Robot Calibration Research Articles

An Improved Design of the MultiCal On-Site Calibration Device for Industrial Robots.

MultiCal is an affordable, high-precision measuring device designed for the on-site calibration of industrial robots. Its design features a long measuring rod with a spherical tip that is attached to the robot. By restricting the rod's tip to multiple fixed points under different rod orientations, the relative positions of these points are accurately measured beforehand. A common issue with MultiCal is the gravitational deformation of the long measuring rod, which introduces measurement errors into the system. This problem becomes especially serious when calibrating large robots, as the length of the measuring rod needs to be increased to enable the robot to move in a sufficient space. To address this issue, we propose two improvements in this paper. Firstly, we suggest the use of a new design of the measuring rod that is lightweight yet has high rigidity. Secondly, we propose a deformation compensation algorithm. Experimental results have shown that the new measuring rod improves calibration accuracy from 20% to 39%, while using the deformation compensation algorithm, the accuracy increases from 6% to 16%. In the best configuration, the calibration accuracy is similar to that of a measuring arm with a laser scanner, producing an average positioning error of 0.274 mm and a maximum positioning error of 0.838 mm. The improved design is cost-affordable, robust, and has sufficient accuracy, making MultiCal a more reliable tool for industrial robot calibration.

Precision Denavit–Hartenberg Parameter Calibration for Industrial Robots Using a Laser Tracker System and Intelligent Optimization Approaches

Precision object handling and manipulation require the accurate positioning of industrial robots. A common practice for performing end effector positioning is to read joint angles and use industrial robot forward kinematics (FKs). However, industrial robot FKs rely on the robot Denavit–Hartenberg (DH) parameter values, which include uncertainties. Sources of uncertainty associated with industrial robot FKs include mechanical wear, manufacturing and assembly tolerances, and robot calibration errors. It is therefore necessary to increase the accuracy of DH parameter values to reduce the impact of uncertainties on industrial robot FKs. In this paper, we use differential evolution, particle swarm optimization, an artificial bee colony, and a gravitational search algorithm to calibrate industrial robot DH parameters. A laser tracker system, Leica AT960-MR, is utilized to register accurate positional measurements. The nominal accuracy of this non-contact metrology equipment is less than 3 μm/m. Metaheuristic optimization approaches such as differential evolution, particle swarm optimization, an artificial bee colony and a gravitational search algorithm are used as optimization methods to perform the calibration using laser tracker position data. It is observed that, using the proposed approach with an artificial bee colony optimization algorithm, the accuracy of industrial robot FKs in terms of mean absolute errors of static and near-static motion over all three dimensions for the test data decreases from its measured value of 75.4 μm to 60.1 μm (a 20.3% improvement).

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.

Modeling and calibration of high-order joint-dependent kinematic errors of serial robot based on local POE

PurposeThis paper aims to address the issue of model discontinuity typically encountered in traditional Denavit-Hartenberg (DH) models. To achieve this, we propose the use of a local Product of Exponentials (POE) approach. Additionally, a modified calibration model is presented which takes into account both kinematic errors and high-order joint-dependent kinematic errors. Both kinematic errors and high-order joint-dependent kinematic errors are analyzed to modify the model.Design/methodology/approachRobot positioning accuracy is critically important in high-speed and heavy-load manufacturing applications. One essential problem encountered in calibration of series robot is that the traditional methods only consider fitting kinematic errors, while ignoring joint-dependent kinematic errors.FindingsLaguerre polynomials are chosen to fitting kinematic errors and high-order joint-dependent kinematic errors which can avoid the Runge phenomenon of curve fitting to a great extent. Levenberg–Marquard algorithm, which is insensitive to overparameterization and can effectively deal with redundant parameters, is used to quickly calibrate the modified model. Experiments on an EFFORT ER50 robot are implemented to validate the efficiency of the proposed method; compared with the Chebyshev polynomial calibration methods, the positioning accuracy is improved from 0.2301 to 0.2224 mm.Originality/valueThe results demonstrate the substantial improvement in the absolute positioning accuracy achieved by the proposed calibration methods on an industrial serial robot.

