Modified Denavit Hartenberg Research Articles

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.

Dynamic Analysis and Path Planning of a Turtle-Inspired Amphibious Spherical Robot.

A dynamic path-planning algorithm based on a general constrained optimization problem (GCOP) model and a sequential quadratic programming (SQP) method with sensor input is proposed in this paper. In an unknown underwater space, the turtle-inspired amphibious spherical robot (ASR) can realise the path-planning control movement and achieve collision avoidance. Due to the special underwater environments, thrusters and diamond parallel legs (DPLs) are installed in the lower hemisphere to realise accurate motion control. A propulsion model for a novel water-jet thruster based on experimental analysis and a modified Denavit-Hartenberg (MDH) algorithm are developed for multiple degrees of freedom (MDOF) to realize high-precision and high-speed motion control. Simulations and experiments verify that the effectiveness of the GCOP and SQP algorithms can realize reasonable path planning and make it possible to improve the flexibility of underwater movement with a small estimation error.

A positioning error compensation method for multiple degrees of freedom robot arm based on the measured and target position error

A novel positioning error compensation method (PECM) based on the measured and target position error for multiple degrees of freedom (DOF) robot arm control is proposed, which is used to improve positioning accuracy of multiple-DOF robot arm end-effector in accurate positioning applications such as in the medical and mechanical fields. Based on the idea of PID to increase adaptiveness and robustness of the method, a positioning compensation model between the measured and target position error tracked by an optical tracking system and compensated joint angle is derived with inverse kinematic model. Based on error analysis of the compensation model regarding geometry errors, the proportional joint angle compensated coefficient deduced from Jaccobian matrix of the error is proposed and identified with position error data. Calibration experiments for position conversion matrix and positioning accuracy verification experiments are conducted consisting of an optical tracking system and a robot arm. The results of positioning accuracy verification experiments show that the average resultant positioning error in three directions reduces from 1.89 mm (before compensation, model based on Denavit-Hartenberg (DH)), 0.39 mm (model based on modified Denavit-Hartenberg (MDH) with Levenberg-Marquardt (LM)) to 0.34 mm (decreasing 82%, 15%), which demonstrates the efficiency and robustness of the method.

Error modeling and compensating of a novel 6-DOF aeroengine rotor docking equipment

In the docking process of aeroengine rotor parts, docking accuracy that indicates the gaps between the end faces is strictly required. A key issue is improving docking accuracy using automated docking equipment. In this paper, a systematic study is carried out on the error modeling and compensation of a novel six-degrees-of-freedom (6-DOF) docking equipment for aeroengine rotors. First, a new model for indicating the main indexes of docking accuracy is proposed. Then, the error model of a specially designed 6-DOF docking equipment is established based on a modified Denavit Hartenberg method with five parameters. Subsequently, two error compensation methods are proposed. Based on the above models, a docking accuracy simulation algorithm is proposed using the Monte Carlo method. Finally, verification experiments are conducted. The results show that, for the maximum values and standard deviations of the gaps between the rotor end-faces in the actual and target positions and attitudes, i.e., main indexes that represent docking accuracy, the deviation rates between the simulation and experimental results are less than 20%. The modeling methods have referential significance. The decline rates of these values are 50–65% when using the two proposed compensation methods. The compensation methods significantly improve the docking accuracy.

Compensation for absolute positioning error of industrial robot considering the optimized measurement space

Industrial robots are getting widely applied due to their low use-cost and high flexibility. However, the low absolute positioning accuracy limits their expansion in the area of high-precision manufacturing. Aiming to improve the positioning accuracy, a compensation method for the positioning error is put forward in terms of the optimization of the experimental measurement space and accurate modelling of the positioning error. Firstly, the influence of robot kinematic performance on the measurement accuracy is analysed, and a quantitative index describing the performance is adopted. On this basis and combined with the joints motion characteristics, the optimized measurement space in joint space as well as Cartesian space is obtained respectively, which can provide accurate measurement data to the error model. Then the overall model of the positioning error is constructed based on modified Denavit–Hartenberg method, in which the geometric errors and compliance errors are considered comprehensively, and an error decoupling method between them is carried out based on the error-feature analyses. Experiments on the KUKA KR210 robot are carried out finally. The mean absolute positioning accuracy of the robot increases from 1.179 mm to 0.093 mm, which verifies the effectiveness of the compensation methodology in this article.

