Open-vocabulary 3D maps let robots answer language queries about what and where, but they assume a static world and cannot answer queries about how scene elements behave. We introduce Vision-Language-Motion Maps (VLMM), an open-vocabulary, language-queryable 3D map - queried through a rule-based intent router over open-vocabulary object nouns, not a general natural-language interface - in which each element carries a fused motion attribute: a VLM/LLM semantic movability prior combined with geometrically observed cross-frame motion, together with a per-element uncertainty. Queries reduce to attribute filters that distinguish what has been seen to move, what could move but has not, and what stays still. On a controlled simulator benchmark with exact ground truth (AI2-THOR, three scene types) we show through ablation that the schema fields are non-substitutable: a semantic-only baseline fails motion queries even with strong features, and neither motion field substitutes for the other (the prior cannot answer"what is moving,"observed motion cannot answer"what could move"). On real dynamic RGB-D (TUM and Bonn, six sequences) we show the uncertainty channel - our key difference from prior fused-motion work - consistently improves moving-vs-static average precision and reduces false motion flags, and that it is robust to estimated (noisy) poses. The raw confidence is not calibrated, but post-hoc isotonic calibration reaches an expected calibration error of 0.10. VLMM is a representation contribution: the closest prior maps each lack at least one of the four properties - open-vocabulary, language-queryable, fused prior-and-observed motion, and per-element uncertainty - that our combination provides.
A robot carrying a persistent, behavior-annotated map faces two planning questions, and its memory answers only one well. The \emph{spatial-navigation} question -- how to walk around a room -- we address first and report a negative: building on Vision--Language--Motion Maps (VLMM), a behavior-aware planner cost cuts a planning-time objective by $\sim$35\% over 28 AI2-THOR scenes, but under closed-loop execution the real benefit nearly vanishes ($\sim$4\%) and an on-demand vision--language model (VLM) does as well. The \emph{resource-allocation} question differs: under a limited perception budget, what should the robot re-observe now to keep its map fresh? Framing re-perception as this attention decision, we show a persistent map's memory (change-history, or even just recency of last sighting) yields the best schedule (held-out), matching an oracle, while the memoryless VLM prior is poor. Because the schedule reallocates budget toward what matters, memory's benefit concentrates on the important objects ($\sim$1.6$\times$ the mean), and a downstream fetch task confirms fewer wasted trips; the gain grows with per-instance heterogeneity exactly as a Cauchy--Schwarz bound predicts -- it equals $\mathrm{Var}(\sqrt\lambda)$, the variance of root-volatility. With a real CLIP prior on rendered objects the advantage is $+21$--$26\%$. The map's distinctive value appears when the task is \emph{language-conditioned}: told what to track, VLMM grounds the relevant objects (open-vocabulary) and tracks their change (memory), beating even a strong relevance-weighted recency baseline ($+2.5\%$) -- so its motion channel adds value beyond a last-seen timestamp -- and an on-demand VLM ($+8.9\%$); neither language nor dynamics alone suffices. The map earns its keep not by telling the robot how to walk around a room, but by telling it what to pay attention to.
