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A self-calibration method utilizing spherical constraints is proposed for calibration of robot end-effectors. The method establishes a mathematical model to account for both the geometric errors of the robot and the deformation errors of the end-effector. A nonlinear least-squares parameter identification technique based on spherical constraints is employed to achieve autonomous calibration of the end-effector. Contrasted with methodologies relying on point plane or distance constraints, this novel technique delivers superior positioning accuracy, streamlined operational procedures and enhanced efficiency. Both simulation and experimental validation confirm that the self-calibration method using spherical constraints improves the positioning accuracy of the robot end-effector from 3 mm to 0.3 mm, showing the effectiveness of the method.

To improve the machining accuracy of free-form surface parts, a coarse-to-fine free-form surface machining error decomposition and compensation method is proposed in this paper. First, the machining error was coarsely decomposed using variational mode decomposition (VMD), and the correlation coefficients between the intrinsic mode function (IMF) and the machining error were obtained to filter out the IMF components that were larger than the thresholding value of the correlation coefficients, which was the coarse systematic error. Second, the coarse systematic errors were finely decomposed using empirical mode decomposition (EMD), which still filters out the IMF components that are larger than the thresholding value of the set correlation coefficient based on the correlation coefficient. Then, the wavelet thresholding method was utilized to finely decompose all the IMF components whose correlation coefficients in the first two decomposition processes were smaller than the threshold value of the correlation coefficient set. The decomposed residual systematic errors were reconstructed with the IMF components screened in the EMD fine decomposition, which gave the fine systematic error. Finally, the machining surface was reconstructed according to the fine systematic error, and its corresponding toolpath was generated to compensate for the machining error without moving the part. The simulation and analysis results of the design show that the method has a more ideal processing error decomposition ability and can decompose the systematic error contained in the processing error in a more complete way. The results of actual machining experiments show that, after using the method proposed in this paper to compensate for the machining error, the maximum absolute machining error decreased from 0.0580 mm to 0.0159 mm, which was a 72.5% reduction, and the average absolute machining error decreased from 0.0472 mm to 0.0059 mm, which was an 87.5% reduction. It was shown that the method was effective and feasible for free-form surface part machining error compensation.

In order to solve the problem of the low end positioning accuracy of large hydraulic rock drilling robotic arms due to machining error and the working environment, this paper proposes an end positioning error compensation method based on an Improved Secretary Bird Optimization Algorithm (ISBOA) optimized Back Propagation (BP) neural network. Firstly, the good point set strategy is used to initialize the secretary bird population position to make the initial population distribution more uniform and accelerate the convergence speed of the algorithm. Then, the ISBOA is used to optimize the initial weights and biases of the BP neural network, which effectively overcomes the defect of the BP neural network falling into a local optimum. Finally, by establishing the mapping relationship between the joint value of the robot arm and the end positioning error, the error compensation is realized to improve the positioning accuracy of the rock drilling robot arm. The experimental results show that the average positioning error of the rock drilling robotic arm is reduced from 187.972 mm to 28.317 mm, and the positioning accuracy is improved by 84.94%, which meets the engineering requirements.

In order to solve the problem of insufficient end positioning accuracy due to factors such as gravity and material strength during the inverse solution process of a large hydraulic robotic arm, this paper proposes an inverse solution algorithm based on an adaptive spider wasp optimization (ASWO) optimized back propagation (BP) neural network. Firstly, the adaptability of the SWO algorithm is enhanced by analyzing the phase change in population fitness and dynamically adjusting the trade-off rate, crossover rate, and population size in real time. Then, the ASWO algorithm is used to optimize the initial weights and biases of the BP neural network, effectively addressing the problem of the BP neural network falling into local optima. Finally, a neural network mapping relationship between the actual position of the robotic arm’s end-effector and the corresponding joint values is established to reduce the influence of forward kinematic errors on the accuracy of the inverse solution. Experimental results show that the average positioning error of the robotic arm in the XYZ direction is reduced from (91.3, 87.38, 117.31) mm to (18.16, 24.67, 27.21) mm, significantly improving positioning accuracy by 80.11%, 71.78%, and 76.81%, meeting project requirements.

Deadbeat predictive current control (DPCC) has excellent dynamics and can achieve current control with less computational effort. However, its control performance relies on the precision of the parameters of the motor. Current static error will be generated and control performance will be decreased when the predictive model parameters do not correspond to the practical parameters of the motor. In this article, a weakened integral sliding mode compensation method is proposed which converts the current error into a voltage compensation term and adds it to the prediction control output to effectively compensate for the steady-state error. In addition, a boundary layer is introduced to weaken the integral so as to solve the problems of integral saturation and overshoot caused by the introduction of the integral term when the error is large. Moreover, weight factors are introduced to optimize the feedback current, which enhances the robustness of the system. In the end, the effectiveness of this method is verified via simulation and experimental results.

