Formation control of wheeled mobile robots (WMRs) has been extensively studied due to its broad applications in fields such as logistics transportation, environmental monitoring, and search and rescue. However, most existing works mainly focus on tracking predefined formations, which limits their adaptability to complex real-world environments. To address this, we propose REACT (Real-time Environment-Adaptive architecture for Continuous formation navigaTion), a hierarchical architecture integrating centralized formation generation and distributed formation maintenance. Specifically, our upper layer generates new environment-adaptive formations when necessary and uses our proposed TCF-R2T (Trajectory-Conflict-Free Robot-to-Target assignment) algorithm to compute conflict-free WMR-to-target assignments in polynomial time, enabling timely formation transitions without trajectory conflicts. At the lower layer, each WMR executes our developed JSTP (Joint Spatio-Temporal trajectory Planning) method to maintain the generated formation by simultaneously optimizing spatial positions and temporal durations, thereby enhancing coordination among WMRs and enabling continuous navigation in obstacle-rich environments and dynamic-obstacle scenarios. Both simulation and real-world experiments validate the effectiveness and practical applicability of REACT. Experimental videos are available on our project website: https://dongjh20.github.io/REACT-website.

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