Modified Denavit Hartenberg Research Articles

Investigation of axis-fitting-based measurement and identification techniques for kinematic parameters in multi-joint industrial robots

To improve the positioning accuracy of industrial robots and meet the requirements of industrial applications, this study begins with the structural design of multi-jointed industrial robots and proposes a kinematic calibration method based on axis fitting. The proposed method introduces an axis fitting technique based on circle fitting. Utilizing the results of the axis fitting, a method for establishing link coordinate systems by referencing the Modified Denavit-Hartenberg (MD-H) model is presented. Subsequently, a kinematic parameter identification method is proposed. This study primarily investigates the impact of joint rotation angles on the accuracy of axis fitting. The study reveals that when the rotation angle is greater than or equal to 20°, the circularity of the circle fitting is less than 0.008 mm, and the planarity is less than 0.01 mm, indicating that the proposed fitting algorithm meets the required precision for small angle rotations. Finally, the positioning accuracy of the target robot is verified according to ISO 9283:1998. After calibration, the positioning accuracy at point P1 improves from 1.64 mm to 0.46 mm, an enhancement of 71.95 %, which is the most significant improvement. At point P2, the positioning accuracy improves from 1.75 mm to 0.69 mm, an enhancement of 60.5 %, which is the least improvement. The advantage of this method lies in its ability to identify kinematic parameters that align with the actual structure of the robot using a simple measurement method, thereby improving the robot's positioning accuracy.

Research on the Optimal Trajectory Planning Method for the Dual-Attitude Adjustment Mechanism Based on an Improved Multi-Objective Salp Swarm Algorithm

In this study, an optimization method for the motion trajectory of attitude actuators was investigated in order to improve assembly efficiency in the automatic docking process of large components. The self-developed dual-attitude adjustment mechanism (2-PPPR) is used as the research object, and the structure is symmetrical. Based on the modified Denavit–Hartenberg (MDH) parameter description method, a kinematic model of the attitude mechanism is established, and its end trajectory is parametrically expressed using a five-order B-spline curve. Based on the constraints of the dynamics and kinematics of the dual-posture mechanism, the total posturing time, the degree of urgency of each joint, and the degree of difficulty of the mechanism’s posturing are selected as the optimization objectives. The Lévy flight and Cauchy variation algorithms are introduced into the salp swarm algorithm (SSA) to solve the parameters of the multi-objective trajectory optimization model. By combining the evaluation method of the multi-objective average optimal solution, the optimal trajectory of the dual-tuning mechanism and the motion trajectory of each joint are obtained. The simulation and experiment results show that the trajectory planning method proposed in this paper is effective and feasible and can ensure that the large-part dual-posture mechanism can complete the automatic docking task smoothly and efficiently.

Two-step calibration of 6-DOF industrial robots by grouping kinematic parameters based on distance constraints

The positioning accuracy of industrial robots is critical for their applications, which can be improved through calibration. This paper proposes a two-step calibration method for six-degree-of-freedom (6-DOF) industrial robots to reduce couplings of their modified Denavit-Hartenberg (MD-H) model parameters during optimization processes of kinematic calibration. In this method, a distance error model is established based on the distance constraints, and the MD-H model parameters of the industrial robots are identified group by group using the Levenberg-Marquardt (LM) algorithm. To determine the optimal MD-H model parameter grouping, the different grouping strategies are simulated and analyzed. In the proposed method, the coordinate system transformation between the measurement frame and the robot base frame can be avoided based on the distance error model, thereby reducing the errors introduced by the coordinate system transformation during the calibration process. Finally, the proposed two-step calibration method is verified through an experiment. The experimental result shows that the distance/positioning accuracy on the robot end-effector is improved from 0.602 mm/2.7317 mm to 0.151 mm/0.717 mm after calibration. The presented study may be beneficial for improving performance of industrial robots.

