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In this study, the theoretical analysis and controller design are developed for a generalized multi-robot system. The derived formulations are not restricted to a specific number of robots and can be naturally extended to larger formations, provided that the underlying communication topology satisfies the connectivity condition. For experimental validation, the main evaluations in the paper are conducted using three physical robots. This configuration is chosen to balance system stability, experimental reproducibility, and hardware availability, while enabling fair and repeatable performance comparison. A three-robot formation already captures the essential coupling characteristics of formation control and is sufficient to verify the proposed method in terms of tracking accuracy and formation consistency. To further illustrate the scalability of the proposed framework, supplementary demonstrations with five robots are provided in both simulation and real-world environments. It should be noted that the environment perception module of the system, including LiDAR data partitioning, segmentation, and fusion strategies, is designed based on a predefined formation geometry and scale. Extending the system to different formation sizes under full obstacle-avoidance conditions would therefore require corresponding adjustments to the perception and fusion modules. Considering system integration complexity and experimental fairness, the five-robot demonstrations are conducted without obstacle avoidance and are intended solely to illustrate feasibility under increased robot numbers, rather than to serve as part of the main performance evaluation.