In partially automated manufacturing, humans work together with mobile robots. Trajectory prediction, i.e. predicting future positions of human workers, improves collaboration and coexistence between humans and robots on the shop floor. In this paper, we discuss the interrelated research questions of how human motion trajectories can be predicted and how mobile robots such as Autonomous Mobile Robots and Automated Guided Vehicles can take such predictions into account in their pathfinding and navigation. On the robot side, advanced D* pathfinding algorithms allow robots to take dynamic obstacles into account. For trajectory prediction, the position of human workers is determined by an Ultra-Wideband-based Real-Time Locating System. A trajectory prediction framework is introduced to support the implementation and use of pattern- and planning-based trajectory prediction algorithms. The evaluation is based on scenarios from the addressed problem area of manufacturing.