Trajectory Tracking Algorithm Study of Coal Mine Water Detector Drilling Bar Installation

Mechanical water detection is recognized as the most reliable and safe production technology for coal mines, mainly for the detection of water hazards in pre-mining operations. Intelligent water detectors are currently the main research direction in mechanical water detection, and the automatic installation of drilling bars is the key to achieving intelligent water detection. Improving the connection accuracy in the process of installing drilling bars is an important research topic for the improvement of control links. To improve the connection accuracy of the drilling bars at the time of supplying material, we used the modified Denavit–Hartenberg method to analyze the motion gestures of the supplied material device and the Lagrange equation to establish a dynamic analysis model. We aimed at better control precision by improving the sliding mode control algorithm and at increasing the convergence rate of tracking errors with a sliding controller based on an exponential approximation law and using saturated functions instead of the symbol functions in the reaching law to weaken the vibration in the control process. We then used particle swarm optimization (PSO) to find the optimum combination parameters of the sliding mode controllers and test the performance of the sliding mode controllers before and after PSO with MATLAB/Simulink. The results showed that the optimized controller has a strong resistance to parameter fluctuations, and the system responds quickly, achieves a good performance, and improves the convergence rate of tracking errors.

Rapid Tracking Satellite Servo Control for Three-Axis Satcom-on-the-Move Antenna

To overcome the possible gimbal lock problem of the dual-axis satcom-on-the-move (SOTM) antenna, a three-axis tracking satellite SOTM antenna structure appears. The three-axis SOTM antenna is realized by adding a roll axis to the azimuth axis and pitch axis in the dual-axis SOTM structure. There is coupling among the azimuth axis, pitch axis and roll axis in the mechanical structure of the three-axis SOTM antenna, which makes the kinematic modeling of the antenna difficult. This paper introduces a three-axis SOTM antenna kinematic modeling method based on the modified Denavit–Hartenberg (MDH) method, named the new modified Denavit–Hartenberg (NMDH) method. In order to meet the modeling requirements of the MDH method, the NMDH method adds virtual coordinate systems and auxiliary coordinate systems to the three-axis SOTM antenna and obtains the kinematic model of the three-axis SOTM antenna. During the motion of the carrier, the SOTM antenna needs to adjust the antenna pointing in real time according to the changes of the location and attitude of the moving carrier. Therefore, this paper designs a servo control system based on the active disturbance rejection controller (ADRC), introducing a smooth and continuous ADRC fal function to enhance the tracking speed of the servo control system and reduce the overshoot of the output response. Finally, system experiments were carried out with a 60 cm caliber three-axis SOTM antenna. The experiment results show that the proposed servo control method achieves higher antenna tracking satellite accuracy and better communication effects.

Multibody dynamics modeling and simulation of a three-wheeled mobile robot using a robotic approach

PurposeThis paper focuses on the application of a robotic technique for modeling a three-wheeled mobile robot (WMR), considering it as a multibody polyarticulated system. Then the dynamic behavior of the developed model is verified using a physical model obtained by Simscape Multibody.Design/methodology/approachFirstly, a geometric model is developed using the modified Denavit–Hartenberg method. Then the dynamic model is derived using the algorithm of Newton–Euler. The developed model is performed for a three-wheeled differentially driven robot, which incorporates the slippage of wheels by including the Kiencke tire model to take into account the interaction of wheels with the ground. For the physical model, the mobile robot is designed using Solidworks. Then it is exported to Matlab using Simscape Multibody. The control of the WMR for both models is realized using Matlab/Simulink and aims to ensure efficient tracking of the desired trajectory.FindingsSimulation results show a good similarity between the two models and verify both longitudinal and lateral behaviors of the WMR. This demonstrates the effectiveness of the developed model using the robotic approach and proves that it is sufficiently precise for the design of control schemes.Originality/valueThe motivation to adopt this robotic approach compared to conventional methods is the fact that it makes it possible to obtain models with a reduced number of operations. Furthermore, it allows the facility of implementation by numerical or symbolical programming. This work serves as a reference link for extending this methodology to other types of mobile robots.

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.

The structure design and kinematics analysis of the manipulator for the upper port remote maintenance in DEMO

As part of the upper port remote maintenance in DEMO, the design of seven degrees of freedom (DOFs) redundant manipulator with a ceiling-mounted configuration was presented in this work. The proposed manipulator is capable of flexibly maneuvering around the big manipulator, extracting the stop elements, and placing them into a basket. It can also fold itself to create more space for the operation of the big manipulator. The kinematic model of the redundant manipulator was established based on the application of the Modified Denavit-Hartenberg (MDH) method, and an unconstrained optimization equation was formulated using quaternions. To solve this equation, an improved artificial bee colony (IABC) algorithm was developed by enhancing the local search capability of the employed bees and improving the search efficiency of the observation bees. The feasibility of the structural design and the IABC algorithm was verified by carrying out trajectory planning simulations of the manipulator. The design of the 7 DOFs manipulator and the corresponding offline inverse kinematics algorithm provide valuable references for the maintenance work in the upper port remote maintenance of the DEMO.

