用网格计数避免重复搜索，让机器人小队更快收完残余资源。

The complete collection of sparse resources in large, unknown environments remains a challenging problem for autonomous robot swarms. Previous studies have shown that a substantial portion of total mission time is consumed during the final stage of collection, where only a small fraction of randomly scattered resources remain. Consequently, many existing swarm foraging algorithms (search and collection) focus on collecting most resources within a limited time window, rather than improving end-stage efficiency for collecting all resources. We propose a grid-based stochastic foraging strategy that explicitly reduces redundant visits and accelerates late-stage collection. The unknown search area is partitioned into a grid map, which is maintained by a lightweight central server. To maintain scalability, both robots and the server operate within limited memory and computational constraints. The server updates the grid-level visitation counts based on robot-reported locations, producing a global estimate of the exploration density. For each new foraging trip, a robot selects its next search area from a local 3 X 3 neighborhood of grids probabilistically with the lowest visitation count, thus biasing exploration toward under-visited regions while maintaining stochasticity. Extensive simulation experiments demonstrate that the proposed strategy consistently outperforms the canonical centrally placed baseline foraging algorithm (CPFA). Compared to CPFA, the proposed method reduces the total collection time by up to 33% and improves collection efficiency by more than 48% during the final stage of the mission. These results indicate that the proposed strategy is robust, flexible, and scalable for near-complete and complete resource collection in robot swarms and can serve as a general enhancement for stochastic swarm foraging methods under limited onboard resources.