Draping is a process that is used for about 30% of all carbon fibre composite parts to place layers of carbon fiber fabric in a mould. During this process the flat fabric distorts to fit to the shape of the mould. Ensuring the accuracy of the draping in terms of position and fiber orientation and avoiding wrinkles is a challenging task. The DrapeBot project aims at human-robot collaborative draping, where the robot assists during the transport of the large material patches and drapes the areas of low curvature, while the human deals with high-curvature regions. To enable an efficient collaboration DrapeBot will develop a gripper system with integrated instrumentation, AI-driven human perception and task planning models and a low-level control structure. All of these developments aim at a smooth and efficient interaction between the human and the robot. Specific emphasis is put on trust and usability, due to the complexity of the task and the size of the robots that are involved. Two different robotic work-cells will be adapted for the use cases in project and will remain available after the end of the project for dissemination to stakeholders. The use cases in the project include the aerospace, automotive and shipbuilding industry. There are about 4000 companies in Europe that use draping processes and a potential of about 20.000 installations of collaborative robotic draping exists. Beyond this market, DrapeBot will have a wider impact on human-robot collaboration, especially in areas where efficiency of the collaboration is relevant.