Accuracy of robot-assisted stereotactic MRI-guided laser ablation in children with epilepsy.

Robot-assisted (RA) stereotactic MRI-guided laser ablation has been reported to be a safe and effective technique for the treatment of epileptogenic foci in children and adults. In this study the authors aimed to assess the accuracy of RA stereotactic MRI-guided laser fiber placement in children and to identify factors that might increase the risk of misplacement. A retrospective single-institution review of all children from 2019 to 2022 who underwent RA stereotactic MRI-guided laser ablation for epilepsy was undertaken. Placement error was calculated at the target by measuring the Euclidean distance between the implanted laser fiber position and the preoperatively planned position. Collected data included age at surgery, sex, pathology, date of robot calibration, number of catheters, entry position, entry angle, extracranial soft-tissue thickness, bone thickness, and intracranial catheter length. A systematic review of the literature was also performed using Ovid Medline, Ovid Embase, and the Cochrane Central Register of Controlled Trials. In 28 children with epilepsy, the authors assessed 35 RA stereotactic MRI-guided laser ablation fiber placements. Twenty (71.4%) children had undergone ablation for hypothalamic hamartoma, 7 children (25.0%) for presumed insular focal cortical dysplasia, and 1 patient (3.6%) for periventricular nodular heterotopia. Nineteen children were male (67.9.%) and 9 were female (32.1%). The median age at the time of the procedure was 7.67 years (IQR 4.58-12.26 years). The median target point localization error (TPLE) was 1.27 mm (IQR 0.76-1.71 mm). The median offset error between the planned and actual trajectories was 1.04° (IQR 0.73°-1.46°). Patient age, sex, pathology and the time interval between date of surgery and robot calibration, entry position, entry angle, soft-tissue thickness, bone thickness, and intracranial length were not associated with the placement accuracy of the implanted laser fibers. However, the number of catheters placed did correlate with the offset angle error on univariate analysis (ρ = 0.387, p = 0.022). There were no immediate surgical complications. Meta-analysis indicated that the overall pooled mean TPLE was 1.46 mm (95% CI -0.58 to 3.49 mm). RA stereotactic MRI-guided laser ablation for epilepsy in children is highly accurate. These data will aid surgical planning.

Highly Stretchable Printed Poly(vinylidene fluoride) Sensors through the Formation of a Continuous Elastomer Phase

Stretchable piezoelectric stress/strain sensing materials have attracted substantial research interest in the fields of wearable health monitoring, motion capturing, and soft robotics. These sensors require operation under dynamic loading conditions with high strain range, changing strain/loading rates, and varying pre-stretch states, which are challenging conditions for existing sensors to produce reliable measurements. To overcome these challenges, an intrinsically stretchable poly(vinylidene fluoride) (PVDF) sensor is developed through the polymer blending of PVDF and acrylonitrile butadiene rubber (NBR). Through precipitation printing and vulcanization, the resulting PVDF/NBR blends exhibit strong β phase PVDF and a blend morphology with submicron-level phase separation, but also strains up to 544%. Both the blend morphology and the mechanical properties indicate that this PVDF/NBR blend can be considered as a continuous elastomer phase above micron scale. After electric poling and adding electrodes, the PVDF/NBR blends have excellent piezoelectric properties to be used as both stretching mode strain sensors and compression mode stress/force sensors. The stretching mode sensors can measure strain up to 70% without strain rate and pre-stretch dependence, while the compression mode sensors have a loading-rate-independent linear voltage-stress relationship up to 4.8 MPa stress and a negligible pre-stretch dependence. Therefore, the PVDF/NBR sensors can provide accurate and reliable stress/strain measurements when attached to soft structures, which paves the way for sensing and calibration of soft robots under dynamic loading conditions.