The CFETR multi-purpose overload robot (CMOR) is a key subsystem of the remote handling system of the China fusion engineering test reactor (CFETR). This paper first establishes the kinematic and dynamic models of CMOR and analyzes the working process in the vacuum chamber. Based on the uncertainty of rigid-flexible coupling, a CMOR adaptive robust sliding mode controller (ARSMC) is designed based on the Hamilton-Jacobi equation to enhance the robustness of the control system. In addition, to compensate the influence of non-geometric factors on position accuracy, an error compensation method is designed. Based on the matrix differentiation method, the CMOR coupling parameter errors are decoupled, and then the gridded workspace principle is used to identify the parameter errors and improve the motion control accuracy. Finally, the CMOR rigid-flexible coupling simulation system is established by ADAMS-MATLAB/Simulink to analyze the dynamic control effect of ARSMC. The simulation results show that the CMOR end position error exceeds 0.1 m for single joint motion. The average value of CMOR end position error is less than 0.025 m after compensation, and the absolute error value is reduced by 4 times, improves the dynamic control accuracy of CMOR.

The sight of the high-orbit thermal infrared staring camera is concentrated and sensitive to temperature changes, and therefore its image point positioning is key to ensuring the geometric quality of the thermal infrared staring image and eliminating the errors of the imaging system in orbit. According to the geometric imaging characteristics of the high-orbit thermal infrared staring camera, internal and external positioning compensation models are proposed in this paper based on the two-dimensional pointing angle of temperature change, and four kinds of experimental schemes of image point positioning compensation are designed. The experimental results show that the method proposed in this paper has a good compensation effect on the image point positioning error.

The hybrid kinematic mechanism (HKM) as an alternative remote handling subsystem of the Demonstration Fusion Power Plant (DEMO) breeding blanket (BB) is undergoing extensive theoretical analysis and feasibility verification. In this paper, the forward and inverse kinematic models of the HKM are derived by combining the Newtonian iterative method and the analytical method. Cartesian space trajectory planning is designed based on the trajectories of the HKM lifting of inboard and outboard BBs. The continuous smooth inverse kinematic solutions in the HKM joint space are obtained based on the polynomial interpolation method. For the characteristics of the HKM piston thread driving, the end-effector position error caused by the degradation of the spherical joint into a universal joint is analyzed and calculated. During the lifting of the left inboard BB, there is a maximum absolute error ∆P = 3.1 mm, and as the error continues to expand to the bottom of the BB it causes a risk of collision. Combining the overall effects of driving control, rigid–flexible coupling, etc., on position accuracy, an open-loop variable parameter error compensation plan based on the Levenberg–Marquardt (LM) nonlinear damping least-squares algorithm is proposed and validated in this paper. The simulation results show that the maximum absolute error after compensation is less than 1 mm as the mesh density increases, and the absolute position accuracy can be further improved by local mesh encryption. This study verifies the feasibility of the HKM as a BB remote handling subsystem and provides an option for high-precision control of the HKM.

Intelligent mining is the demand and inevitable development direction of China’s coal industry, and the shearer attitude based on the 3D spatial scale is the essential basic information for realizing intelligent mining at the fully mechanized mining face. The traditional shearer attitude monitoring technology cannot meet the accuracy requirements of attitude sensing of mining equipment at an intelligent working face. In this paper, based on the basic principle of strapdown inertial navigation system (SINS), a real-time solution algorithm for shearer attitude is constructed, and the specific process of SINS coarse alignment and fine alignment is studied. The main error terms affecting the accuracy of SINS are analyzed, and the initial alignment error, installation deviation angle error, and vibration effect error are compensated and analyzed through simulation one by one. According to the working characteristics of the shearer, the coning error and sculling error of the shearer’s SINS are compensated and analyzed through simulation. This paper provides a complete set of theories and methods for improvement of the accuracy of the shearer attitude sensing in underground operation; simulation results also verify that the theories and methods can significantly improve the perception accuracy which can provide theoretical and technical reference for the production state prediction of fully mechanized mining face and intelligent control of underground mining equipment.