Plane kinematic calibration method for industrial robot based on dynamic measurement of double ball bar

A new calibration method is proposed to improve the circular plane kinematic accuracy of industrial robot by using dynamic measurement of double ball bar (DBB). The kinematic model of robot is established by the MDH (Modified Denavit-Hartenberg) method. The error mapping relationship between the motion error of end-effector and the kinematic parameter error of each axis is calculated through the Jacobian iterative method. In order to identify the validity of the MDH parameter errors, distance errors and angle errors of each joint axis were simulated by three orders of magnitude respectively. After multiple iterations, the average value of kinematic error modulus of end-effector was reduced to nanometer range. Experiments were conducted on an industrial robot (EPSON C4 A901) in the working space of 180 mm × 490 mm. Due to the measuring radius of DBB, the working space was divided into 30 sub-planes to measure the roundness error before and after compensation. The average roundness error calibrated by the proposed method at multi-planes decreased about 21.4%, from 0.4637 mm to 0.3644 mm, while the standard deviation of roundness error was reduced from 0.0720 mm to 0.0656 mm. In addition, by comparing the results of positioning error measured by the laser interferometer before and after calibration, the range values of motion errors of end-effector were decreasing by 0.1033 mm and 0.0730 mm on the X and Y axes, respectively.

Research on robot kinematic calibration based on hand-eye vision and distance error model

Based on the Modified Denavit-Hartenberg (MDH) kinematic model of industrial robot, the homogeneous transformation error model between the coordinates of each joint is established; The distance error model is combined with the established homogeneous transformation error model to obtain the kinematic calibration model based on distance error avoiding the transformation of the coordinate system; Then, the position of the robot’s end point is measured by using tahe visual measurement method, and the calibration model is introduced to simplify the calculation and improve the accuracy of the measurement; Finally, the ABB1410 robot is used as the experimental object. Through the compensation and correction of each joint parameter, the experimental results prove that the positioning accuracy and distance accuracy of the robot can be greatly improved, and it can be applied to the experimental industrial field.

Coupled longitudinal/lateral controllers for autonomous vehicles navigation, with experimental validation

In this work, the coupled control of the lateral and the longitudinal dynamics of an autonomous vehicle is addressed. As a first step, a multi-body modeling technique is used to develop a four wheeled vehicle planar model. This technique considers the vehicle as a robot consisting of articulated bodies. The geometric description of the vehicle system is derived using the modified Denavit–Hartenberg parameterization and then the dynamic model of the vehicle is computed by applying a recursive method used in robotics, namely Euler–Lagrange based Algorithm. The validation of the developed vehicle model was then conducted using an automotive simulator, the Scaner-Studio simulator. The developed vehicle model is then used to derive coupled control laws for the lateral and the longitudinal vehicle dynamics. Two coupled controllers are proposed: In the first controller, the control is realized using Lyapunov control techniques while in the second one an Immersion and Invariance with sliding mode approach is used. Both of the controllers aim to ensure a robust tracking of the reference trajectory and the desired speed while taking into account the strong coupling between the lateral and the longitudinal vehicle dynamics. In fact, the coupled controller is a key step for the vehicle safety handling, especially in coupled maneuvers such as lane-change maneuvers, obstacle avoidance maneuvers and combined maneuvers in critical driving situations.The developed controllers were validated in simulation under Matlab/Simulink using experimental data. Subsequently, an experimental validation of the proposed controllers was conducted using a robotized vehicle (Renault-ZOE) present in the Heudiasyc laboratory within the Equipex Robotex project.

