The positional accuracy and orientation accuracy of industrial robots are crucial technical indicators for determining their applicability in industrial scenarios. However, the majority of current calibration methods for industrial robots only consider positional errors, neglecting the significance of orientation accuracy. This paper presents a more accurate error model and parameter calibration method for industrial robots based on six degrees-of-freedom position and orientation to identify the actual structural parameters. Firstly, based on the modified Denavit–Hartenberg parameters, the transformation errors of the tool coordinate system and measurement coordinate frame were introduced to establish a geometric parameter error model with positional and orientation accuracy as the optimization objectives. Secondly, to address the drawback of falling into local optima when identifying geometric parameters simultaneously, a geometric parameter cross-identification method based on the Levenberg–Marquardt algorithm is proposed. Lastly, the linear relationship between the parameters was analyzed, and a scheme for not calibrating some geometric parameters under specific conditions was given. Simulation results demonstrated that, under the premise of existing transformation errors, the proposed geometric parameter error model can accurately identify the actual structural parameters of industrial robots. After calibration, the positional error at the robot’s flange end decreased from 1.9536 mm to 0.0122 mm, and the orientation error decreased from 1.46 × 10⁻² rad to 1.31 × 10⁻⁴ rad. Furthermore, compared to identifying the geometric parameters simultaneously, the proposed cross-identification method has a wider convergence range.

In this study, a static railway track smoothness detection system based on laser reference, which can measure various track smoothness parameters by using multiple sensors, is proposed. Furthermore, in order to improve the measurement accuracy and stability of the system, this paper also conducted three key analyses based on the static track measurement system. By using a liquid double-wedge automatic compensation device to compensate the horizontal angle of the beam, a mathematical model of liquid double-wedge automatic compensation was established. Then, by using an optical ring grating system to ring-grate and characterize the laser spot, the collimation efficiency of the system was improved when measuring at long distances. For the special ring grating spot image, an adaptive image processing algorithm was proposed, which can achieve sub-pixel-level positioning accuracy. This study also conducted a field measurement experiment, comparing the experimental data obtained via the static track measurement system with the results of existing track measurement products, and verifying that the static track measurement system has high measurement accuracy and stability.