This study investigates the application of unmanned aerial vehicles (UAVs) in public management, focusing on optimizing path planning to address challenges such as energy consumption, obstacle avoidance, and airspace constraints. As UAVs transition from 'technical tools' to 'governance infrastructure', driven by advancements in low-altitude economy policies and smart city demands, efficient path planning becomes critical. The research proposes an enhanced Rapidly-exploring Random Tree algorithm (dRRT), incorporating four strategies: Target Bias (to accelerate convergence), Dynamic Step Size (to balance exploration and obstacle navigation), Detour Priority (to prioritize horizontal detours over vertical ascents), and B-spline smoothing (to enhance path smoothness). Simulations in a 500 m3 urban environment with randomized buildings demonstrate dRRT's superiority over traditional RRT, A*, and Ant Colony Optimization (ACO). Results show dRRT achieves a 100\% success rate with an average runtime of 0.01468s, shorter path lengths, fewer waypoints, and smoother trajectories (maximum yaw angles <45°). Despite improvements, limitations include increased computational overhead from added mechanisms and potential local optima due to goal biasing. The study highlights dRRT's potential for efficient UAV deployment in public management scenarios like emergency response and traffic monitoring, while underscoring the need for integration with real-time obstacle avoidance frameworks. This work contributes to interdisciplinary advancements in urban governance, robotics, and computational optimization.