New Forward Kinematic Model of Parallel Robot Par4

Modeling parallel robots is a famous problem of research especially the Forward Kinematic Model (FKM). It is very difficult to solve it compared to serial manipulators and it is also hard to obtain its analytic solution. Most researchers have resorted to the numerical methods. But, these have a lot of problems : the divergence caused by the bad choice of the initial condition and providing more than one feasible solution. To solve these problems, an analytical method is proposed in this article. In this paper, the FKM of the parallel robot Par4 is determined using the Modified Denavit Hartenberg Method (MDHM). This method facilitates greatly the forward kinematic problem of parallel robot. The MDHM is powerful, useful and can be easily used for the closed loop robots. It is very accurate and provides a unique solution. In the best of our knowledge, the MDHM isn’t applied to the parallel robot Par4 to give a relationship between its operational and articular variables. After a short presentation of the robot Par4, the FKM is determined using the MDHM method. The results of this method will be compared to the existing numerical method like the iterative Newton method (INM).

Locomotion analysis and optimization of actinomorphic robots with soft arms actuated by shape memory alloy wires

This article presents the locomotion analysis and optimization of actinomorphic soft robots, which are composed of soft arms actuated by shape memory alloy wires. The soft arm that is a composite modular structure is actuated by a self-sensing feedback control strategy. A theoretical model was established to describe the deformation of the soft arm, combining the Euler–Bernoulli beam model of the soft arm with the constitutive model and the heat transfer model of the shape memory alloy wire. The kinematics of the actinomorphic soft robot was analyzed using the modified Denavit–Hartenberg method, and the motion equation of the actinomorphic soft robot was presented based on the quasi-static hypothesis. Results show that the actinomorphic soft robot moves with a zig-zag pattern. The locomotion of four actinomorphic soft robots with three to six arms was analyzed, and the gait parameters of each locomotion type were optimized. The optimization results indicate that the three-arm actinomorphic robot with certain gait parameters has the best performance and achieves a maximum stride length of 75 mm. A series of experiments were conducted to investigate the movement performance of the three-arm actinomorphic robot in various environments.

Kinematic calibration and investigation of the influence of universal joint errors on accuracy improvement for a 3-DOF parallel manipulator

This paper focuses on the accuracy enhancement of a 3-PRRU parallel manipulator and the influence of imperfect universal joints on calibration result through kinematic calibration. The error model of the PRRU limb that contains all of the identifiable kinematic errors is established based on modified Denavit–Hartenberg method and Hayati convention. By eliminating the motion errors of passive joints and combining all of the limbs’ error models, the calibration model of the parallel manipulator is obtained. To verify the effectiveness of the error model and investigate the influence of the imperfect universal joints on positioning accuracy improvement, numerical simulations and experiments of kinematic calibration are respectively conducted and total least squares method is used to identify the kinematic parameters. The results of the simulations and experiments show that the defects of universal joints have smaller effect on the accuracy improvement for this manipulator when compared with the cases that the universal joints are perfectly manufactured and assembled.

Structural parameter identification for 6 DOF industrial robots

Abstract To decrease the movement uncertainty of industrial robots, a parameter identification method based on the Denavit-Hartenberg (DH) model is presented in this paper, where the redundant parameters are particularly addressed in the identifier procedure. In order to be consistent with the kinematic model used in robot controllers, we use DH method to establish the kinematic model instead of the modified DH (MDH) method that was used in most identification schemes. The kinematic model of a 6 degree of freedom (DOF) industrial robot is first developed, which is linearized to obtain the parameter identification coefficient matrix. Further analysis shows that this matrix is not with full rank, which means some parameters in this matrix are linearly dependant. This fact makes the direct identification of unknown parameters in this matrix unfeasible. To solve this problem, singular value decomposition (SVD) is used to determine the redundant parameters, which are then removed from the matrix. Then, an alternative identification algorithm with a modified least-square scheme is suggested to estimate the structural parameters of the robot. For this purpose, an identification calculation scheme is designed to minimize the residual movement uncertainties. Experimental studies based on a 6 DOF industrial robot show that the proposed identification method, which detects and removes the redundant parameters, can greatly reduce the residual movement uncertainties and calculation costs. Thus, this newly proposed method can improve the movement accuracy of the industrial robot significantly.

