The increasing demand for flexible automation has accelerated the adoption of heterogeneous automated guided vehicles (AGVs). This work investigates a new scheduling problem in a material transportation system consisting of attachable heterogeneous AGVs, including carriers and shuttles, that flexibly attach and detach for cooperative task execution. While such collaboration enhances operational efficiency, the attachment-induced synchronization renders the system highly coupled and susceptible to deadlocks. To address this, we propose a Petri net (PN)-based deadlock-free scheduling framework integrated into an adaptive large neighborhood search (ALNS) algorithm. The PN is introduced to map candidate solutions from static permutations into dynamic collaborative processes, enabling performance evaluation via state evolution and proactive deadlock prevention through structural analysis. Extensive experiments on real-world and synthetic instances demonstrate that the proposed framework significantly improves computational efficiency, with the developed ALNS outperforming the current on-site policy, exact solvers, and state-of-the-art metaheuristics. Finally, sensitivity analysis yields managerial insights for optimal fleet sizing.