Kinematic calibration of over-constrained robot with geometric error and internal deformation

In the over-constrained robot with geometric errors, internal forces would occur and lead to deformation due to redundant constraints and common constraints. In current kinematic calibration approaches, since the deformation, geometric errors and pose errors cannot be described in a unified framework, the error propagation fails to be solved intuitively and generically. In this article, a general calibration framework of over-constrained robots is proposed to unify geometric errors and internal deformation through the least action principle. In the framework, considering the interaction between errors and deformation, the difference map between geometric errors and pose errors is explicitly and analytically revealed. The mapping matrix can degenerate to be consistent with the previous research under non-over-constrained robots. In addition, the error forward propagation method and the error identification algorithm are proposed to solve the error nonlinear propagation and the ill-posed identification equations, respectively. Finally, the calibration simulation and experiment results of a 5-DOF over-constrained hybrid robot show that the proposed method can accurately predict the pose of the end-effector under geometric errors robustly and effectively.

Precise Robot Calibration Method-Based 3-D Positioning and Posture Sensor

This article presents a distance accuracy technique for zero-offset industrial robot calibration based on 3-D positioning and posture (3DPP) sensor along with modified Denavit–Hartenberg (MDH) for robot kinematics identification. Industrial robots’ distance and positioning accuracy tend to diminish rapidly due to repetitive tasks and heavy loads. Many aspects can be involved in reducing the distance and positioning accuracy of the industrial robot; therefore, using the proper sensors and identification methods is essential to increase or restore the accuracy back to the original state. Normally, maintenance requires apparatus made specifically for robot kinematic calibration which are costly, time-consuming, and must be done by trained operators, while traditional calibration techniques suffer from cumulative error between the calibration device coordinates and robot coordinates. In this article, a 3DPP measurement device and MDH robot kinematic identification method is proposed for a six-degree-of-freedom (6DOF) industrial manipulator calibration, and a distance error calibration model is applied. The results indicate that the proposed 3DPP sensor and calibration model based on MDH improved the absolute position accuracy and distance accuracy greatly, the positioning maximum and average error were reduced by 94% and 96% respectively, and the distance maximum and average error were reduced by 95% and 96% respectively. The experimental results confirm the efficiency of the sensor and proposed method.

Robot grasping system based on deep learning target detection

The traditional robot grasping system often uses fixed point grasping or demonstrative grasping, but with the increase in the diversity of grasping targets and the randomness of poses, the traditional grasping method is no longer sufficient. A robot grasping method based on deep learning target detection is proposed for a high error rate of target recognition and low success rate of grasping in the robot grasping process. The method investigates the robotic arm hand-eye calibration and the deep learning-based target detection and poses estimation algorithm. The Basler camera is used as the visual perception tool of the robot arm, the AUBO i10 robot arm is used as the main body of the experiment, and the PP-YOLO deep learning algorithm performs target detection and poses estimation on the object. Through the collection of experimental data, several grasping experiments were conducted on the diversity of targets randomly placed in the poses under real scenes. The results showed that the success rate of grasping target detection was 94.93% and the robot grasping success rate was 93.37%.

Error Similarity Analysis and Error Compensation of Industrial Robots with Uncertainties of TCP Calibration

The machining system based on an industrial robot is a new type of equipment to meet the requirements of high quality, high efficiency and high flexibility for large and complex components of aircraft and spacecraft. The error compensation technology is widely used in robotic machining to improve the positioning accuracy of an industrial robot with the intention of meeting the precision requirements of aerospace manufacturing. However, the robot’s positioning accuracy decreases significantly when the orientation of the tool changes dramatically. This stems from the fact that the existing robot compensation methods ignore the uncertainties of Tool Center Point (TCP) calibration. This paper presents a novel regionalized compensation method for improving the positioning accuracy of the robot with calibration uncertainties and large orientation variation of the TCP. The method is experimentally validated through the drilling of curved surface parts of plexiglass using a KUKA KR2830MT robot. Compared with a published error compensation method, the proposed approach improves the positioning accuracy of the robot under the large orientation variation to 0.235 mm. This research can broaden the field of robot calibration technology and further improve the adaptability of robotic machining.

