This study is based on new requirements of an advance microproduction system in nearly future where all necessary production and assembly processes are connected in a very flexible way using autonomous mobile transport and handling robots. One main problem herein is the coordinated navigation of the multi-robot system during their transportation tasks. The robots have to follow previously planned paths while avoiding collisions with other robots and also human workers moving around. Moreover, problem-specific constraints for a defined microproduction system like limitations of the velocity and accelerations of the robots have to be fulfilled. This study focuses on a collaborative, model-predictive control approach to solve the collision avoidance and path following problem of the mobile robots in parallel. In addition, the model-predictive approach also offers the possibility to guarantee the fulfillment of the velocity and acceleration constraints of the robots.