The measurement of Earth’s gravitational field is important in geophysics, geodynamics, geodesy, oceanography, and space science. The ocean covers 71% of the earth’s surface; therefore, measuring the ocean’s gravitational field is crucial. Compared with shipborne gravimetry, underwater gravimetry near the seafloor is closer to gravity sources and can obtain short-wavelength gravity information that is useful for small-scale deposit detection and seawater intrusion monitoring. This article focuses on gravimetric errors caused by the poor dynamics of the carrier; an error compensation method for underwater gravimetry based on correlation analysis is proposed. By analyzing the error sources that affect the dynamics of the carrier, the relationship between the gravimetry error and impact factors related to the dynamics was established, and the model’s parameters were estimated by the least-squares fitting method. The experimental data show that this method can effectively compensate for gravimetric errors caused by carrier dynamics and provide the theoretical basis and algorithm model for underwater gravimetry in the bottom-tracking mode.

Flexible-joint manipulators (FJMs) have been widely used in the fields of industry, agriculture, medical service, aerospace, etc. However, the FJMs in practical applications inevitably encounter various uncertainties including matched and mismatched disturbances. In this paper, we consider the high precision tracking control problem of FJMs in the presence of unknown lumped matched and mismatched disturbances. An efficient model-assisted composite control approach is proposed by integrating two reduced-order extended state observers (RESOs), a second-order command filtered backstepping (SCFB) technique and an error compensation dynamic system. Unlike some existing methods, the RESOs constructed with partial known model information are capable of estimating and compensating the matched and mismatched disturbances simultaneously. In addition, by employing the SCFB with an error compensation system, the proposed approach can not only overcome the problem of “explosion of complexity” inherent in backstepping, but also reduce the filtering errors arising from the command filters. The stability of the resulting control system and the convergence of error signals are guaranteed by Lyapunov stability theory. Comparative simulations are conducted for a single-link FJM with both matched and mismatched disturbances, and the results show that the proposed approach achieves a better tracking performance, i.e., compared with conventional backstepping method and adaptive fuzzy command filtered control method, the tracking accuracy is improved by 99.5% and 99.2%, respectively.

This paper presents a novel method for inner profile measurement and geometric parameter evaluation, such as the radius of the bottom, steepness and straightness of the steep sidewall of a high aspect ratio aspheric workpiece, by utilizing a two-probe measuring system, which includes a lateral displacement gauge for the inner steep sidewall profile measurement and an axial displacement gauge for the inner deep underside profile measurement. To qualify the measurement accuracy, the systematic errors associated with the measurement procedure, including the miscalibration, misalignment and the roundness error of the gauge probes, as well as the slide motion error of the four-axis motion platform, are all evaluated and separated from the measurement results. A point cloud registration algorithm is employed to stitch the evaluated inner sidewall profile and the inner underside profile to form an entire inner profile of the workpiece. To verify the performance of the newly proposed method, the inner profile of a high aspect ratio aspheric workpiece, which has a tapered cone shape with a maximum inner radius of 40 mm, a maximum inner depth of 140 mm and a steep sidewall angle approaching 85°, is measured in experiments. The measurement result is compared with that of a coordinate measuring machine (CMM), and the comparison verifies the feasibility of the proposed measurement system.

Six degree-of-freedom (6-DOF) robotic manipulators have been increasingly adopted in various applications in industries due to various advantages, such as large operation space, more degrees of freedom, low cost, easy placement, and convenient programming. However, the robotic manipulator has the problem of insufficient stiffness due to the series structures, which will cause motion errors of the manipulator end. In this paper, taking a 6-DOF robotic manipulator as an example, forward and inverse kinematics models are established, and a new modeling method for the joint angle and space stiffness of the end of the manipulator is proposed, which can establish the composite stiffness model of joint link stiffness and joint stiffness. An error compensation model is subsequently established. The experimental results indicate that the proposed error compensation method can effectively reduce the end motion error of the robotic manipulator, and hence, the working performance and accuracy of the manipulator can be improved. The proposed research is helpful for extending the application of robotic manipulators in precision machining and measurement.

Robot dynamics and its parameter identification are of great significance to the realization of optimal control and human–machine interaction. The objective of this research is to address the shortcomings of establishing and identifying the self-developed six-degree-of-freedom (6-DoF) collaborative robot dynamics, which leads to a large error in the predicted torque of the proposed robot. A long short-term memory (LSTM) in an optimized recurrent neural network (RNN) is proposed to compensate the dynamic model of the proposed 6-DoF collaborative robot based on the consideration of gravity, Coriolis force, inertial force, and friction force. The analysis and experimental findings provide promising results. The compensated collaborative robot dynamic model based on LSTM in an optimized RNN displays a good prediction on the actual torque, and the root-mean-square (RMS) error between predicted and actual torques are reduced by 61.8% to 78.9% compared to the traditional dynamic model. Results of the experimental applications demonstrate the validity of the proposed systematic error compensation strategy.

