Position Error Model Research Articles

Vision-based autonomous robots calibration for large-size workspace using ArUco map and single camera systems

The low positioning accuracy of industrial robots limits their application in industry. Vision-based kinematic calibration, known for its rapid processing and economic efficiency, is an effective solution to enhance this accuracy. However, most of these methods are constrained by the camera's field of view, limiting their effectiveness in large workspaces. This paper proposes a novel calibration framework composed of monocular vision and computer vision techniques using ArUco markers. Firstly, a robot positioning error model was established by considering the kinematic error based on the Modified Denavit-Hartenberg model. Subsequently, a calibrated camera was used to create an ArUco map as an alternative to traditional single calibration targets. The map was constructed by stitching images of ArUco markers with unique identifiers, and its accuracy was enhanced through closed-loop detection and global optimization that minimizes reprojection errors. Then, initial hand-eye parameters were determined, followed by acquiring the robot's end-effector pose through the ArUco map. The Levenberg-Marquardt algorithm was employed for calibration, involving iterative refinement of hand-eye and kinematic parameters. Finally, experimental validation was conducted on the KUKA kr500 industrial robot, with laser tracker measurements as the reference standard. Compared to the traditional checkerboard method, this new approach not only expands the calibration space but also significantly reduces the robot's absolute positioning error, from 1.359 mm to 0.472 mm.

High-precision robotic kinematic parameter identification and positioning error compensation method for industrial robot

Abstract A method based on laser tracing multi-station measurement technology is proposed in this paper. The method identifies the robotic kinematic parameters and compensates for the absolute positioning errors of industrial robots to improve the absolute positioning accuracy further. The position coordinates of industrial robots are typically measured using laser tracking devices. In this study, the measurement accuracy of an industrial robot is further enhanced using laser tracer multi-station measurement technology. Additionally, the least absolute shrinkage and selection operator (LASSO) algorithm was used to identify the robotic kinematic parameters. Compared with the commonly used least squares algorithm, the LASSO algorithm improved the parameter identification accuracy and the compensation effect on absolute positioning errors. A position error model was established based on the parameters of the modified Denavit–Hartenberg model of an industrial robot. Using the LASSO algorithm, the robotic kinematic parameters were accurately identified, and the original data in the controller were replaced to compensate for the geometric errors of the industrial robot. In the compensation experiments, after implementing the geometric error compensation, the average absolute positioning error of the industrial robot decreased by 41.15%, demonstrating a significant improvement in the absolute positioning accuracy.

Research on Position Error Prediction and Compensation of Direct Drive Turntable Based on WOABP Network

A method to identify the position error of direct drive numerical control turntable by measuring current and eccentric load is proposed, and the position error model of direct drive numerical control turntable based on whale Optimized BP (WOABP) neural network is established. The test-bed is built to measure the current, eccentric load and position error. The measured current and eccentric load are trained by WOABP neural network, and the position error of direct drive numerical control turntable is obtained. By comparing the original error, the error obtained by BP neural network and the error obtained by WOABP neural network, the effectiveness of WOABP neural network model is verified. The position error of direct drive numerical control turntable is compensated by the error obtained by the model.

Attitude control of multi-spacecraft systems on SO(3) with stochastic links failure

In this paper, for Multi-Spacecraft System (MSS) with a directed communication topology link and a static virtual leader, a controller is proposed to realize attitude consensus and attitude stabilization with stochastic links failure and actuator saturation. First, an MSS attitude error model suitable for a directed topology link and with a static virtual leader based on SO(3) is derived, which considers that the attitude error on SO(3) cannot be defined based on algebraic subtraction. Then, we design a controller to realize the MSS on SO(3) with attitude consensus and attitude stabilization under stochastic links failure and actuator saturation. Finally, the simulation results of a multi-spacecraft system with stochastic links failure and a static virtual leader spacecraft are demonstrated to illustrate the efficiency of the attitude controller.

