används för att utvärdera effektiviteten hos ett förbättrat tvådimensionellt tid-till-kollision (TTC)-mått för tunga fordonskombinationer. Till skillnad från konventionell TTC, som främst behandlar påkörningar bakifrån, fångar den föreslagna formuleringen både bakifrån- och sidokollisionsrisker, vilket gör den mer lämplig för långa fordonskombinationer.

Sammanfattningsvis ämnar avhandlingen öka förståelsen för beteendet hos tunga fordonskombinationer, särskilt LCV:er i verklig trafik, och föreslår ramverk för att stödja framtida studier av deras prestanda och säkerhet.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2025. p. 24
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 2489
National Category
Vehicle and Aerospace Engineering
Identifiers
urn:nbn:se:liu:diva-219331 (URN)10.3384/9789181183283 (DOI)9789181183276 (ISBN)9789181183283 (ISBN)
Public defence
2025-12-12, Ada Lovelace, B-building, Campus Valla, Linköping, 09:00 (English)
Opponent
Supervisors
Note

Funding Agencies: The research presented in this thesis was supported through national and in-ternational projects. Funding was provided by Vinnova, Sweden’s innovation agency, through the projects HCT-II (grant no. 2019-03103), Autofreight II (grant no. 2021-05027), Foundation Models for Time-Series Automotive Large-Scale Data (grant no. 2024-01568), and TRENoP (Transport Research Environment with Novel Perspectives). The research also received support from the European project ROADVIEW (grant no. 101069576).

Available from: 2025-11-07 Created: 2025-11-07 Last updated: 2025-11-10Bibliographically approved

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Behera, AbhijeetKharrazi, SogolFrisk, Erik

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