Embodied planning is dedicated to the goal of building agents capable of perceiving, reasoning, and executing long-horizon tasks in physical environments. However, existing embodied benchmarks predominantly focus on single-agent execution or restricted multi-agent settings, leaving long-horizon tasks that involve complex inter-agent dependencies largely underexplored despite their prevalence in real-world embodied scenarios. To address this gap, we introduce CoEmbod, the first realistic 3D simulated embodied benchmark for long-horizon multi-agent embodied cooperation with diverse inter-agent dependencies. CoEmbod contains 155 expert-curated tasks across 40 scenes and 10845 objects, covering three cooperation regimes: spatial distribution, parallel constraint, and failure recovery. These regimes cover a broad spectrum of cooperative requirements, ranging from distributed task allocation to synchronized execution and assisted failure recovery. CoEmbod further provides a process-level evaluation framework with Budgeted Cooperative Success (BCS), which jointly measures goal completion, cooperation fidelity, and execution efficiency. Experiments reveal that even the leading LMM powering a well-established agentic workflow achieves only 20.23% success, highlighting the difficulty of long-horizon multi-agent cooperation with diverse inter-agent dependencies in complex embodied environments.

Vision-Language-Action (VLA) models have shown strong performance in language-conditioned robotic manipulation, yet their robustness to linguistic variation remains poorly understood. In this work, We present the first systematic multilingual evaluation of VLA models by translating the LIBERO benchmark into ten languages, revealing severe performance degradation under non-English instructions, with success rates dropping by 30–50%. Through fine-grained analysis of task executions, we find that language influence is highly non-uniform across steps: certain steps exhibit strong language dependence and dominate overall task failure, while others are largely language-agnostic. Based on this insight, we propose a step-wise inference-time intervention that aligns representations according to step language sensitivity, substantially improving performance under linguistic variation. Our results indicate that language robustness in VLA models is fundamentally a step-wise control problem, highlighting the importance of temporally structured analysis for reliable embodied agents.