A Unified Calibration Framework for High-Accuracy Articulated Robot Kinematics

TL;DR

The paper introduces a unified, static calibration framework for articulated robots that jointly identifies geometric offsets, compliance, thermal deformation, and gear-transmission errors by augmenting the robot's kinematic chain with virtual joints. It employs differentiable submodels and a regularized Gauss-Newton optimization to fit end-effector measurements collected in a single experiment, achieving high accuracy and robustness validated through five-fold temporal cross-validation and repeatability studies. The approach yields a mean end-effector error of approximately $26.8\, ext{m}$ and a maximum error of about $97.4\,\text{m}$ on a KUKA KR30-3, significantly improving over purely geometric calibration, and demonstrates the practical viability of jointly estimating multiple non-geometric effects. The work also analyzes gradient conditioning and submodel interactions, discusses limitations (e.g., backlash and time-varying thermal behavior), and argues for the method’s applicability to other open-chain robot designs.

Abstract

Researchers have identified various sources of tool positioning errors for articulated industrial robots and have proposed dedicated compensation strategies. However, these typically require individual, specialized experiments with separate models and identification procedures. This article presents a unified approach to the static calibration of industrial robots that identifies a robot model, including geometric and non-geometric effects (compliant bending, thermal deformation, gear transmission errors), using only a single, straightforward experiment for data collection. The model augments the kinematic chain with virtual joints for each modeled effect and realizes the identification using Gauss-Newton optimization with analytic gradients. Fisher information spectra show that the estimation is well-conditioned and the parameterization near-minimal, whereas systematic temporal cross-validation and model ablations demonstrate robustness of the model identification. The resulting model is very accurate and its identification robust, achieving a mean position error of 26.8 $μm$ on a KUKA KR30 industrial robot compared to 102.3 $μm$ for purely geometric calibration.

Figures (11)

• Figure 1: Visualization of the joint modeling: unaugmented (left) versus augmented with virtual joints (right).
• Figure 2: Lab setup: payload and reflector on the tool (left) and laser tracker (right).
• Figure 3: Histogram of the variation in laser tracker measurements. The dashed line indicates the applied threshold, effectively removing roughly 5.2% of data points.
• Figure 4: Dataset filtering to ensure a minimum amount of data per joint model support point.
• Figure 5: Ambient temperature during the experiment. Note that the discrete levels are due to the inherent resolution of the temperature sensor used.