Accurate and affordable cobot calibration without external measurement devices

To reliably perform everyday tasks, collaborative robots must be accurate, not merely repeatable. Unfortunately, precise kinematic calibration often relies on tools that are more expensive than the robots themselves. We address this limitation by proposing a low-cost and effective calibration method aimed at democratizing cobot calibration. Our minimalist approach uses a single 3D-printable two-socket spherical-joint tool to kinematically constrain the robot end effector during data collection. An optimization routine updates the nominal kinematic model to ensure consistent socket predictions while preserving their mean distance. We validate the method on Franka, KUKA, and Kinova cobots, consistently reducing mean absolute errors, for example, from approximately 10 mm to 0.2 mm on Franka robots. To demonstrate practical impact, we further evaluate the calibrated model on a Franka robot in a peg-in-the-hole task with 0.4 mm tolerance and in a repeated drawing task using Cartesian control and learning from demonstration. Both tasks fail without calibration and consistently succeed with the calibrated model. The proposed method enables affordable and practical cobot calibration, providing a foundation for accurate manipulation tasks.