Unified Robot and Inertial Sensor Self-Calibration.

Robots and inertial measurement units (IMUs) are typically calibrated independently. IMUs are placed in purpose-built, expensive automated test rigs. Robot poses are typically measured using highly accurate (and thus expensive) tracking systems. In this paper, we present a quick, easy, and inexpensive new approach to calibrate both simultaneously, simply by attaching the IMU anywhere on the robot's end effector and moving the robot continuously through space. Our approach provides a fast and inexpensive alternative to both robot and IMU calibration, without any external measurement systems. We accomplish this using continuous-time batch estimation, providing statistically optimal solutions. Under Gaussian assumptions, we show that this becomes a nonlinear least squares problem and analyze the structure of the associated Jacobian. Our methods are validated both numerically and experimentally and compared to standard individual robot and IMU calibration methods.

Modeling and Parameter Identification of a 3D Measurement System Based on Redundant Laser Range Sensors for Industrial Robots.

The low absolute positioning accuracy of industrial robots is one of the bottlenecks preventing industrial robots from precision applications. Kinematic calibration is the main way to improve the absolute positioning accuracy of industrial robots, which greatly relies on three-dimensional (3D) measurement instruments, including laser trackers and pull rope mechanisms. These instruments are costly, and their required intervisibility space is large. In this paper, a precision 3D measurement instrument integrating multiple laser range sensors is designed, which fuses the information of multiple redundant laser range sensors to obtain the coordinates of a 3D position. An identification model of laser beam position and orientation parameters based on redundant distance information and standard spherical constraint is then developed to reduce the requirement for the assembly accuracy of laser range sensors. A hybrid identification algorithm of PSO-LM (particle swarm optimization Levenberg Marquardt) is designed to solve the high-order nonlinear problem of the identification model, where PSO is used for initial value identification, and LM is used for final value identification. Experiments of identification of position and orientation, verifications of the measuring accuracy, and the calibration of industrial robots are conducted, which show the effectiveness of the proposed 3D measurement instrument and identification methods. Moreover, the proposed instrument is small in size and can be used in narrow industrial sites.

Elasto-geometrical calibration of a hybrid mobile robot considering gravity deformation and stiffness parameter errors

• An elasto-geometrical calibration method taking into account structural and stiffness parameter errors is proposed for a hybrid mobile robot. • A compensation strategy comprehensively considering the pose errors of the 3-RCU parallel module and 2-DoF robotic arm is put forward to improve the accuracy of the robot. • Calibration experiments based on three different models are conducted and the accuracy of the robot before and after calibration is tested to show the validity of the proposed method. Hybrid mobile robots, which combine the advantages of serial and parallel robots and have the ability to realize processing in situ , have considerable application potential in the field of processing and manufacturing. In this paper, a hybrid mobile robot used for wind turbine blade polishing is presented. The robot combines an automated guided vehicle, a 2-DoF robotic arm, and a 3-RCU parallel module. To improve the accuracy, investigating the elasto-geometrical calibration of the robot is necessary. Considering that the 3-RCU parallel module has weak stiffness along the gravitational direction, the stiffness model was established to estimate the deformation caused by the gravity of the mobile platform, ball screws, and motors. Subsequently, a rigid-flexible coupling error model considering structural and stiffness parameter errors is established. Based on these, a parameter identification method for the simultaneous identification of structural and stiffness parameter errors is proposed herein. For the 2-DoF robotic arm with parallelogram mechanisms, an intuitive error model considering the posture error caused by the parallelogram mechanism errors is established. The regularized nonlinear least squares method was adopted for parameter identification. Thereafter, a compensation strategy for the hybrid mobile robot that comprehensively considers the pose errors of the 3-RCU parallel module and 2-DoF robotic arm is proposed. Finally, a verification experiment was performed on the prototype, and the results indicated that after elasto-geometrical calibration, the maximum/mean of the position and posture errors of the hybrid mobile robot decreased from 3.738 mm/2.573 mm to 0.109 mm/0.063 mm and 0.236°/0.179° to 0.030°/0.013°, respectively. Owing to the decrease in the robot pose errors, the quality of the polished surface was more uniform. The range and standard deviation of roughness distribution of the polished surface were reduced from 0.595 μm and 0.248 μm to 0.397 μm and 0.127 μm. The methods proposed herein have reference significance for elasto-geometrical calibration of other parallel or hybrid robots.

