Since 2016, extensive research has been conducted on highly automated driving in real road traffic. The projects Safety Control Center and MUTIG-VORAN have established a comprehensive infrastructure, including automated research vehicles, a teleoperation control center, V2X‑enabled traffic lights, and a private test site. The presentation outlines hardware and software across the AD function chain, from mapping and localization to decision-making and control. Industrial mathematics supports robust, scalable algorithms. Video sequences provide practical insights into challenges and solutions for safe and explainable autonomous systems.

• Understanding how industrial mathematics enables robust algorithms for automated driving.
• Insights into mapping, localization, perception, planning, and decision-making pipelines.
• How research vehicles, teleoperation, and V2X infrastructure support real-world validation.
• Methods for optimizing trajectories and verifying safety‑critical decisions mathematically.
• Practical challenges and solutions demonstrated through real‑operation video sequences.