This paper demonstrates an autonomous mobile robot that follows a walking user while staying ahead of them. Despite several useful applications for autonomous push-carts, this problem has received much less attention than the easier problem of following from behind. In contrast to previous work, we use multi-modal person detection and a human-motion model that considers obstacles to predict the future path of the user. We implement the system with a modular architecture of obstacle mapper, human tracker, human motion model, robot motion planner and robot motion controller. We report on the performance of the robot in real-world experiments. We believe that approaches to this largely overlooked problem could be useful in real industrial, domestic and entertainment applications in the near future. This paper published at ICRA 2018.