The intricate and multi-stage task in dynamic public spaces like luggage trolley collection in airports presents both a promising opportunity and an ongoing challenge for automated service robots. Previous research has primarily focused on handling a single trolley or individual functional components, creating a gap in providing cost-effective and efficient solutions for practical scenarios. In this paper, we propose a mobile manipulation robot incorporated with an autonomy framework for the collection and transportation of multiple trolleys that can significantly enhance operational efficiency. We address the key challenges in the trolley collection problem through the novel design of the mechanical system and the vision-based control strategy. We design a lightweight manipulator and docking mechanism, optimized for the sequential stacking and transportation of multiple trolleys. Additionally, based on the Control Lyapunov Function and Control Barrier Function, we propose a novel vision-based control with the online Quadratic Programming which significantly improves the accuracy and efficiency of the collection process. The practical application of our system is demonstrated in real world scenarios, where it successfully executes multiple-trolley collection tasks.