arXiv:2609.09591v1 Announce Type: cross Abstract: Sixth-generation (6G) wireless networks are expected to provide a key infrastructure for large-scale embodied intelligence, where heterogeneous robots collaborate through low-latency connectivity, edge intelligence, and distributed sensing. Vision-language-action (VLA) models offer a foundation by integrating visual perception, language understanding, and action generation into a unified closed-loop policy. However, training and adapting VLA models to distributed robotic agents introduce challenges in privacy protection, communication efficiency, and model heterogeneity. Existing federated learning (FL) methods overlook the intrinsic differences among vision, language, and action pathways in parameter scale, privacy exposure, update dynamics, and tolerance to compression or perturbation. To address this issue, this article proposes FedMVLA, a modality-decoupled FL framework for privacy-preserving embodied intelligence in 6G networks. FedMVLA incorporates three mechanisms: modality-aware federated aggregation (MAFA), modality-aware privacy allocation (MAPA), and modality-aware communication compression (MACO), together with a modality-sliced transport design that routes the precision-critical action stream through a protected ultra-reliable low-latency slice. A case study on federated robotic manipulation over the Third Generation Partnership Project (3GPP)-based wireless substrate, covering fading, co-channel interference, and malicious jamming, shows that FedMVLA achieves an 84.8% task success rate, exceeds FedAvg by 22.2 percentage points, sustains a widening margin when scaling to 128 clients across eight cells, and reduces the schedule-averaged per-client uplink model-update payload by 95.6% (approximately 96%), while keeping the 95th percentile (p95) of the round-critical uplink completion time near 1.5s.