This paper demonstrates the capabilities of three-dimensional (3D) LiDAR scanners in supporting a safe distance maintenance functionality in human–robot collaborative applications. The use of such sensors is severely under-utilised in collaborative work with heavy-duty robots. However, even with a relatively modest proprietary 3D sensor prototype, a respectable level of safety has been achieved, which should encourage the development of such applications in the future. Its associated intelligent control system (ICS) is presented, as well as the sensor’s technical characteristics. It acquires the positions of the robot and the human periodically, predicts their positions in the near future optionally, and adjusts the robot’s speed to keep its distance from the human above the protective separation distance. The main novelty is the possibility to load an instance of the robot programme into the ICS, which then precomputes the future position and pose of the robot. Higher accuracy and safety are provided, in comparison to traditional predictions from known real-time and near-past positions and poses. The use of a 3D LiDAR scanner in a speed and separation monitoring application and, particularly, its specific placing, are also innovative and advantageous. The system was validated by analysing videos taken by the reference validation camera visually, which confirmed its safe operation in reasonably limited ranges of robot and human speeds.