Elasto-geometrical error and gravity model calibration of an industrial robot using the same optimized configuration set

Position error is a significant limitation for industrial robots in high-precision machining and manufacturing. Efficient error measurement and compensation for robots equipped with end-effectors are difficult in industrial environments. This paper proposes a robot calibration method based on an elasto–geometrical error and gravity model. Firstly, a geometric error model was established based on the D-H method, and the gravity and compliance error models were constructed to predict the elastic deformation caused by the self-weight of the robot. Subsequently, the position error model was established by considering the attitude error of the robot flange coordinate system. A two-step robot configuration selection method was developed based on the sequential floating forward selection algorithm to optimize the robot configuration for calibrating the position error and gravity models. Then, the geometric error and compliance coefficient were identified simultaneously based on the hybrid evolution algorithm. The gravity model parameters were identified based on the same algorithm using the joint torque signal provided by the robot controller. Finally, calibration and compensation experiments were conducted on a KR-160 industrial robot equipped with a spindle using a laser tracker and internal robot data. The experimental results show that the robot tool center point error can be significantly improved by using the proposed method.     

Kinematic analysis and error modeling of TAU parallel robot

The TAU robot presents a new configuration of parallel robots with three degrees of freedom. This robotic configuration is well adapted to perform with a high precision and high stiffness within a large working range compared with a serial robot. It has the advantages of both parallel robots and serial robots. In this paper, the kinematic modeling and error modeling are established with all errors considered using Jacobian matrix method for the robot. Meanwhile, a very effective Jacobian approximation method is introduced to calculate the forward kinematic problem instead of Newton–Raphson method. It denotes that a closed form solution can be obtained instead of a numerical solution. A full size Jacobian matrix is used in carrying out error analysis, error budget, and model parameter estimation and identification. Simulation results indicate that both Jacobian matrix and Jacobian approximation method are correct and with a level of accuracy of micron meters. ADAMS's simulation results are used in verifying the established models.     

Geometric calibration of industrial robots using enhanced partial pose measurements and design of experiments

The paper deals with geometric calibration of industrial robots and focuses on reduction of the measurement noise impact by means of proper selection of the manipulator configurations in calibration experiments. Particular attention is paid to the enhancement of measurement and optimization techniques employed in geometric parameter identification. The developed method implements a complete and irreducible geometric model for serial manipulator, which takes into account different sources of errors (link lengths, joint offsets, etc). In contrast to other works, a new industry-oriented performance measure is proposed for optimal measurement configuration selection that improves the existing techniques via using the direct measurement data only. This new approach is aimed at finding the calibration configurations that ensure the best robot positioning accuracy after geometric error compensation. Experimental study of heavy industrial robot KUKA KR-270 illustrates the benefits of the developed pose strategy technique and the corresponding accuracy improvement.     

Accurate error compensation for a MR-compatible surgical robot based on a novel kinematic calibration method

Kinematic calibration is an effective and economical way to improve the accuracy of surgical robot, and in most cases, it is a necessary procedure before the robot is put into operation. This study investigates a novel kinematic calibration method where the effect of controller error is taken into account when formulating the model based on screw theory, which is applied to the kinematic control of magnetic resonance compatible surgical robot. Based on screw theory, the kinematic error model is established for the relationship between error of controller and the deviation of the measured pose of the end-effector. Therefore, the error of controller can be figured out and parameters of controller can be adjusted accordingly. Control strategy based on the kinematic calibration framework is proposed. According to artificial neural network, the deviation of end-effector in arbitrary configuration can be effectively obtained. Comparative experiments are carried out to show the validity and effectiveness of the proposed framework with the help of commercial visual system and joint encoders.     

A method for robot placement optimization based on two-dimensional manifold in joint space

This article addresses a method for placement determination of robotic drilling system on two-dimensional manifold in robot joint space. It has been proved that the feasibility of positioning error compensation on two-dimensional manifold, and that the continuity of the robot parameters in the two-dimensional space is the prerequisite to perform the compensation in previous study. It appears that there are bifurcations which might break the continuity of the robot parameters on the two-dimensional manifold due to improper placement. To avoid bifurcations, a performance index and a set of optimization procedure are proposed to achieve proper placement of robotic machining system. Experiments conducted on a KUKA robot have verified the effectiveness of the proposed placement optimization method. Experiment results indicated that positioning errors were significantly improved with the proposed method, which is beneficial for robotic machining accuracy.     