Kinematic calibration for collaborative robots on a mobile platform using motion capture system

For modern robotic applications that go beyond the typical industrial environment, absolute accuracy is one of the key properties that make this possible. There are several approaches in the literature to improve robot accuracy for a typical industrial robot mounted on a fixed frame. In contrast, there is no method to improve robot accuracy when the robot is mounted on a mobile base, which is typical for collaborative robots. Therefore, in this work, we proposed and analyzed two approaches to improve the absolute accuracy of the robot mounted on a mobile platform using an optical measurement system. The first approach is based on geometric operations used to calculate the rotation axes of each joint. This approach identifies all rotational axes, which allows the calculation of the Denavit–Hartenberg (DH) parameters and thus the complete kinematic model, including the position and orientation errors of the robot end-effector and the robot base. The second approach to parameter estimation is based on optimization using a set of joint positions and end-effector poses to find the optimal DH parameters. Since the robot is mounted on a mobile base that is not fixed, an optical measurement system was used to dynamically and simultaneously measure the position of the robot base and the end-effector. The performance of the two proposed methods was analyzed and validated on a 7-DoF Franka Emika Panda robot mounted on a mobile platform PAL Tiago-base. The results show a significant improvement in absolute accuracy for both proposed approaches. By using the proposed approach with the optical measurement system, we can easily automate the estimation of robot kinematic parameters with the aim of improving absolute accuracy, especially in applications that require high positioning accuracy. • A geometric and numerical approach for the calibration of collaborative robots. • Sensitivity analysis for MoCap noise position measurement on DH parameter estimation. • A novel approach to map the optical base frame and robot base frame. • Statistical analysis of different methods for estimating DH parameters.

Robot-mounted sensing and local calibration for high-accuracy manufacturing

Positional accuracy is critically important for application of industrial robots in fixtureless precision manufacturing; thus, this paper presents a method for simultaneously calibrating the kinematic parameters of robot and robot-mounted measurement devices. In the modeling step, the Modified Denavit–Hartenberg parameters are extended to include the world and tool frames within a minimal parameter set using a systematic approach. Closed-loop calibration is performed using the data collected in the local target workspace using the robot-mounted measurement device. The presented modeling and calibration methods are applied to a case study in which a machining task is performed using a DENSO VS-6556 W industrial robot equipped with a cutting tool, force sensor, and laser profile scanner. In the case study, local models are calibrated for the laser and tool frames using common 1-2-3 blocks as calibration artifacts . The robot/laser model is identified by scanning the artifacts with a robot-mounted laser scanner , and the robot/tool model is calibrated by touching the artifacts with a robot-mounted force sensor. In this application, the robot/laser model is used to scan and register a sheet metal workpiece, and the robot/tool model is used to plan a tool path to machine the periphery. Positional accuracy of the tool path was evaluated to be ± 0.15 mm within the target workspace, which shows significant improvement compared with the mean error of 0.8 mm achieved by global calibration of the robot/tool model. • Simultaneous calibration of robot and extrinsic parameters of robot-mounted sensors. • Closed-loop calibration without external measurement devices. • Local calibration to improve accuracy within target workspace. • Systematic approach to include world and tool/sensor frame in MDH parameter set. • Case study for high-accuracy robotic machining application.

