The current trajectory planning methods for multi‐robot systems face challenges due to high computational burden and inadequate adaptability in complex constrained environments, obstructing efficiency improvements in production and logistics. This article presents an innovative solution by integrating model predictive contouring control (MPCC) and long short‐term memory (LSTM) networks for real‐time trajectory planning of multiple mobile robots. Based on the datasets generated by MPCC, a customized LSTM network is constructed to learn the collaborative planning behavior from these datasets offline, subsequently producing smooth and efficient trajectories online with a low computational burden. Moreover, a hybrid control scheme, incorporating a lidar‐based safety evaluator, avoids unexpected collision risks by switching to MPCC when necessary, ensuring the overall safety and reliability of the multi‐robot system. The proposed hybrid LSTM method is implemented and tested in the robot operating system (ROS) within diverse constrained scenarios. Experimental results demonstrate that the hybrid LSTM method achieves ≈6% enhancements in trajectory productivity and a reduced computational burden of roughly 75% compared to MPCC, thereby providing a promising solution for local multi‐robot trajectory planning in logistics transportation tasks.