G${}^3$VLA: Geometric Inductive Bias for Vision-Language-Action Models

Abstract

Vision-language-action (VLA) models have rapidly advanced generalist robot manipulation by harnessing the semantic knowledge of pretrained vision-language backbones. However, their visual representations are typically grounded in 2D image coordinates rather than calibrated camera geometry. This limitation is especially pronounced in multi-camera systems, where views are coupled by known intrinsics and extrinsics but processed as independent images. We propose G${}^3$VLA, a camera-aware geometric module that injects calibrated structure into the visual-token stream of a pretrained VLA without altering its action space or original action-learning objective. G${}^3$VLA combines intrinsic-conditioned ray embeddings, projective positional encoding (PRoPE), and bidirectional cross-view fusion to establish geometrically consistent representations across camera views. Geometric supervision is provided by ground-truth point maps or confidence-gated ${\pi }^3$X teacher predictions, enabling training without depth sensors or manual geometric annotations. On ${\pi }_0$, G${}^3$VLA consistently improves performance on LIBERO and RoboCasa24 under both supervision regimes, while ground-truth supervision improves five-task RoboTwin2.0 averages with three cameras. Experiments on camera-shifted LIBERO-Goal and real robots demonstrate improved robustness to unseen camera viewpoints. Controlled calibration studies across ${\pi }_0$ and ${\pi }_{0.5}$ show that these gains depend on correct camera geometry while remaining stable under mild calibration perturbations. These results demonstrate that grounding VLA visual tokens in calibrated camera geometry provides a simple and general mechanism for improving geometric consistency, multi-view reasoning, and viewpoint robustness in pretrained robot policies.