The poor absolute positioning accuracy of industrial robots has limited their application in fields such as aerospace manufacturing. To address this issue, the spatial grid compensation method has been proposed as an effective solution. In this paper, we propose a sampling method based on three-dimensional discrete point space circular fitting for grid points to significantly reduce the sampling workload and improve compensation accuracy compared to traditional joint space grid compensation methods. Additionally, we use the Kriging interpolation algorithm instead of the inverse distance weighting (IDW) algorithm for spatial interpolation prediction of pose error. Based on this, the proposed sampling and interpolation prediction method in this paper was verified on a Comau NJ500–2.7 manipulator equipped with a fiber-laying end effector. The experimental results demonstrate that using our proposed sampling method yields pose data of grid points that have only a small deviation from directly sampled results and are only slightly higher than the robot's repeat positioning accuracy. Moreover, our proposed method can significantly reduce the sampling workload by 60% under the experimental conditions of this study (sampling 10 groups of data within 90 degrees range), with increasing sampling range leading to more obvious efficiency improvements. Finally, we show that compared to the IDW algorithm, the Kriging interpolation algorithm yields better results and improves the mean absolute positioning accuracy of robots after compensation by 30%.

中文翻译：

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基于三维离散点空间圆拟合的机器人关节空间网格误差补偿

工业机器人绝对定位精度较差，限制了其在航空航天制造等领域的应用。针对这一问题，空间网格补偿方法被提出作为一种有效的解决方案。本文提出一种基于三维离散点空间圆形拟合网格点的采样方法，与传统的关节空间网格补偿方法相比，显着减少采样工作量并提高补偿精度。此外，我们使用克里金插值算法代替反距离加权（IDW）算法来进行位姿误差的空间插值预测。基于此，本文提出的采样插值预测方法在配备铺纤末端执行器的柯马NJ500-2.7机械手上进行了验证。实验结果表明，使用我们提出的采样方法产生的网格点位姿数据与直接采样结果只有很小的偏差，并且仅略高于机器人的重复定位精度。此外，我们提出的方法在本研究的实验条件下（在90度范围内采样10组数据）可以显着减少60%的采样工作量，并且随着采样范围的增加，效率的提高更加明显。最后，我们表明，与 IDW 算法相比，Kriging 插值算法产生了更好的结果，并且补偿后机器人的平均绝对定位精度提高了 30%。