Practical whole-body elasto-geometric calibration of a humanoid robot: Application to the TALOS robot

The whole-body elasto-geometrical calibration of humanoid robots is critical particularly for their control and accurate simulation. However, it is often not considered probably since it is a nontrivial task due to the mechanical complexity and inherent constraints of anthropomorphic structures. Also, humanoid robots have to sustain great efforts on their support legs, leading to link and joint being deformed, and are prone to auto-collision. Thus, elastic parameters have to be factored in addition to the geometric ones and to improve the precision of the pose of all robot segments. This is much more cumbersome and time consuming than the classical calibration of serial manipulators that deals solely with the estimation of the pose of the end-effector. Finally, due to the complexity of the task, a manual intervention in several steps of the calibration is no longer possible and a thorough automation of the approach is needed. Therefore, we propose to use a stereophotogrammetric system along with embedded joint torque sensors to calibrate the pose of all robot links with a fully automatic procedure. The generation of the minimal set of optimal calibration postures is based on a new iterative optimization process that leads to a stable maximum of an observability index. Then full set of geometrical parameters but also joint and base elastic parameters were calibrated using a single least-square optimization program. The proposed method was validated on a TALOS humanoid robot allowing to obtain an accurate whole-body calibration in less than 10 min. The proposed approach was cross-validated experimentally and showed an average RMS error of the tracked markers of 2.2 mm.

Influence of the velocity on quasi-static deflections of industrial articulated robots

This article presents the measurement and analysis of the influence of velocity on the quasi-static deflections of industrial manipulators of three different manufacturers. Quasi-static deflection refers to the deflection of the end effector position of articulated robots during movement at low velocity along a predefined trajectory. Based on earlier reported observations by the authors, there exists a difference in the static and quasi-static deflections considering the same points along a trajectory. This work investigates this difference to assess the applicability of robotic compliance calibration at low velocities. For this assessment, the deflections of three industrial articulated robots were measured at different speeds and loads. Considering the similarity among the robot models used in this investigation, this work also elaborates on the potential influence of the measurement procedure on the measured deflections and its implications for the compliance calibration of articulated robots. For all industrial articulated robots in this investigation, the quasi-static deflections are significantly larger than the static ones but similar in trend. Additionally, the magnitude of the quasi-static deflections presents a proportional relationship to the Cartesian velocity.

Efficient Industrial Robot Calibration via a Novel Unscented Kalman Filter-Incorporated Variable Step-Size Levenberg–Marquardt Algorithm

Robots facilitate a critical category of equipments to implement intelligent production. However, due to extensively inevitable factors like structural errors and gear tolerances, the positioning error of an industrial robot is several millimeters, therefore failing in fulfilling the high-precision manufacture requirements. To address the critical problem, this work develops a novel calibration algorithm incorporates an Unscented Kalman Filter and a Variable Step-size Levenberg-Marquardt (UKF-VSLM) algorithm for efficient industrial robot calibration with the following two-fold ideas: a) developing a novel Variable Step-size Levenberg-Marquardt algorithm to address the local optimum issues encountered by a standard Levenberg-Marquardt algorithm; and b) incorporating an unscented Kalman filter into the proposed Variable Step-size Levenberg-Marquardt algorithm to suppressing the measurement noises during the calibration process. Empirical studies on an HSR JR680 industrial robot demonstrate that compared with state-of-the-art calibration algorithms, the calibration accuracy of the developed UKF-VSLM is 19.51% higher than that of the most accurate Levenberg-Marquardt algorithm measured by the maximum error. The empirical results strongly support the superior performance of the proposed algorithm in addressing robot calibration issues.

Kinematic Calibration and Compensation of Industrial Robots Based on Extended Joint Space

Kinematic Calibration and Compensation of Industrial Robots Based on Extended Joint Space

A Single 2-D LiDAR Extrinsic Calibration for Autonomous Mobile Robots

A Single 2-D LiDAR Extrinsic Calibration for Autonomous Mobile Robots