Compliance measurement for the Mitsubishi PA-10 robot

In this study, we measure the compliance characteristics of the 7-degree-of-freedom (DOF) vertical multiarticulated Mitsubishi PA-10 robot. To determine the compliance characteristics of the robot, numerical values of joint compliance are identified by a partial simultaneous measurement method using a force/torque sensor and a 3-D measurement system. The identified compliance is derived from an extended 10-DOF link model that comprises three additional virtual joints and seven actual joints. The virtual joints, which can be handled in the same manner as the actual joints, can be used for more accurate identification. The modeling error derived from link flexibility may be compensated by introducing the extended link model with additional virtual joints. To investigate the accuracy of the compliances identified with the extended link model, verification experiments were conducted. The results show that precise compliance characteristics are obtained from the extended link model. Finally, we reveal the compliance model of the Mitsubishi PA-10 robot, which comprises the numerical values of the joint compliance and a simple kinematic modeling.     

An efficient calibration method for serial industrial robots based on kinematics decomposition and equivalent systems

Calibration of the serial industrial robot with large workspace usually requires a time-consuming measurement task due to the exponential growth of measurement configurations with respect to degrees of freedom (DOFs). To improve efficiency, this paper presents a novel calibration method based on kinematics decomposition and equivalent systems. The trick is to use three lower-mobility sub-robot systems to replace the original robot, where these sub-robots possess quite the same base and end effector to avoid detection of any intermediate frame. For calibration, each sub-robot is treated as a kinematically equivalent system that only contains configuration-dependent joint motion errors, and least-squares support vector regression (LS-SVR) is utilized for joint motion error function approximation. Calibration experiments are conducted on a 6-DOF serial robot ABB IRB 2600. Compared with other methods, the proposed method can significantly save the required measurement configurations and the controller's memory space without losing high calibration accuracy. Experimental results show that the maximum position/orientation errors can be reduced to 0.393 mm/0.038 deg. After calibration, the robot can be applied to assemble parts with small clearance successfully, further demonstrating the effectiveness of the proposed method.     

Kinematic calibration of a five-bar planar parallel robot using all working modes

We present a simple low-cost calibration procedure that improves the planar positioning accuracy of a double-arm SCARA robot to levels difficult or impossible to achieve using an equivalent serial robot. Measurements are based on the use of five custom designed magnetic tooling balls fixed to the periphery of a detachable working plate. Three of these tooling balls define the world reference frame of the robot, and the positions of the centers of all balls are measured on a CMM. A special magnetic cup end-effector is used. Measurements are taken by manually positioning the end-effector over each of the tooling balls, with each of the maximum of four possible robot configurations. Each of these measurements is repeatable to within±0.015 mm. The robot calibration model includes all 12 kinematic parameters, and the calibration method used is based on the linearization of the direct kinematics model in each calibration configuration. The optimal number and location of the tooling balls is obtained by studying the observability index. Finally, an experimental validation at 14 additional tooling balls shows that the maximum position error with respect to the world frame is reduced to 0.080 mm within the entire robot's workspace of 600 mm×600 mm.     

Posture optimization methodology of 6R industrial robots for machining using performance evaluation indexes

For industrial robots, the relatively low posture-dependent stiffness deteriorates the absolute accuracy in the robotic machining process. Thus, it is reasonable to consider performing machining in the regions of the robot workspace where the kinematic, static and even dynamic performances are highest, thereby reducing machining errors and exhausting the advantages of the robot. Simultaneously, an optimum initial placement of the workpiece with respect to the robot can be obtained by optimizing the above performances of the robot. In this paper, a robot posture optimization methodology based on robotic performance indexes is presented. First, a deformation evaluation index is proposed to directly illustrate the deformation of the six-revolute (6R) industrial robot (IR) end-effector (EE) when a force is applied on it. Then, the kinematic performance map drawn according to the kinematic performance index is utilized to refine the regions of the robot workspace. Furthermore, main body stiffness index is proposed here to simplify the performance index of the robot stiffness, and its map is used to determine the position of the EE. Finally, the deformation map obtained according to the proposed deformation evaluation index is used to determine the orientation of the EE. Following these steps, the posture of the 6R robot with the best performance can be obtained, and the initial workpiece placement can be consequently determined. Experiments on a Comau Smart5 NJ 220-2.7 robot are conducted. The results demonstrate the feasibility and effectiveness of the present posture optimization methodology.     

A point and distance constraint based 6R robot calibration method through machine vision

This paper proposes a 6R robot closed-loop kinematic calibration method to improve absolute position accuracy with point and distance constraints though machine vision. In the calibration process, a camera attached to the mounting plate of the robot is used to capture a fixed reference sphere as a point constraint and to record robot joint angles and gauge block lengths that are used as a distance constraint. A first-order difference quotient is used to calculate the Jacobian matrix in the joint parameter identification process. The Staübli TX60 robot is successfully calibrated using the proposed method. After calibration, the average distance error of robot motion is decreased from 2.05 mm to 0.24 mm.     

