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.

翻译：研究人员已识别出关节式工业机器人工具定位误差的多种来源，并提出了专门的补偿策略。然而，这些方法通常需要各自独立、专门的实验，并采用单独的模型和辨识流程。本文提出了一种工业机器人静态标定的统一方法，该方法仅通过一次简单直接的实验进行数据采集，即可辨识出包含几何效应与非几何效应（柔性弯曲、热变形、齿轮传动误差）的机器人模型。该模型通过为每种建模效应添加虚拟关节来扩展运动学链，并利用解析梯度的高斯-牛顿优化算法实现参数辨识。费舍尔信息谱表明该估计是良态的且参数化接近最小，而系统性的时间交叉验证与模型消融实验则证明了模型辨识的鲁棒性。所得模型精度极高且辨识过程稳健，在KUKA KR30工业机器人上实现了26.8 $μm$的平均位置误差，而纯几何标定的误差为102.3 $μm$。