## 1 Introduction
Research has shown that if the measurement poses for kinematic calibration are selected based on the criteria for maximizing the observability index, the impact of measurement noise can be reduced and the accuracy of calibration can be improved [24]. However, there are as many as five commonly used observability indices, so which one to choose for calibration of six-hardpoint positioning mechanisms has become another issue that needs to be addressed. [PERSON] et al. [25] proposed a method to calibrate a parallel robot by using a measurement system specially installed on the external fixed frame, and then compared the performance of the first four observability indices. The results show that \(O_{4}\) has relatively good performance. [PERSON] et al. [23] studied the physical meaning and properties of observability indices and carried out mathematical analysis. \(O_{1}\) and \(O_{3}\) were described as relatively good choices. [PERSON] and [PERSON] [26] investigated the performances of the observability indices through the simulation of a 2-DOF planar manipulator. The simulation results revealed that \(O_{5}\) and \(O_{3}\) had good and bad performances, respectively. [PERSON] et al. [27] studied the performances of the observability indices through the calibration of a 2-link planar robot, and \(O_{4}\) is the best observability index. To sum up, there are different viewpoints on the performance of the observability indices at present, and further research is needed. In order to improve the accuracy of the proposed calibration method for six-hardpoint positioning mechanisms, this paper attempts to find the most suitable observability index for this mechanism. Therefore, many simulations of calibration have been conducted for this mechanism, and the performance of the five observability indices have been compared. Finally, the best performance observability index \(O_{1}\) has been obtained. Specific algorithms are required for measurement pose selection based on \(O_{1}\), such as genetic algorithmsand DETMAX. This paper improves the DETMAX algorithm by setting a tabu list in the algorithm, which improves the problem that DETMAX is greatly affected by initial values, and the problem that DETMAX easily converges to the local maximum value. Finally, in order to validate the proposed kinematic calibration method for six-hardpoint positioning mechanisms, an overall evaluation of the method was conducted. Comparing the effectiveness and accuracy of traditional calibration method and the proposed calibration methods, the results show that the proposed method has higher effectiveness and accuracy compared to traditional methods. The main contributions of this paper are as follows: (1) A kinematic calibration method is proposed which selects the optimal measurement poses based on the observability index \(O_{1}\). The method can not only identify and compensate for the kinematic errors of the six-hardpoint positioning mechanism, but can also have higher calibration accuracy than traditional methods. (2) This paper improves the DETMAX algorithm for selecting the optimal measurement pose. Based on the DETMAX algorithm, a tabu list is added, effectively improving its problems of easy convergence to a local optimal solution and being greatly affected by initial values. (3) Through many simulations of calibration, this paper compares the performance of observability indices in the calibration of six-hardpoint positioning mechanisms, and ultimately obtains the best performance indicator. The proposed calibration method is based on this index. The simulation is equivalent to 2000 calibrations, so the conclusions are universal and statistically significant. The content of the rest of this article is arranged as follows: Section 2 introduces the mathematical model and derivation process of the six-hardpoint positioning mechanism. Section 3 introduces observability indices and the algorithm used to select optimal measurement poses.