Estimation model for kinematic calibration of manipulators with a parallel structure

This article provides an estimation model for calibrating the kinematics of manipulators with a parallel geometrical structure. Parameter estimation for serial link manipulators is well developed, but fail for most structures with parallel actuators, because the forward kinematics is usually not analytically available for these. We extend parameter estimation to such parallel structures by developing an estimation method where errors in kinematical parameters are linearly related to errors in the tool pose, expressed through the inverse kinematics, which is usually well known. The method is based on the work done to calibrate the MultiCraft robot. This robot has five linear actuators built in parallel around a passive serial arm, thus making up a two-layered parallel-serial manipulator, and the unique MultiCraft construction is reviewed. Due to the passive serial arm, for this robot conventional serial calibration must be combined with estimation of the parameters in the parallel actuator structure. The developed kinematic calibration method is verified through simulations with realistic data and real robot kinematics, taking the MultiCraft manipulator as the case. © 1994 John Wiley & Sons, Inc.     

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

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.     

Application of Joint Error Mutual Compensation for Robot End-effector Pose Accuracy Improvement

A method of robot end-effector pose accuracy improvement using joint error mutual compensation is presented. The developed method allows locating special robot configurations with the highest robot end-effector pose accuracy using joint error maximum mutual compensation. The computer simulation and experimental results confirmed the theory. The method provides the basis for an industrial application of joint error mutual compensation in the conventional robotic manipulators and allows improving robotic manipulator end-effector pose accuracy up to 2 times. The practical areas and typical robotic systems, where the developed framework of joint error mutual compensation could be applied, were presented.     

Passive Compliance from Robot Limbs and its Usefulness in Robotic Automation

Robots have been traditionally used as positioning devices without muchregard to external forces experienced by the tool. This has limited furtherpotential applications of robots in automation. Most tasks that remain to beautomated require constrained robot motion and/or involve work done by therobot on the environment. Such tasks require both force and positioncontrol. The ability to control the end-effector compliance is critical tosuccessful force and position control tasks. Although the end-effectorcompliance can be actively controlled through the joint flexibilitiesprovided by the joint servos or by active force sensing, the usefulness ofhaving the minimum passive compliance in addition to active compliancecontrol can improve performance. In surface following, for example, it isnecessary to make the end-point of a robot have the right compliance toprevent jamming. The usefulness of passive compliance has been demonstratedby the use of compliance-devices on the robot end-effector such as theRemote Center Compliance. The natural compliance inherent in light weightand flexible robot structures, however, can be exploited to provide thenecessary passive compliance required.In this paper we present a novel framework for computing the end-effectorcompliance from the compliance offered by the limbs of a serial robot. Theemphasis is on the explanation of the passive end-effector complianceresulting from these structures, and particular attention is given to theuse of these results in the selection of the type of robot for a particulartask. We show examples of end-effector compliances as functions of jointconfigurations for the SCARA- and PUMA-type robots. The joint-configurationdependent end-effector compliance can be used to select the desired robotpose for the performance of a robotic task.     

Calibration of an smt robot assembly cell

A new calibration method for an assembly robot cell is described. The proposed method is a combination of a model-free, numerical, relative robot calibration procedure and a procedure for the robot periphery calibration. Two important simplifications based on the study of an assembly process are introduced into the calibration strategy. A robot is calibrated in a task (Cartesian) space. The robot workspace and the number of calibrated degrees of freedom (dof) in the task space are reduced in accordance with the difficulty measure of the task. An automatic measurement system for measuring the relative robot accuracy was developed. An original principle of transforming the robot endpoint approach distance into the one-dimensional position displacement error is introduced. The accuracy errors of each particular calibrated dof in the task space is measured separately. The error tables are used in a direct robot calibration procedure that is based on the linear interpolation of the discrete position-error functions. An iterative inverse calibration algorithm used in a particular robot cell is described. An efficient sensor-based system for an additional simultaneous robot periphery calibration is presented. The implementation of the proposed calibration methodology in the pick-and-place robot cell for Surface Mount Technology (SMT) is presented. © 1994 John Wiley & Sons, Inc.     

