3D visual grounding (3DVG) localizes language-referred objects in 3D scenes, with broad applicability in both indoor and outdoor environments. However, existing 3DVG research focuses on static indoor objects, limiting its use in dynamic outdoor autonomous driving. Motion descriptions, which capture the temporal dynamics of moving objects, offer a promising way to address this challenge. We therefore introduce MoT3DVG, a large-scale dataset for dynamic-aware outdoor 3DVG with temporally evolving motion descriptions. It contains 850 scenarios with 31,128 frames from nuScenes dataset, and provides 144,568 language prompts with motion-aware descriptions for dynamic objects across time. We further propose DynaVG, a novel framework that effectively leverages temporal cues for outdoor 3DVG. In addition to the standard modality-specific encoders, DynaVG introduces a Short-Long Integrated Dynamic Encoding (SLIDE) module before the language-point cloud alignment. SLIDE models both local motion cues and global temporal context via short-term window encoding and long-term window shifting. Extensive experiments demonstrate its state-of-the-art performance on MoT3DVG, validating the effectiveness of motion-aware encoding. Our work reveals open challenges and promising directions for future research in outdoor 3DVG.

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