Kinematics Parameter Calibration of Serial Industrial Robots Based on Partial Pose Measurement

The kinematics parameter error is the main error factor that affects the absolute accuracy of industrial robots. The absolute accuracy of industrial robots can be effectively improved through kinematics calibration. The error model-based method is one of the main methods for calibrating the kinematics parameter error. This paper presents a kinematics parameter calibration method for serial industrial robots based on partial pose measurement. Firstly, the kinematics and the pose error models have been established based on the modified Denavit–Hartenberg (MDH) model. By introducing the concept of error sensitivity, the average significance index is proposed to quantitatively analyze the effects of the kinematics parameter error on the pose error of a robot. The results show that there is no need to measure the full pose error of the robot. Secondly, a partial pose measurement device and method have been presented. The proposed device can measure the position error and the attitude error on the x-axis or y-axis. Finally, the full pose error model, the NP-type partial pose error model, and the OP-type partial pose error model have been applied for calibrating the kinematics parameter errors. The experimental results show that the effectiveness of the OP-type partial pose error model is consistent with the full pose error model.

Kinematic analysis of a finger-mimicking pneumatic network actuator consisting of parallelogram-shaped chambers

Fast pneumatic network (fast Pneu-Net, fPN) actuators made of silicone materials have aroused increasing attention these years for their promising applications in soft robotics. To enrich current research, we present a novel fPN actuator that consists of parallelogram-shaped chambers and aluminum endoskeleton that takes the shape of human finger. The proposed actuator can bend at multi-positions when inflated, bringing about more degrees of freedom controllability. Additionally, the performed finite element analysis indicates that the parallelogram-shaped chamber that tilts 30° towards the distal end exhibits an increase in deformation for about 11 % compared to the rectangle-shaped counterpart, offering an improved bending performance. An analytical model that based on the pressurized hyperelastic membrane theory is developed to estimate the actuator’s bending angles/profiles at varied pressures. Geometric relation of the chamber interactions upon deformation is discussed depending on whether the lateral walls are contact or not. The stress-strain relation of the elastomer is described using 3-term Yeoh constitutive model. Experimental validations on the theoretical calculations are carried out, from which the coefficient of proportionality that takes into account the effect on deformation caused by the embedded endoskeleton is determined. Furthermore, the Modified Denavit-Hartenberg (MDH) notation is employed to establish the forward kinematics of the actuator, and the numerical calculations are compared with the physical actuator.

Design and Analysis of Bionic Continuum Robot With Helical Winding Grasping Function

Abstract In the field of grasping application, continuum robots are characterized by flexible grasping and high adaptability. Based on research on the physiological structure and winding method of seahorses, a continuum robot with a helical winding grasping function is presented in this paper. The continuum robot is driven by cables and uses a new flexural pivot with large deformation as a rotation joint. Firstly, based on the Serret–Frenet frame of the spatial cylindrical helix, the helical winding continuum robot is modeled and solved. The change rules of parameters such as the rotation angle of the joint and the helix parameters under the helical winding method are derived. Then, the compliance matrix of the joint is solved using the structural matrix method, and a stiffness model is established to analyze the relationship between the load and deformation of the continuum robot. The kinematics model of the continuum robot is established by using the modified Denavit–Hartenberg parameter method. The static model of the continuum robot is solved by vector analysis under the condition of considering gravity, and the relationship between the length change of cables and joint curvature is obtained. Finally, the stiffness model and static model of the continuum robot are verified by simulations and experiments. The test results show that within a certain radial range, the continuum robot has the function of helical winding and grasping for objects. Compared to the previous imitation seahorse tail robot, the helical winding structure not only provides a larger grasping area compared to in-plane form but also achieves a better bionic effect.

