Determining the controllable range of reversing multi-articulated vehicles using a geometric method

Journal article, 2026

Reversing a car with a trailer is a challenging task for drivers.  The car and trailer will unavoidably fold towards each other, regardless of steering control, when reversing after the articulation angle exceeds a specific limit. Articulated vehicles in those states are defined as outside their controllable range of reversing. Reversing multi-articulated long combination vehicles (LCVs) is even more challenging, as the combinations of articulation angles must remain within the controllable range, which is not easily identifiable for drivers. A clear boundary of the controllable range for reversing is important for drivers and for developing driver-assistance functions for LCVs. This study uses articulation-angle dynamics to investigate the controllable range of LCV articulation angles. The controllable range includes vehicle poses that allow an LCV to be reversed into a straight line. A geometric method is developed to determine the boundary of the controllable range of reversing for LCVs up to three articulation joints. The method’s core is visualising the articulation-angle paths and examining their geometric properties. The method is validated with high-fidelity simulations. The resulting controllable boundaries reveal the potential to reverse LCVs at articulation angles close to their mechanical limits, thereby increasing flexibility in path planning and reducing space requirements.