Unmanned Aircraft Systems (UAS) provide the platform of many applications such as efficient package delivery, monitoring, surveillance, search and rescue, and more. As the density of UAS deployed in urban areas for delivery and monitoring operations is expected to increase in the near future, it becomes critical to design an efficient collision-free UAS path planning system to be used by a centralized traffic manager. In this article we propose an on-demand, scalable, collision-free trajectory planning mechanism that processes routing requests in batches, with the objective of improving the ratio of successfully admitted requests. The planner transforms the input map to a unit graph discretized on the safety distance and computes trajectories using search in the derived space-time graph. The planner generates trajectories that are by design conflict-free and deadlock-free. The performance of our algorithm is analyzed with simulations. We measure admission ratio, the delay overhead vs. optimal path delay, the algorithm running time, and we compare results with prior work. The proposed batch planner yields better admission ratio and delay overhead in low and medium density scenarios. In all scenarios it has a running time that is 4-7 times shorter, showing its scalability in practical situations.