A Cooperative Positioning Enhancement for Self-Powered Vehicular Networks With V2I Trustworthy Data Sharing

The emergence of connected vehicles (CV) and cooperative vehicle-infrastructure systems (CVIS) have paved the way for new innovative prospects for improving the safety and efficiency of transportation systems. Unleashing the communication and positioning capabilities of connected vehicles and roadside units’ storage and computing capabilities, the CVIS can enhance the positioning signal coverage and improve the positioning accuracy of the vehicles with low positioning accuracy by sharing the positioning error correction model. In particular, based on the particle swarm optimization algorithm, we first design an improved deep neural network to train the positioning error model. Second, the selection crossover factors of the genetic algorithm are used to optimize the network. Then, based on the consensus algorithms, the positioning error model is shared and stored in the blockchain network to ensure the security of vehicles and roadside units that provide positioning correction information. Finally, the trained network is used to predict and correct the positioning errors of other vehicles with low positioning accuracy. Additionally, the proposed method’s performance and effectiveness in terms of accuracy, timeliness, and security are verified in different scenarios.

A Novel Error Sensitivity Analysis Method for a Parallel Spindle Head

Geometric errors are the main factors affecting the output accuracy of the parallel spindle head, and it is necessary to perform a sensitivity analysis to extract the critical geometric errors. The traditional sensitivity analysis method analyzes the output position and orientation errors independently, defining multiple sensitivity indices and making it difficult to determine critical geometric errors. In this paper, we propose sensitivity indices that can comprehensively consider position and orientation errors. First, the configuration of the hybrid machine tool is introduced, and the TCP position error model is derived. Then, the tool radius and the effective cutting length are introduced, and the sensitivity indices are defined. After that, the sensitivity analysis of the 3-DOF parallel spindle head is performed using the proposed sensitivity indices, and six critical geometric errors are extracted. The machining accuracy of the parallel spindle head can be greatly improved by improving the critical geometric errors. The proposed sensitivity analysis method can provide important guidance for machine tool accuracy design.

The Demand for Satellite Attitude Error for High-Resolution Spaceborne SAR Image Quality

Because of the prominent problem of insufficient index decomposition of satellite-earth integration indicators and attitude control demand analysis for spaceborne SAR, this paper made studies on the effect of attitude measurement error and attitude pointing error for spaceborne SAR images. The attitude error model of azimuth and range antennae was constructed. The quantitative transfer relationships, which contain the attitude measurement error model determined by azimuth Doppler parameters and the attitude pointing error model determined by ambiguity and system sensitivity, were analyzed. Theoretical analysis and simulation results are shown as follows: for the X-band SAR satellite, the attitude measurement error should be better than 0.01° for 0.5 m azimuth resolution, and the attitude pointing error should be better than 0.03°. The research results can provide theoretical support for the error allocation phase of the satellite scheme and the analysis of attitude control requirements.

Trajectory planning method for docking of large aircraft components

PurposeIn the digital assembly system of large aircraft components (LAC), the docking trajectory of LAC is an important factor affecting the docking accuracy and stability of the LAC. The main content of docking trajectory planning is how to move the LAC from the initial posture and position to the target posture and position (TPP). This paper aims to propose a trajectory planning method of LAC based on measured data.Design/methodology/approachFirst, the posture and position error model of the wing is constructed according to the measured data of the measurement points (MPs) and the fork lug joints. Second, the particle swarm optimization algorithm based on the dynamic inertia factor is used to optimize the TPP of the wing. Third, to ensure the efficiency and stability of posture adjustment, the S-shaped curve is used as the motion trajectory of LAC, and the parameters of the trajectory are solved by the generalized multiplier method. Finally, a series of docking experiments are carried out.FindingsDuring the process of posture adjustment, the motion of the numerical control locator (NCL) is stable, and the interaction force between the NCLs is always within a reasonable range. After the docking, the MPs are all within the tolerance range, and the coaxiality error of the fork lug hole is less than 0.2 mm.Originality/valueIn this paper, the measured data rather than the theoretical design model is used to solve the TPP, which improves the docking accuracy of LAC. Experiment results show that the proposed trajectory method can complete the LAC docking effectively and improve the docking accuracy.

