Generating a collision-free robot motion is crucial for safe applications in real-world settings. This requires an accurate model of all obstacle shapes within the constrained robot cell, which is particularly challenging and time-consuming. The difficulty is heightened in flexible production lines, where the environment model must be updated each time the robot cell is modified. Furthermore, sensor-based methods often necessitate costly hardware and calibration procedures and can be influenced by environmental factors (e.g., light conditions or reflections). To address these challenges, we present a novel data-driven approach to modeling a cluttered workspace, leveraging solely the robot internal joint encoders to capture exploratory motions. By computing the corresponding swept volume (SV), we generate a (conservative) mesh of the environment that is subsequently used for collision checking within established path planning and control methods. Our method significantly reduces the complexity and cost of classical environment modeling by removing the need for computer-aided design (CAD) files and external sensors. We validate the approach with the KUKA LBR iisy collaborative robot in a pick-and-place scenario. In less than three minutes of exploratory robot motions and less than four additional minutes of computation time, we obtain an accurate model that enables collision-free motions. Our approach is intuitive and easy to use, making it accessible to users without specialized technical knowledge. It is applicable to all types of industrial robots or cobots.