Currently, most computer numerical control (CNC) controllers lack the function needed to compensate machining errors for free-form surfaces. The objective of this research was to enhance the accuracy and precision of the machined free-form surfaces of a workpiece using the mirror compensation method with the on-measurement data. By mirroring the points measured after semi-finishing, a new free-form surface for finishing machining can be automatically reconstructed. The surface can then be used to generate the cutting tool path to reduce the errors during finishing machining. In this research, three different types of surfaces were used for evaluating the proposed method. The results show that the proposed method reduced the standard deviations of the three surface geometries by 61%, 61%, and 32%, respectively. We also evaluated the tool radius modification method commonly used in the industry for error compensation and found that there is no substantial reduction on standard deviation. Therefore, the effectiveness of the error compensation method proposed in this research is evident.

It is well known that most of the industrial robots have excellent repeatability in positioning. However, the absolute position errors of industrial robots are relatively poor, and in some cases the error may reach even several millimeters, which make it difficult to apply the robot system to vehicle assembly lines that need small position errors. In this paper, we have studied a method to reduce the absolute position error of robots using machine vision and neural network. The position/orientation of robot tool-end is compensated using a vision-based approach combined with a neural network, where a novel indirect calibration approach is presented in order to gather information for training the neural network. In the simulation, the proposed compensation algorithm was found to reduce the positional error to 98%. On average, the absolute position error was 0.029 mm. The application of the proposed algorithm in the actual robot experiment reduced the error to 50.3%, averaging 1.79 mm.

In frequency-sweep polarization-modulation ranging, distance is determined by the frequency of modulated waves and the corresponding wavelength multiple when emitted and returned waves are in phase. However, measurement of the frequency and the wavelength multiple is affected by thermally induced phase delay of the polarized wave. In this article we systematically discuss the principle of the ranging method and analyze the influences of thermally induced phase delay. New approaches to measurement are proposed to eliminate the impact on frequency and the wavelength multiple. Theoretical analysis and experimental results proved the efficiency and applicability of the methods.

In gear measuring machines (GMMs), the tested gear is mounted on a mandrel, which is pivoted at both ends by two centers in a vertical arrangement. The upper center is fixed and the lower center is driven by the spindle of rotation. The coaxiality error between the central line of the mandrel and the spindle average line of a GMM always exists in terms of the offset and angle measured in one plane. Such a coaxiality error would cause an angular indexing error of tested gear resulting in measurement error. This phenomenon has rarely been investigated. In this paper, a GMM is taken as an example and its coaxiality error of the mandrel and spindle error of the rotary stage are measured. The difference of rotated angles between the mandrel and spindle is theoretically analyzed by derived formulae. Calibrated by a precision polygon and an autocollimator, the predicted angular index error of the mandrel was consistent with experimental results. Through the experimental verification, it was found that, when the coaxial deviation between the two centers was 10 μm and the lower center tip’s radial motion error was 1.6 μm, the angular indexing deviation of the mandrel was ±5″. If the errors were compensated according to the analyzed model, the residual error was reduced to ±2″. A significant improvement in the angular positioning accuracy of the GMM can be achieved.

Structural deformations are one of the most significant factors that affects machine tool (MT) positioning accuracy. These induced errors are complex for accurate representation by a model, nevertheless they need to be evaluated and predicted in order to increase the machining performance. This paper presents a novel approach to calibrate a machine tool in real-time, analyzing the thermo-mechanical errors through fiber Bragg grating (FBG) sensors embedded in the MT frame. The proposed configuration consists of an adaptronic structure of passive materials, Carbon Fiber Reinforced Polymers (CFRP), equipped with FBG sensors that are able to measure in real-time the deformed conditions of the frame. By using a proper thermo-mechanical kinematic model, the displacement of the end effector may be predicted and corrected when it is subjected to external undesired factors. By starting from a set of Finite Element (FE) simulations to develop a model able to describe the MT structure stresses, a prototype has been fabricated and tested. The aim of this study was to compare the numerical model with the experimental tests using FBG sensors. The experimental campaign has been performed by varying the structure temperature over time and measuring the tool tip point (TTP) positions. The obtained results showed a substantial matching between the real and the predicted position of the TTP, thereby confirming the effectiveness of the proposed system.