A unified dynamic algorithm for wheeled multibody systems with passive joints and nonholonomic constraints

This paper presents a systematic approach to develop a generalized symbolic/numerical dynamic algorithm for modeling and simulation of multibody systems with branches and wheels. The proposed dynamic algorithm includes the direct kinematic and inverse dynamic models of the wheeled systems with prismatic/revolute as well as actuated/passive degrees of freedom. Using the geometric configuration of the system through modified Denavit–Hartenberg convention, symbolic equations in general algorithmic form are developed for kinematic constraints associated with the wheel–ground contacts. The Newton–Euler equations are used to develop an algorithm for the inverse dynamic model of the multibody system. The complete algorithm is then used to solve the kinematics and dynamics of the system, and computes: (i) the kinematics of the external/internal passive degrees of freedom of the system, (ii) the Lagrange multipliers associated with the wheel–ground contacts, and (iii) the driving forces/torques of the actuated degrees of freedom. Some examples are solved with the help of the proposed algorithm, using MATLAB, to illustrate its implementation on different wheeled systems. These examples include a differential wheeled robot, a snake-like wheeled system, and a bicycle.

Two Error Models for Calibrating SCARA Robots based on the MDH Model

This paper describes the process of using two error models for calibrating Selective Compliance Assembly Robot Arm (SCARA) robots based on the modified Denavit-Hartenberg(MDH) model, with the aim of improving the robot's accuracy. One of the error models is the position error model, which uses robot position errors with respect to an accurate robot base frame built before the measurement commenced. The other model is the distance error model, which uses only the robot moving distance to calculate errors. Because calibration requires the end-effector to be accurately measured, a laser tracker was used to measure the robot position and distance errors. After calibrating the robot and, the end-effector locations were measured again compensating the error models' parameters obtained from the calibration. The finding is that the robot's accuracy improved greatly after compensating the calibrated parameters.

A distance error based industrial robot kinematic calibration method

Purpose– The purpose of this paper is to present a distance accuracy-based industrial robot kinematic calibration model. Nowadays, the repeatability of the industrial robot is high, while the absolute positioning accuracy and distance accuracy are low. Many factors affect the absolute positioning accuracy and distance accuracy, and the calibration method of the industrial robot is an important factor. When the traditional calibration methods are applied on the industrial robot, the accumulative error will be involved according to the transformation between the measurement coordinate and the robot base coordinate.Design/methodology/approach– In this manuscript, a distance accuracy-based industrial robot kinematic calibration model is proposed. First, a simplified kinematic model of the robot by using the modified Denavit–Hartenberg (MDH) method is introduced, then the proposed distance error-based calibration model is presented; the experiment is set up in the next section.Findings– The experimental results show that the proposed calibration model based on MDH and distance error can improve the distance accuracy and absolute position accuracy dramatically.Originality/value– The proposed calibration model based on MDH and distance error can improve the distance accuracy and absolute position accuracy dramatically.

Errors Analysis and Calibration on Measuring Mechanical Arm for EVA Spacesuit Ergonomics Research

A combined coordinate measuring mechanical arm (CCMMA) was developed to test the operational ability of astronaut in the EVA spacesuit. The equipment measures the space region coordinates of the astronaut’s hand-reach while forces act on a handle. The homogeneous transformation equations of CCMMA are established based on Modified Denavit-Hartenberg (MDH). Measurement error was analyzed and distance error model of CCMMA was set up to improve measurement precision. The improved genetic algorithm is applied to the identification of CCMMA structure parameters. The calibration experiment of CCMMA was carried out using such model and algorithm. The result showed that with identification, the repeatability and length measurement precision were improved by 5.38 and 3.11 times respectively.

