Neighborhood-Aware Fuzzy Rough Action Selection for Vision-Language-Action Manipulation

Vision-Language-Action (VLA) models map visual observations and language instructions to robot actions, but the highest-scoring action is not always the most reliable one for physical execution. A candidate may satisfy the language instruction and remain collision-free at its nominal pose, while nearby actions exhibit less favorable physical properties. We present FRS-Grounding, a fuzzy rough set-based action-selection framework that evaluates each VLA candidate together with its local execution structure. Given a finite candidate set, FRS-Grounding combines a normalized VLA-conditioned candidate score and a physical-distance value to form a semantic–physical fuzzy action set. Pairwise translational and rotational differences, together with collision-free states, define a physics-informed fuzzy action relation. Fuzzy rough lower and upper approximations are then used to characterize local support within the candidate set. Candidates with stronger neighborhood-consistent support are distinguished from those lying in the boundary region, and these regions are mapped to normal execution, compliant execution, or rejection. Across 1500 randomized simulation trials, FRS-Grounding achieves a success rate of 86.4% and a safety-violation rate of 2.1%, compared with 74.8% and 8.2% for VLA-HC. Its semantic compliance is 0.89, close to RT-2 (0.91) and higher than VoxPoser (0.85) and VLA-HC (0.88). Under positional noise with σ = 10 mm, FRS-Grounding retains a success rate of approximately 78%, compared with approximately 28% for VLA-HC. Real-robot experiments further show how the boundary branch can be coupled with force-compliant control. The results support candidate-set evaluation as a practical way to combine VLA preferences with local physical structure in the tested manipulation tasks.