This study proposes the Density-Weighted Space-Time Rapidly Exploring Random Tree Star (DST-RRT*) algorithm to improve safe navigation of fire-fighting robots in crowded dynamic environments. The algorithm integrates density weighting into the cost function and adopts an adaptive sampling strategy to prioritize less crowded areas. By using space-time transformation, the method converts 2D dynamic path planning into a 3D static problem while incorporating a Gaussian density model to represent obstacle distributions. The proposed DST-RRT* extends the traditional STK-RRT* algorithm by adding density-aware cost functions and implementing a three-region adaptive sampling strategy that balances goal-biased, kinematic, and density-based sampling. Simulation environments with varying obstacle densities from 60 to 140 dynamic obstacles are used to evaluate the algorithm’s performance across multiple metrics including collision avoidance rate, goal achievement rate, path density, and computational efficiency.