Objective  To ensure the high precision of robot operations, it is imperative to calibrate the robot, enhancing its absolute positional accuracy. The most commonly employed method is the distance error model, which requires obtaining distance information between the robot's end-effector and the measurement device. While laser trackers are widely used due to their high accuracy in directly measuring the position information of the end-effector, they are general-purpose and often expensive devices with many features that go unused in the context of robot calibration. To address these concerns, a custom-designed Laser Tracking Interferometer System (LTIS) has been developed for scenarios requiring high accuracy at a lower cost. The LTIS comprises a tracker module and an interferometer module. In this system, a reference point, termed the base point, is essential for measuring absolute distances. All distances measured by the LTIS are referenced to this base point. Consequently, the accuracy of the distance from the LTIS to the base point, known as the Distance of Base Point (DBP), is crucial as it directly influences the overall accuracy of the LTIS. Designing a high-accuracy calibration method for the DBP is essential for achieving precise and cost-effective robot calibration in various applications.

  Methods  The present study introduces a novel method for calibrating the Distance of Base Point (DBP) in a LTIS using a linear constraint approach. As only the DBP is needed in robot calibration, the outgoing light of the laser interferometer is employed as the x-axis to establish the coordinate system (Fig.2). The constraint points utilized for DBP calibration are situated on the line defined by the x-axis. The least square method is then applied to calculate the DBP. The optimal parameters for this calibration method are determined through a combination of theoretical analyses and simulations (Fig.3 and Fig.4). Finally, the proposed method is applied to calibrate the LTIS and obtain its DBP (Fig.5). To validate the calibration result, the DBP of the API radian tracker is calibrated and compared with the normal value (Fig.6).

  Results and Discussions   The number and distribution of constraint points, as well as the layout of the calibration system, can significantly influence the calibration results, as indicated by theoretical analyses and simulations. The analysis results suggest that the constraint points used for calibration should be evenly and equidistantly distributed on the constrained line around the laser tracking system. Furthermore, the constraint points should be dispersed as widely as possible along the constrained line to ensure that the distances l_i measured by the LTIS exhibit noticeable differences, thereby reducing calibration errors. Optimal calibration parameters were determined through simulation experiments and actual experimental conditions. The constraint line was set to 3 400 mm, with 20 constraint points evenly and equidistantly placed on the x-axis, symmetrically positioned around the LTIS.

  Conclusions  In the DBP calibration method for laser tracking interferometry based on the linear constraint approach, all constraint points used for calibration are distributed along a line. The interferometer measures the displacement of the target mirror along the linear direction to obtain the coordinate of the constraint point. Simultaneously, the LTIS measures the change in distance between the target mirror and the base point. The least squares principle is then employed to calculate the DBP. The weighted average DBP in the LTIS is found to be 290.076 4 mm, with a standard deviation of 4.4 μm. To validate this result, the DBP of an API radian laser tracker was calibrated using this method. The measured DBP of the API radian is 154.194 0 mm, with an error of 3 μm compared to the normal value. The API radian, which has an accuracy of 10 μm+5 μm/m in space, demonstrates that the linear constraint approach for calibrating the DBP in the Laser Tracking Interferometer System meets the requirements of robot calibration. This method holds significant importance for the industrial robot industry.