A biomimetic approach to inverse kinematics for a redundant robot arm

Redundant robots have received increased attention during the last decades, since they provide solutions to problems investigated for years in the robotic community, e.g. task-space tracking, obstacle avoidance etc. However, robot redundancy may arise problems of kinematic control, since robot joint motion is not uniquely determined. In this paper, a biomimetic approach is proposed for solving the problem of redundancy resolution. First, the kinematics of the human upper limb while performing random arm motion are investigated and modeled. The dependencies among the human joint angles are described using a Bayesian network. Then, an objective function, built using this model, is used in a closed-loop inverse kinematic algorithm for a redundant robot arm. Using this algorithm, the robot arm end-effector can be positioned in the three dimensional (3D) space using human-like joint configurations. Through real experiments using an anthropomorphic robot arm, it is proved that the proposed algorithm is computationally fast, while it results to human-like configurations compared to previously proposed inverse kinematics algorithms. The latter makes the proposed algorithm a strong candidate for applications where anthropomorphism is required, e.g. in humanoids or generally in cases where robotic arms interact with humans.     

Adaptive hierarchical positioning error compensation for long-term service of industrial robots based on incremental learning with fixed-length memory window and incremental model reconstruction

Industrial robots have been extensively used in industry, however, geometric errors mainly caused by connecting rod parameter error and non-geometric errors caused by deflection and friction, etc., limit its application in high-accuracy machining. Aiming at addressing these two types of errors, parametric methods for error compensation based on the kinematic model and non-parametric methods of directly establishing the mapping relationship between the actual and target poses of the robot end-effector are investigated and proposed. Currently both types of methods are mainly offline and will be no longer applicable when the pose of the end-effector in the workspace changes dramatically or the working performance of the robot degrades. Thus, to compensate the positioning error of an industrial robot during long-term operation, this research proposes an adaptive hierarchical compensation method based on fixed-length memory window incremental learning and incremental model reconstruction. Firstly, the correlation between positioning errors and robot poses is studied, a calibration sample library is created, and thus the actively evaluating mechanism of the pose mapping model is established to overcome the problem of the robot’ workspace having a differential distribution of error levels. Then, an incremental learning algorithm with fixed-length memory window and an incremental model reconstruction algorithm are designed to optimize the pose mapping model in terms of its parameters and architecture and overcome the problem that the performance degradation of the robot exacerbates the positioning error and affects the applicability of the pose mapping model, ensuring that the pose mapping model runs stably above the target accuracy level. Finally, the proposed method is applied to the long-term compensation case of a Stäubli industrial robot and a UR robot, and compared to state-of-art methods. Verification results show the proposed method reduces the position error of the Stäubli robot from 0.85mm to 0.13mm and orientation error from 0.68° to 0.07°, as well as reduces the position error of the UR robot from 2.11mm to 0.17mm, demonstrating that the proposed method works in real world scenarios and outperforms similar methods.     

Robot calibration using the CPC error model

The complete and parametrically continuous (CPC) robot kinematic modeling convention has no model singularities and allows the modeling of the robot base and tool in the same manner by which the internal links are modeled. These two properties can be utilized to construct robot kinematic error models employing the minimum number of kinematic error parameters. These error parameters are independent and span the entire geometric error space. The BASE and TOOL error models are derived as special cases of the regular CPC error model. The CPC error model is useful for both kinematic identification and kinematic compensation. This paper focuses on the derivation of the CPC error models and their use in the experimental implementation of robot calibration.     

Measurement and analysis of structural dynamics properties of robotic joint transmission system

The flexibility of a robotic manipulator is considered an important factor, especially the joint compliance for improving the accuracy and operating speed of a robot application. In this article, two methods are employed to identify the structural dynamic characteristics of each joint transmission system of an ITRI-U type robot. The driving system of each joint is modeled as a mass-spring-damper mechanism that has a second-order dynamic mathematical equation. Then, the response experiments of hammer impact excitation and motor driving actuation are done and the difference between them compared. Those are used to simulate two different operation situations, the robot colliding with the environment and the discontinuing dynamic operation impacts. The system's parameters of each joint axis are obtained by the system identification technique. From the experimental results, the angular error of the motor shaft can be compensated by the control gain of the motor controller. However, the small damping ratio of the robotic mechanism limits the magnitude of servo gain. If the servo gain increases, the robot arm has oscillation phenomenon during dynamic operation. In addition, the error due to joint elasticity cannot be overcome by the current industrial robotic controller. Therefore, a suitable controller should be designed to compensate the dynamic effects of joint compliance with the identified parameters.     

Robot manipulator kinematic compensation using a generalized jacobian formulation

The kinematic error compensation of robot manipulators is at present being attempted by improving the precision of the nominal robot kinematic parameters. This paper addresses the problem of kinematic compensation using a new mathematical joint model proposed to account for shortcomings in existing methods. The corrected manipulator transformation is formulated in terms of “generalized Jacobians”: relating differential errors at the joints to the differential change in the manipulator transformation. The details of application are discussed for a particular industrial manipulator.