Accuracy improvement of a 3D passive laser tracker for the calibration of industrial robots

The laser tracker has been used as the mainstream instrument for the position accuracy calibration of industrial robots for quite a long time. However, due to the complexity of the built-in dual-axis active servo tracking system, its cost is high and the target reflector has to adjust its pose frequently, so it cannot be popularized in the production and application sites of industrial robots. Based on this drawback, a 3D passive laser tracker (3DPLT) with high precision, simple structure, easy operation and low cost is proposed in this paper. Firstly, the overall structure of the system is designed, and its position error model based on the principle of spherical coordinate measurement and vector transfer method is established. Then, the error parameters are identified by experiments to formulate the error compensation model. Finally, the multi-pose and large-range spatial error compensation verification experiments of the system are carried out on a commercial coordinate measuring machine. The results show that the spatial volumetric errors of the 3DPLT can achieve within 40 μm after compensation with a good repeatability of ±4 μm. A comparison contouring test with a commercial ballbar is also carried out to validate its applicability of robot calibration.

Comprehensive Compensation Method for Motion Trajectory Error of End-Effector of Cable-Driven Parallel Mechanism

The accuracy of the end-effector motion trajectory is a critical performance indicator for cable-driven parallel mechanisms. This study aims to address the problem of trajectory error during the end-effector motion in a cable-driven parallel mechanism. It proposes a comprehensive compensation method based on the simultaneous application of the improved sparrow search algorithm and the cable length space error compensation algorithm, leveraging kinematic analysis. To compensate for the motion trajectory error of the end-effector caused by the geometric parameter error, the study establishes the kinematic model of the cable-driven parallel mechanism using the vector method. It creates the end-effector position error model and motion trajectory error model using the differential kinematic theory, analyzes the impact of the geometric parameter error on the motion trajectory error, constructs the kinematic parameter identification matrix, and uses an improved sparrow search algorithm to compensate for the position error of the motion trajectory interpolation point. For the motion trajectory error of the end-effector caused by non-geometric parameter error, the study analyzes the intrinsic correlation between the adjacent position error of the end-effector and the variation of the cable length using the error similarity theory. It then compensates for the position error of the interpolation point of the trajectory using a cable length space interpolation compensation method to enhance the motion trajectory accuracy of the end-effector. The study experimentally verifies the proposed comprehensive compensation method for end-effector motion trajectory error on a 4-cable-driven 2-DOF parallel mechanism, which reduces the motion trajectory error of the end-effector by 75%.

Research on GPS/INS/WIFI Personnel Tight Combination Positioning Method

With the development of current information technology, it has become a common demand to obtain accurate location information quickly. However, in the indoor environment where people generally live, GPS signals are partially occluded, and the INS of inertial navigation system will significantly increase the error due to the integral accumulation error. In view of the problems of poor robustness and low accuracy of the existing loose combination positioning methods, a GPS/INS/WIFI personnel tight combination positioning method was proposed by using the WIFI network signals with wide coverage at present. Firstly, the characteristics of WIFI positioning technology were analyzed, and the INS positioning error model was established. The measurement equation under tight coupling was established by using the pseudo range value of GPS and the RSSI parameters of WIFI system, and the state equation was established by using the INS error model, so as to realize the establishment of the combined GPS/INS/WIFI positioning state space equation. Then, based on unscented Kalman filter theory, a GPS/INS/WIFI based compact combined position solution model is established. Finally, the human wearable combined positioning experiment platform was used for experimental verification. The experimental results show that the GPS/INS/WIFI based tight combined positioning method can significantly adapt to the indoor environment with complex interference, has high positioning stability and positioning accuracy, and the maximum positioning error is 0.45m. Compared with the extended Kalman filter and Kalman filter, the positioning accuracy of unscented Kalman filter is improved by 56% and 89% respectively, which can meet the requirements of field use.

Research on Position Error Model and Simulation Analysis of Magnetic Field Excitation Coil in Magnetic Nanoparticles Thermometer

The relative error of the magnetic induction intensity caused by the magnetic field excitation device of multiple air-core coils is caused by the position error during the assembly process. The error of temperature measured by the magnetic nanoparticles thermometer (MNPT) increases significantly when the error of excited magnetic fields is greater than 0.1%. The theoretical model of the position error for the air-core coil is constructed based on the Biot-Savart law. The simulation results show that the relative error of the magnetic induction intensity in the assembly process of a single air-core coil can be reduced by adding compensation coils, so that the minimum error is less than 0.1%. This method is also applicable to multiple air-core coils. Moreover, we also obtained the minimum error transfer route during the construction of multiple air-core coils. It is expected to provide an effective solution for reducing the temperature error of MNPT caused by the assembly process of multiple air-core coils.

