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The use of multiple robots to manufacture composite components represents a critical development direction for fiber placement systems (FPSs). In multi-robotic fiber placement systems (MRFPSs) with heterogeneous mechanical structures, robots collaborate to perform fiber placement tasks. Consequently, robot synchronization emerges as a primary factor in determining the performance of the fiber placement process. However, the difficulty in establishing accurate system models and the presence of disturbances are two significant challenges to achieving precise robot synchronization. Additionally, the system is expected to exhibit desirable dynamic characteristics, such as finite-time error convergence. To address these issues and requirements, we propose a novel adaptive finite-time synchronization control (AFSC) algorithm for the system. Specifically, a finite-time sliding mode observer is developed to handle kinematic uncertainty. A novel fast non-singular terminal sliding mode (FNTSM) manifold is constructed in the AFSC algorithm. Moreover, the control algorithm integrates an adaptive law to handle dynamic uncertainty and an adaptive term to counteract disturbances. Performance analysis demonstrates that the AFSC ensures that the coupled, synchronization, and tracking errors converge to zero within finite time. Furthermore, simulations and experiments are conducted to validate the effectiveness of the AFSC algorithm.