Embodied Multimodal Grounding for Open-Vocabulary Mobile Manipulation via Semantic 3D Gaussian Splatting

Spatial grounding remains a key limitation of vision-language-action (VLA) systems for robotic manipulation. While current models can recognize objects and follow language instructions, they often lack an explicit representation of how objects are arranged in space, including support, containment, ordering, occlusion, and depth-sensitive relations. We introduce EmbodimentSemantic, a spatial scene-graph dataset and benchmark for evaluating relational grounding in embodied manipulation. EmbodimentSemantic represents scenes as directed object-relation-object triplets, where each triplet specifies a spatial relation between an ordered pair of objects using a fixed set of relations. This representation enables direct evaluation of object binding, relation prediction, and spatial consistency. The dataset includes real-world manipulation observations collected with the low-cost SO101 robot arm, together with generated scene graphs for studying spatial grounding in practical robotic settings. To provide controlled validation, we also introduce a simulator-grounded LIBERO benchmark with over 60K manipulation frames and more than 120K camera-specific scene graphs across paired third-person and wrist views, where ground-truth relations are derived automatically from MuJoCo geometry, world coordinates, camera projections, and visibility constraints. We further test whether scene graphs improve downstream control by injecting them into existing VLA policy prompts. Experiments across open-source and commercial VLMs show that current models often predict plausible relations but struggle with exact depth-aware and viewpoint-dependent spatial structure. EmbodimentSemantic provides a unified framework for diagnosing spatial grounding in VLM perception and testing its utility for VLA manipulation.

Vision-Language-Action (VLA) models have emerged as a powerful end-to-end paradigm for robotic manipulation by mapping language instructions and 2D visual inputs directly to actions. However, these models lack an explicit, scene-level 3D representation, limiting their ability to reason over spatial layouts and geometric constraints. While recent efforts incorporate explicit 3D cues, such as depth maps or point clouds, to improve geometric awareness, they primarily capture low-level structures and lack high-level semantic grounding in 3D space. In human cognition, interaction with the physical world relies on a 3D semantic cognitive map - an internal mental model that integrates spatial layouts with semantic context to enable persistent, viewpoint-invariant reasoning. In light of this, we present VistaVLA, a novel two-stage framework that constructs a geometry- and semantics-aware 3D cognitive representation from 3D Gaussian primitives and grounds it as compact context tokens for VLA policy learning. Specifically, VistaVLA lifts multi-view vision-language features into 3D Gaussian primitives, forming geometry-anchored semantic tokens that align view-consistent spatial grounding with 2D visual feature spaces. To make this 3D representation computationally tractable for effective VLA control, we introduce Merge-then-Query (MtQ), a token summarization mechanism. MtQ compresses dense Gaussian primitives into a highly compact set of spatially informative tokens, achieving a 99% token reduction while preserving action-relevant 3D layouts and semantic context. Extensive evaluations in both simulated and real-world environments demonstrate the effectiveness of VistaVLA. Notably, in real-world scenarios, VistaVLA improves success rates by 22.8% across seven real-world tasks and by 30.0% over the VLA-Adapter baseline on challenging out-of-distribution tasks.

We introduce Forecast-aware Gaussian Splatting (Forecast-GS), a predictive 3D representation framework for language-conditioned robotic manipulation. While recent manipulation systems have made progress by grounding language instructions into robot affordances, value maps, or relational keypoint constraints, they usually reason over the current scene and do not explicitly model the task-completed state. This limitation is critical when success depends on satisfying spatial and semantic goals under partial observations, where the robot must evaluate whether a candidate action leads to a feasible task-consistent outcome. We validate Forecast-GS on real-world pick-and-place manipulation tasks, including Cutter-to-Box, Apple-to-Bowl, and Sponge-to-Tray. For each task, we conduct 25 real-world trials under varied initial object configurations using the same robot platform and sensing setup. Forecast-GS with automatic candidate selection achieves success rates of 21/25, 23/25, and 16/25 on the three tasks, respectively, outperforming the ReKep baseline, which achieves 15/25, 19/25, and 10/25. A diagnostic human-assisted setting further improves success rates to 23/25, 24/25, and 19/25, suggesting that candidate generation is effective while automatic ranking remains imperfect. These results suggest that explicitly forecasting task-completed 3D states enables more reliable action evaluation, while the gap between automatic and human-assisted selection indicates that robust final-state ranking remains an important challenge for fully autonomous manipulation. Overall, Forecast-GS provides an interpretable bridge between language understanding, 3D perception, and robotic manipulation planning.