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This study introduces a novel robust finite-time adaptive sliding mode control (FTSMC) strategy, emphasizing its contributions to the synchronized deployment of hydraulically actuated multi-arm systems in confined environments, such as coal bunker cleaning. Key innovations include the integration of adaptive sliding mode control with guaranteed finite-time convergence, a distributed leader–follower framework, and a graph-theoretical communication topology for localized interactions. Specifically, we developed a dynamic model for a multi-agent system comprising one leader and multiple followers, incorporating nonlinear dynamics and unknown external disturbances. The proposed controller ensures rapid finite-time convergence of tracking errors while maintaining robustness against parameter uncertainties, frictional forces, and external perturbations. The theoretical analysis, based on Lyapunov stability, rigorously proves the boundedness and convergence of all system states. Simulation results on a three-arm robotic platform validate the method’s superiority, demonstrating higher tracking accuracy, faster convergence, and stronger disturbance rejection compared with baseline controllers, including SMC, ETASMC, PID, Fixed-Time Consensus Control (FTCC), Disturbance Observer-Based Control (DOBC), and Adaptive Sliding Mode Control (ASMC). This research provides a practical and scalable solution for multi-arm coordination in unstructured environments, significantly advancing the autonomy and reliability of industrial robotic systems.