Retrieving useful context for a robot requires matching its task, execution stage, and the continuation that should follow. We introduce Robota-Embed, to our knowledge the first vision-language-action (VLA) embedding model to jointly encode all three modalities in both current-state queries and recorded future continuations. Predictive retrieval training aligns these endpoints, enabling historical continuations to serve as context at inference time. We construct a multi-source corpus of 1,695,684 cleaned training anchors and introduce Robota-Embed-Bench, with 4,000 queries and a shared 8,000-entry gallery. Robota-Embed achieves 47.33% clip-level and 81.77% episode-level R@1, exceeding action-free Gemini Embedding 2 by 22.09 and 33.47 percentage points. Controlled retrieval studies show that removing native action degrades retrieval more than removing vision. We study two complementary applications. Embed2ICL uses retrieved experience for training-free and training-based policy conditioning, increasing success from 47.0% to 56.3% in DROID-Sim and from 86.4% to 92.8% on the LIBERO difficult subset, while improving task progress on real robots. Embed2Evolve uses execution feedback to grow task-local memory and refine context use around a frozen GPT-6 Astra policy. Across five ManiSkill tasks, it achieves 68% success, compared with 24% for GPT-6 Astra Direct and 33% for a harness independently evolved with Omni-Embed-Nemotron-3B under the same protocol. Relative to the latter, it uses approximately 79.5% fewer policy tokens per test rollout, counting both successes and failures. These results show that a unified, action-aware retrieval space can support robot in-context learning and task-local context evolution.

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