DRoPE: Directional Rotary Position Embedding for Efficient Agent Interaction Modeling

Accurate and efficient modeling of agent interactions is essential for trajectory generation in autonomous driving. Existing methods, however, present an “impossible triangle,” failing to simultaneously optimize accuracy, computational time, and memory efficiency. To break this limitation, we first pro pose adapting Rotary Position Embedding (RoPE) from natural language processing to improve relative position encoding in the autonomous driving domain. RoPE's design effectively resolves the time and space complexity overhead of prior query-centric methods. However, we identify that RoPE, while effective for spatial positions, inherently fails to model agent headings due to the periodicity of angular information. To solve this, we propose Directional Rotary Position Embedding (DRoPE), a novel and theoretically-grounded adaptation designed specifically for angles. DRoPE introduces a uniform identity scalar into the 2D rotary transformation, creating a principled mapping that correctly and naturally encodes relative angular information. Our final framework employs a hybrid strategy: using the original RoPE for spatial positions and our proposed DRoPE for agent headings. This combined approach is the first query-centric method to achieve optimal efficiency. Empirical evaluations against state-of-the-art models confirm our framework's practical effectiveness, achieving comparable performance while offering significant computational and memory advantages. The video documentation is available at https://drope-traj.github.io/.