An improved two-dimensional time-to-collision for articulated vehicles: predicting sideswipe and rear-end collisions

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, $\text{TTC}_{\text{2D}}$, 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 $\text{TTC}_{\text{2D}}$ 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 $\text{TTC}_{\text{2D}}$. They also detect rear-end collisions similar to the existing methods.