Real-time and high-quailty dense mapping is essential for robots to perform fine tasks. However, most existing methods can not achieve both speed and quality. Recent works have shown that implicit neural representations of 3D scenes can produce remarkable results, but they are limited to small scenes and lack real-time performance. To address these limitations, we propose a real-time scalable mapping method using robot-centric implicit representation. We train implicit features with a multi-resolution local map and decode them as signed distance values through a shallow neural network. We maintain the learned features in a scalable manner using a global map that consists of a hash table and a submap set. We exploit the characteristics of the local map to achieve highly efficient training and mitigate the catastrophic forgetting problem in incremental implicit mapping. Extensive experiments validate that our method outperforms existing methods in reconstruction quality, real-time performance, and applicability. The code of our system will be available at \url{https://github.com/HITSZ-NRSL/RIM.git}.

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