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This paper presents a novel hybrid caging-based approach for cooperative object transport using only two omnidirectional mobile robots equipped with soft grippers inspired by the Fin-Ray effect. The proposed system integrates a Leader-Follower feedback controller that regulates distance and angle between robots to maintain the object closure condition throughout the transport. The soft grippers enhance adaptability to object contours and allow stable manipulation with fewer robots. Extensive real-world experiments were conducted with objects of various shapes, demonstrating the robustness and effectiveness of the proposed strategy. 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