Development of an automatic control system for a hydraulic pruning robot

Automatic pruning is capable of trimming trees into complex shapes efficiently and continuously. However, this technology faces more challenges under unstructured agricultural environments. In the present paper, we describe the development of a hydraulic disc-saw mounted pruning robot with a relatively low cost for automated geometric pruning of fruit trees based on a new automatic pruning scenario. A pruning control strategy based on rolling observations and continuous prediction algorithm was designed to precisely control the motion of hydraulic cylinders. A forward kinematic model was described using modified Denavit–Hartenberg (D-H) notation, and the accessible workspace for the end-effector was analyzed in the simulation. The inverse kinematics model based on geometry was established, which provided the foundation for the development of a control system together with the forward kinematics model. Performance tests showed a sufficient control accuracy within ± 1.8° of all cylinders. The results of the waypoint tracking tests suggest that an increase in the step-size from 20 mm to 60 mm not only increases the moving speed and improves tracking accuracy, but also increases the fluctuation of the end-effector in the Z-axis direction. The movement of the chassis can introduce new errors and results in a larger average absolute positional error along the X-axis. The average startup and stop lag of the control system was 0.55 s and 0.15 s, respectively. This study provides guidance for pruning robot path planning and lays the foundation for future iterations of autonomous pruning robots.

Error Modeling and Parameter Calibration Method for Industrial Robots Based on 6-DOF Position and Orientation

The positional accuracy and orientation accuracy of industrial robots are crucial technical indicators for determining their applicability in industrial scenarios. However, the majority of current calibration methods for industrial robots only consider positional errors, neglecting the significance of orientation accuracy. This paper presents a more accurate error model and parameter calibration method for industrial robots based on six degrees-of-freedom position and orientation to identify the actual structural parameters. Firstly, based on the modified Denavit–Hartenberg parameters, the transformation errors of the tool coordinate system and measurement coordinate frame were introduced to establish a geometric parameter error model with positional and orientation accuracy as the optimization objectives. Secondly, to address the drawback of falling into local optima when identifying geometric parameters simultaneously, a geometric parameter cross-identification method based on the Levenberg–Marquardt algorithm is proposed. Lastly, the linear relationship between the parameters was analyzed, and a scheme for not calibrating some geometric parameters under specific conditions was given. Simulation results demonstrated that, under the premise of existing transformation errors, the proposed geometric parameter error model can accurately identify the actual structural parameters of industrial robots. After calibration, the positional error at the robot’s flange end decreased from 1.9536 mm to 0.0122 mm, and the orientation error decreased from 1.46 × 10−2 rad to 1.31 × 10−4 rad. Furthermore, compared to identifying the geometric parameters simultaneously, the proposed cross-identification method has a wider convergence range.

Robot 10 parameter compensation method based on Newton–Raphson method

AbstractIn this study, a novel kinematic calibration method is proposed to improve the absolute positioning accuracy of 6R robot. This method can achieve indirect compensation of the 25 parameters of modified Denavit–Hartenberg (MDH). The procedures of the method are threefold. Firstly, the 25-parameter errors model of MDH is initially established. However, only the errors of 10 parameters can be directly compensated in the 25-parameter errors model, since the inverse kinematics algorithm has to meet Pieper criterion. Subsequently, a calibration method is proposed to improve accuracy of the absolute position, which uses the Newton–Raphson method to transform the 25-parameter errors into 10-parameter errors (namely T-10 parameter model). Finally, the errors corresponding to 10 parameters in the T-10 parameters model are identified through the least square method. The calibration performances of T-10 parameters model are comprehensively validated by experimentation on two ER6B-C60 robots and one RS010N robot. After kinematic calibration, the average absolute positioning accuracy of the three robots can be improved by about 90%. The results indicate that the proposed calibration method can achieve more precise absolute positioning accuracy and has a wider range of universality.

Development of a Compliant Lower-Limb Rehabilitation Robot Using Underactuated Mechanism

Most existing lower-limb rehabilitation robots (LLRR) for stroke and postoperative rehabilitation are bulky and prone to misalignments between robot and human joints. These drawbacks hamper LLRR application, leading to poor arthro-kinematic compatibility. To address these challenges, this paper proposes a novel robot with portability and compliance features. The developed robot consists of an underactuated mechanism and a crus linkage, respectively corresponding to the hip and knee joints. The underactuated mechanism is a new type of remote center of motion (RCM) mechanism with two sets of contractible slider cranks that can reduce the misalignments between robot and human joints. The underactuated mechanism is then optimized using the particle swarm optimization method, and the developed robot’s kinematic analysis is presented. The proposed robot can be simplified as a two-link mechanism with the ability to easily plan its trajectory using the modified Denavit–Hartenberg method. Finally, passive exercise trials demonstrate that the mismatch angles between the human and robot knee joints are less than 2.1% of the range of motion, confirming the feasibility and effectiveness of the proposed robot.

