Manipulation policies must know which objects matter and where they are, yet the pretrained backbones that current robot foundation models build on, from language in vision-language-action models (VLAs) to video generation in world-action models (WAMs), do not directly require this metric grounding, leaving it to be learned implicitly from robot demonstrations. We propose Grounded Action Models (GAMs), a new paradigm of robot foundation models built with 3D grounding. GAM can be conditioned using language, points, or box prompts, which are first transformed into a shared object-centric representation of the selected objects. This representation captures target-focused visual features and metric object geometry, which is mixed with robot state history through a multi-stream transformer to predict action chunks. Although GAMs can be run autonomously, they can also serve as a low-level controller that a high-level planner controls using its various input modalities, allowing for long-horizon and memory-dependent manipulation. On RoboTwin 2.0, GAM achieves an average success rate of 55.3% across 50 tasks (vs. 52.0% for Spatial Forcing), including 47.6% under scene randomization (vs. 30.4% for Abot-M0), with its action policy trained only on clean-scene demonstrations. On LIBERO-PRO, it achieves a state-of-the-art average success rate of 61% (vs. 53% for $π_{0.5}$) across 16 perturbation settings, with the largest gains when targets are relocated or newly designated. On two real robots, GAM retains 17/20 successes under visual shift on a bimanual YAM versus 4/20 for $π_{0.5}$, while its composition with a Molmo2 planner on a Franka achieves 64.7% ID and 49.8% OOD step completion on long-horizon and memory-dependent tasks.