Time-dependent kinematic reliability of a dual-axis driving mechanism for satellite antenna considering non-uniform planar revolute joint clearance

The dual-axis driving mechanism is a key part of satellite antenna. It is required to operate for millions of motion cycles in space. Wear is inevitable in the joints, which makes the clearance non-uniform. However, the investigations regarding this issue are quite limited. In this study, we conduct time-dependent kinematic reliability analysis for the dual-axis driving mechanism with non-uniform joint clearance. Firstly, an efficient wear prediction method is proposed under the framework of multi-body dynamics. Then, the position error model is established considering non-uniform joint clearance, input uncertainty, and linkage dimension error. On this basis, the mean and covariance matrix are analytically determined for the joint distribution of the position error along x, y, and z axes. The envelopes of the position error functions are derived. Finally, the time-dependent kinematic reliability is estimated with the integration of a multivariable normal distribution at the calculated expansion points. The effectiveness of the proposed method is validated by comparison with the Monte Carlo simulation.

Free-form surface form error evaluation based on smaller-scale sampling points in touch-trigger probing

Surface reconstruction is an essential operation in the evaluation of free-form surface form error. As a feasible technology in free-form surface sampling, touch-trigger probing has been widely used in on-machine measurement and coordinate measurement machine. However, surface reconstruction quality is influenced by limited sampling point size. This study proposes a surface reconstruction method based on surface position error and deformation error model. Surface form error is decomposed into surface position error and deformation error. Then, the design surface is taken as a rigid body, and a point-to-surface function-based iterative algorithm is conducted to adjust surface location and orientation to best match the sampling points. The advantage of this algorithm is that it considers the probe dimension, so further compensation of probe radius is not required. The geometry of the adjusted design surface is modified based on thin plate energy minimization and point-to-surface function. Due to the inherent feature of the proposed method, geometric features of the design surface are kept. Experiments are conducted to verify the effectiveness of the proposed method, and results show that the proposed method can achieve lower error compared with existing methods.

A Cooperative Positioning Method of Connected and Automated Vehicles with Direction-of-Arrival and Relative Distance Fusion

The rapid development of science and technology has created favorable conditions for Connected and Automated Vehicles (CAVs). Accurate localization is one of the fundamental functions of CAV to realize some advanced operations such as vehicle platooning. However, complicated urban traffic environments, such as the flyover, significantly influence vehicular positioning accuracy. The inability of CAV to accurately perceive self-localization information has become an urgent issue to be addressed. This paper proposed a novel cooperative localization method by introducing the relative Direction-of-Arrival (DOA) and Relative Distance (RD) into CAV to improve the localization accuracy of CAV in the multivehicle environment. First, the three-dimensional positioning error model of the host vehicle concerning adjacent vehicles in azimuth angle and pitch angle and intervehicle distances under the vehicle-to-vehicle communication was established. Second, two least-squares estimation algorithms, linear and nonlinear, are established to decrease the position errors by combining relative DOA and RD measurement information. To verify the proposed algorithm's effect, the PreScan-Simulink joint simulation is carried out. The results show that the host vehicle's localization accuracy by the proposed method can be improved by 25% compared with direct linearization. Besides, by combining relative DOA and relative RD measurement, the locating capability of the least-square-based nonlinear optimization method can be enhanced by 22%.

A novel geometric error identification and prediction approach

This paper proposed an integrated geometric error identification and prediction method to solve the uncertainty problem of the PDGEs of rotary axis. First, based on homogeneous transform matrix (HTM) and multi-body system (MBS) theory, The transfer matrix only considering the C-axes rotated is derived to the position error model. Then a geometric errors identification of rotary axis is introduced by measuring the error increment in three directions. Meanwhile the geometric errors of C-axis are described as truncated Fourier polynomials caused by fitting discrete values. Thus, The geometric error identification is converted into the function coefficient. Finally, the proposed new prediction and identification model of PDGEs in the global frame are verified through simulation and experiments with double ball-bar tests.