A novel calibration method for kinematic parameter errors of industrial robot based on Levenberg–Marquard and Beetle Antennae Search algorithm

In this paper, a new kinematic parameter error calibration method based on the Levenberg–Marquard and the beetle antennae search algorithm is proposed to enhance the positioning accuracy of the industrial robot. Firstly, the Modified Denavit–Hartenberg model is chosen to establish the kinematic model for the industrial robot. Secondly, the kinematic parameter errors are calibrated by Levenberg–Marquard algorithm and then obtain the kinematic parameter errors of the industrial robot. Thirdly, these kinematic parameter errors are taken as the center values for the initial individual of the beetle antennae search algorithm. The kinematic parameter errors are accurately calibrated using the beetle antennae search algorithm to obtain the best value for the kinematic parameter errors. Finally, experimental verification results demonstrate that the positioning error of the industrial robot is decreased from 0.7332 mm to 0.1392 mm by using the proposed Levenberg–Marquard and beetle antennae search algorithm. The results also demonstrate that the proposed Levenberg–Marquard and beetle antennae search algorithm calibrate the kinematic parameter errors of the industrial robot effectively and enhance the positioning accuracy of the industrial robot significantly.

Identification of Exoskeleton Dynamics Parameters and Control Based on Series Elastic Actuator

The lower limb exoskeleton is used for rehabilitation, assistance and maturing. Taking an exoskeleton based on a serial elastic actuator as an object, a method of dynamic parameter identification is proposed. Firstly, the modular SEA structure is introduced, and the exoskeleton is modeled by using the Modified Denavit-Hartenberg (MDH) method. Then, the exoskeleton dynamic model is derived and linearized. Secondly, the excitation trajectory required for exoskeleton parameter identification is designed, which is optimized by using the genetic algorithm. Then, the exoskeleton is tested by using the excitation trajectory to decouple the dynamic parameters. Finally, the exoskeleton impedance control algorithm based on dynamic compensation is designed and compared with the algorithm without dynamic compensation. The results show that the parameters obtained from the identification algorithm and the control algorithm are effective.

A kinematic modeling scheme of three-axis "Satcom-on-the-Move" antenna based on modified Denavit-Hartenberg method

The current three-axes Satcom-on-the-Move(SOTM) antenna modeling method has some shortcomings, such as low model accuracy, poor portability and so on. In order to solve the above-mentioned shortcomings, a new modified Denavit-Hartenberg(NMDH) kinematics modeling scheme for the three-axes SOTM antenna was proposed. To overcome the modeling difficulties caused by the inherent mechanical structure of the antenna, and meet the requirements of the modified Denavit-Hartenberg(MDH) method, the virtual coordinate system and auxiliary coordinate systems are designed and added respectively on the basis of the MDH method, the forward kinematics model and inverse kinematics solution of the three-axes SOTM antenna are obtained. The correctness of the NMDH modeling scheme is verified by digital simulation. Finally, the system tests are carried out. The test results show that the NMDH modeling scheme proposed in this paper achieves good effect of antenna tracking satellite, and has stronger portability than the system identification modeling method commonly used in engineering.

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.

Dynamic modeling and vibration analysis for defect identification of single-stage gearboxes in the joints of industrial robots with six DOF

In the age of the future industry, many industrial activities have been entrusted to robots due to their ability to improve both accuracy and production. However, during the manufacturing process, the occurrence of defects in the manipulators transmissions can lead to a significant degradation of the product quality, and consequently financial losses. Hence, this paper aims to present a novel methodology to elaborate a robot dynamic model allowing the detection of the defects arising from the transmissions and more precisely the gears faults. First, a geometric model of the robot was developed based on the Modified Denavit-Hartenberg (MDH) approach, to derive the transfer matrices required to model the different components of the robot. Secondly, thanks to these matrices, to the Euler-Lagrange convention and taking into account the assumption of the joint flexibility, the deduction of the global equation of motion of the robot has been performed. The ability of the developed model to detect defects will then be investigated by a series of numerical simulations performed in the case of healthy gears and in the case where a tooth-cracking fault has been introduced, and also under various velocities. Finally, an experimental study and vibration analysis were conducted to validate the results of the numerical simulations and consequently the effectiveness of the proposed model.