MUKCa: Accurate and Affordable Cobot Calibration Without External Measurement Devices

TL;DR

The paper addresses the challenge of achieving accurate yet affordable cobot kinematics by introducing MUKCa, a minimalist calibration framework that uses a 3D-printed two-socket tool and a parameter-optimization routine over $\Theta \in \mathbb{R}^{6m}$ to minimize nullspace inconsistency while preserving the socket distance $d$. It combines a forward-kinematics model compatible with URDF representations and data collected from two socket configurations, solved with CasADi and IPOPT, to yield submillimeter accuracy on Franka and KUKA robots. The authors validate the approach on three platforms and demonstrate improved performance in high-precision insertion and drawing tasks; Kinova, with more pronounced joint backlash, shows more modest gains. The method eliminates reliance on expensive external measurement devices, enabling practical, accessible precision calibration for affordable cobots and broader applicability in industrial and research contexts.

Abstract

To increase the reliability of collaborative robots in performing daily tasks, we require them to be accurate and not only repeatable. However, having a calibrated kinematics model is regrettably a luxury, as available calibration tools are usually more expensive than the robots themselves. With this work, we aim to contribute to the democratization of cobots calibration by providing an inexpensive yet highly effective alternative to existing tools. The proposed minimalist calibration routine relies on a 3D-printable tool as the only physical aid to the calibration process. This two-socket spherical-joint tool kinematically constrains the robot at the end effector while collecting the training set. An optimization routine updates the nominal model to ensure a consistent prediction for each socket and the undistorted mean distance between them. We validated the algorithm on three robotic platforms: Franka, Kuka, and Kinova Cobots. The calibrated models reduce the mean absolute error from the order of 10 mm to 0.2 mm for both Franka and Kuka robots. We provide two additional experimental campaigns with the Franka Robot to render the improvements more tangible. First, we implement Cartesian control with and without the calibrated model and use it to perform a standard peg-in-the-hole task with a tolerance of 0.4 mm between the peg and the hole. Second, we perform a repeated drawing task combining Cartesian control with learning from demonstration. Both tasks consistently failed when the model was not calibrated, while they consistently succeeded after calibration.

Figures (5)

• Figure 1: Calibration scheme: the optimization minimizes inconsistency and distortion of the predicted ball position attached at the end-effector.
• Figure 2: Robots that were calibrated with the MUKCa tool.
• Figure 6: Changing of converging error when training on multiple tool positions. The overlay shows the prediction after training for the tool. The hashed bar implies that the data for that tool was observed during training.
• Figure 7: Insertion task with the nominal model or calibrated model. After calibration, the robot successfully inserts the peg (10m m) in the hole (10.4m m) despite the changes in the initial starting joint configuration. The nominal model even fails with a hole of 16m m.
• Figure 8: Accuracy of learned drawing motion. By executing the Cartesian motion with different joint configurations, the calibrated models perfectly trace the previous iterations. The nominal model clearly fails on the task.