Positioning error compensation of a flexible track hybrid robot for aircraft assembly based on response surface methodology and experimental study

With the development of aviation industry, more stringent demands are put forward for the performance and manufacturing level of aircraft. Moreover, the automation and precision of aircraft assembly determine the efficiency and quality of aircraft production. In order to improve the positioning precision of the flexible track hybrid robots which are applied to the flexible automatic assembly of aircraft, a precision compensation method based on response surface methodology was proposed in this paper. Firstly, the global positioning error model, optimized by characteristics of error data, was constructed to predict the positioning errors of the flexible track hybrid robot. Secondly, the predicted errors are utilized to realize the compensation of the target points at drilling workspace on nose and front fuselage assembly areas. Finally, a series of experiments of the flexible track hybrid robot with no-load and drilling scenarios are implemented to validate the proposed precision compensation method. The experiment of a hybrid robot for aircraft assembly shows that the mean value of the absolute positioning precision of the end-effector was promoted from 0.081 mm to 0.025 mm, maximum error reduced from 0.143 mm to 0.039 mm, respectively, which means that the position accuracy of the robot is increased by 69.1% and 72.7% for two experimental conditions.

Accurate and stable two-step LED position calibration method for Fourier ptychographic microscopy.

.Significance: Fourier ptychography microscopy (FPM) is a computational optical imaging technology that employs angularly varying illuminations and a phase retrieval algorithm to achieve a wide field of view and high-resolution imaging simultaneously. In the FPM, LED position error will reduce the quality of the reconstructed high-resolution image. To correct the LED positions, current methods consider each of the LED positions as independent and use an optimization algorithm to get each of the positions. When the positional misalignment is large or the search position falls into a local optimal value, the current methods may lack stability and accuracy.Aim: We improve the model of the LED position and propose an accurate and stable two-step correction scheme (tcFPM) to calibrate the LED position error.Approach: The improved LED positions model combines the overall offset, which represents the relative deviation of the LED array and the optical axis, with the slight deviation of each LED’s independent position. In the tcFPM, the overall offset of the LED array is corrected at first, which obtains an approximate value of the overall offset of the LED array. Then the position of each LED is precisely adjusted, which obtains the slight offset of each LED.Results: This LED position error model is more in line with the actual situation. The simulation and experimental results show that the method has high accuracy in correcting the LED position. Furthermore, the reconstruction process of tcFPM is more stable and significantly improves the quality of the reconstruction results, which is compared with some LED position error correction methods.Conclusions: An LED position error correction technology is proposed, which has a stable iterative process and improves the reconstruction accuracy of complex amplitude.

Positioning Accuracy Model of Sailing‐Circle GPS‐Acoustic Method

AbstractSailing‐circle GPS‐acoustic method, prevalently applied for measuring ocean floor crustal deformation, allows the precise positioning of an underwater transponder in a global frame. In the method, distance estimation requires prior information, such as transponder depth or incident angle. However, sometimes the prior information is inaccurate or absent. Under these circumstances, this study proposes two kinds of positioning methods that utilize an iteration composed of an inverse or direct ray tracing method and the least squares approach to constantly modify the initial data to obtain an accurate incident angle and coordinates of an underwater transponder. Even though an accurate incident angle can be got and there is no time delay or spatial‐temporal heterogeneities of SSP (sound speed profile), SSP density and geometric incident angle still influence ranging errors and PDOP (position dilution of precision) during distance intersection. In order to reduce the two kinds of impacts, this paper deduces a positioning error model based on the principle of sailing‐circle method. On the one hand, the proposed algorithms and model are verified by a simulated experiment for various SSP density, geometric incident angle, and transponder depth. On the other hand, in a practical experiment, average positioning accuracy of 0.025 m and vertical accuracy of −0.02 m are achieved, and the improved accuracy is about 85% higher than that of the ordinary sailing‐circle method.

Research on optimization of the number of acoustic arrays

The reasonable number of base stations in multiple acoustic array azimuth cross location is studied. In this paper, the maximum likelihood estimation (MLE) algorithm is used to discuss the problem of increasing the number of arrays to improve the positioning accuracy, and the positioning error model is given. The experimental results show that with the increase of the number of base stations, the positioning accuracy will gradually improve, but if there are too many base stations, the improvement of positioning accuracy will gradually slow down.