Automated Guided Vehicles (AGVs) are widely adopted in various industries due to their efficiency and adaptability. However, safely deploying AGVs in dynamic environments remains a significant challenge. This paper introduces an online trajectory optimization framework, the Fast Safe Rectangular Corridor (FSRC), designed for AGVs in obstacle-rich settings. The primary challenge is efficiently planning trajectories that prioritize safety and collision avoidance. To tackle this challenge, the FSRC algorithm constructs convex regions, represented as rectangular corridors, to address obstacle avoidance constraints within an optimal control problem. This conversion from non-convex to box constraints improves the collision avoidance efficiency and quality. Additionally, the Modified Visibility Graph algorithm speeds up path planning, and a boundary discretization strategy expedites FSRC construction. The framework also includes a dynamic obstacle avoidance strategy for real-time adaptability. Our framework's effectiveness and superiority have been demonstrated in experiments, particularly in computational efficiency (see Fig. \ref{fig:case1} and \ref{fig:case23}). Compared to state-of-the-art frameworks, our trajectory planning framework significantly enhances computational efficiency, ranging from 1 to 2 orders of magnitude (see Table \ref{tab:res}). Notably, the FSRC algorithm outperforms other safe convex corridor-based methods, substantially improving computational efficiency by 1 to 2 orders of magnitude (see Table \ref{tab:FRSC}).

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