The number of applications in which industrial robots share their working environment with people is increasing. Robots appropriate for such applications are equipped with safety systems according to ISO/TS 15066:2016 and are often referred to as collaborative robots (cobots). Due to the nature of human-robot collaboration, the working environment of cobots is subjected to unforeseeable modifications caused by people. Vision systems are often used to increase the adaptability of cobots, but they usually require knowledge of the objects to be manipulated. The application of machine learning techniques can increase the flexibility by enabling the control system of a cobot to continuously learn and adapt to unexpected changes in the working environment. In this paper we address this issue by investigating the use of Reinforcement Learning (RL) to control a cobot to perform pick-and-place tasks. We present the implementation of a control system that can adapt to changes in position and enables a cobot to grasp objects which were not part of the training. Our proposed system uses deep Q-learning to process color and depth images and generates an ϵ-greedy policy to define robot actions. The Q-values are estimated using Convolution Neural Networks (CNNs) based on pre-trained models for feature extraction. To reduce training time, we implement a simulation environment to first train the RL agent, then we apply the resulting system on a real cobot. System performance is compared when using the pre-trained CNN models ResNext, DenseNet, MobileNet, and MNASNet. Simulation and experimental results validate the proposed approach and show that our system reaches a grasping success rate of 89.9% when manipulating a never-seen object operating with the pre-trained CNN model MobileNet.