An effective-wire-radius compensation scheme for enhancing the precision of wire-cut electrical discharge machines

Using a modified Denavit–Hartenberg (D–H notation), we propose with this study a methodology for generating the wire-radius-compensated NC data equations required to carry out the machining of non-column workpieces on a five-axis wire-cut electrical discharge machine (WEDM). In the proposed approach, the designed surfaces of the machined component are constructed using a 4 × 4 homogeneous transformation matrix and ruled surfaces. The modified D–H notation is then employed to derive the machine’s ability matrix and to generate the desired wire location matrices. To ensure the precision of the machining operation, the wire location matrices are modulated by a novel effective-wire-radius compensation scheme. Finally, the NC data equations required to machine the component are derived by equating the ability matrix with the modulated wire location matrix. To validate the proposed methodology, three non-column workpieces with various top and bottom basic curves are machined on a commercial WEDM. The dimensions of the machined components are then compared with those of specimens machined using the built-in WEDM compensation scheme. The results show that the components manufactured using the proposed effective-wire-radius compensation scheme are more geometrically precise than those produced using the conventional WEDM compensation method.

The mathematical models of the basic entities of multi-axis serial orthogonal machine tools using a modified Denavit–Hartenberg notation

The use of virtual techniques as a means of training operators and familiarizing them with the machine tools on which they work has become increasingly widespread throughout the manufacturing industry in recent years. To support the development and implementation of virtual machine tools, this paper constructs the generic mathematical models of the basic building links, joint types, and cutting tools of multi-axis serial orthogonal machine tools. The modeling methodology can support the synthesis of various machine tools with different configurations but similar functions and facilitates the processes of error analysis, numerical control data generation, parameter measurement, and cutting kinematics analysis. The validity of the modeling approach is demonstrated using a six-axis serial orthogonal machine tool for illustration purposes.

Dynamic Modeling and Identification of a Complex-structured Parallel Robot

In this paper a new strategy for dynamic modeling and parameter identification of complex parallel robots including parallel crank mechanisms is presented. Based on a model reduction strategy motivated by the structure of the parallel robot SpiderMill, kinematics and dynamics are derived in a compact form applying the modified Denavit Hartenberg method and the Newton-Euler approach. The obtained parameter-linear inverse dynamical description is reduced to a parameter-minimal form applying only an analytical reduction method. The rigid body parameters of the inverse dynamic model are identified by using optimized trajectories and linear estimators. Due to exclusively analytical reduction a physical interpretation of the parameters is possible. Through the whole modeling and verification process verified MSC.ADAMS models and Solid Edge models of the demonstrator SpiderMill are used.

Modeling and measurement of active parameters and workpiece home position of a multi-axis machine tool

The complex structures of a multi-axis machine tool may produce inaccuracies at the tool tip caused by dimensional errors in the machine's link parameters. This paper addresses two important issues for precision machining: (1) which link parameters (denoted as active parameters) of a machine tool can affect the machining accuracy of a workpiece and (2) how to measure the active parameters by using a grinding wheel as a measuring probe. To achieve this, a modified Denavit–Hartenberg (D–H) notation is introduced to model a multi-axis machine tool. The NC data equations are then derived in terms of the machine's link parameters. It is found that the link parameters of a machine tool can be divided into two types: active and nonactive parameters. The prerequisite for obtaining an accurately machined workpiece is to have correct values of the active parameters and the workpiece home position. Based on the developed NC data equations of a multi-axis machine tool, this paper also addresses the technique of using a grinding wheel as a measuring probe to determine the active parameters and the workpiece home position. Experimental results are also given with illustrative examples.