Individualized manufacturing of cars requires kitting: the collection of individual sets of part variants for each car. This challenging logistic task is frequently performed manually by warehouseman. We propose a mobile manipulation robotic system for autonomous kitting, building on the Kuka Miiwa platform which consists of an omnidirectional base, a 7 DoF collaborative iiwa manipulator, cameras, and distance sensors. Software modules for detection and pose estimation of transport boxes, part segmentation in these containers, recognition of part variants, grasp generation, and arm trajectory optimization have been developed and integrated. Our system is designed for collaborative kitting, i.e. some parts are collected by warehouseman while other parts are picked by the robot. To address safe human-robot collaboration, fast arm trajectory replanning considering previously unforeseen obstacles is realized. The developed system was evaluated in the European Robotics Challenge 2, where the Miiwa robot demonstrated autonomous kitting, part variant recognition, and avoidance of unforeseen obstacles.