Inverse Kinematic Equations Research Articles

Kinematic modeling and control of orthogonal omnidirectional wheeled two-dimensional conveyor platform

This paper proposes an orthogonal omnidirectional wheeled two-dimensional conveyor platform and the inverse kinematic equations based on the cell model and the omnidirectional wheel model are derived, respectively. The two models use the way of the circumcircle of the cargo box and the dot product method to obtain the cell or omnidirectional wheel directly contacted under the cargo box, respectively. This paper uses YOLOV8_OBB and Strong SORT target tracking algorithms to assign tracking IDs to the cargo box and output the box position information. A feedback mechanism for faulty omnidirectional wheels or faulty cells is proposed, where the faulty area is classified as impassable during path planning and the A* path planning algorithm is used for path planning to avoid the faulty area. A visual feedback-based path tracking is adopted to enable timely correction when the cargo box deviates from the established path. The experimental results show that the omnidirectional wheel-based model improves the path-tracking accuracy by 44.52% and reduces the average power consumption by 2.6 times compared to the cell-based model.

Research on designing dynamic model of TITAN-VIII quadruped robot based on the robot structure

Quadruped robots have many advantages over wheeled robots in that they have high mobility and can move on any terrain. However, the control problem of four-legged robots will be more complicated because the robot's kinematic model has a high order and the dynamic process is complicated, so it is necessary to implement order reduction methods when constructing kinematic equations for four-legged robots. The article proposes a simplified method to determine the kinematic equations for four-legged robots called TITAN-VIII. The Denavit-Hartenberg (D-H) rule is used to analyze the forward kinematics. The inverse kinematic equations are determined on the basis of mathematics and the structure of the robot's legs. The research results are simulated on MATLAB Simulink software.

Design, Analysis and Optimization of Four Degrees of Freedom of Parallel Gripper Mechanism for Industrial Automation

Objectives: To obtain the positions, velocities, and acceleration of actuators of the 4-DOF of the parallel gripper, and optimization of the mechanism is carried out to find the optimal dimensions of the mechanism. Methods: Kinematic analysis is carried out to find the positions and velocities of the gripper of the mechanism. The method used to solve the position of the mechanism is inverse kinematics. A source code is written in MATLAB software to find the positions and velocities of the gripper. This software is a computing platform which can solve large size matrices easily which is most suitable for robots. A model of the mechanism is created in CATIA with constraints. The developed CATIA model is used in ANSYS software for structural analysis. The method used for finding optimal dimensions is Genetic algorithms. Optimization is carried out using Genetic Algorithms (GA’s) using the Energy Manipulation Index as an objective for obtaining the optimal dimensions of the parallel gripper mechanism. Finally, ADAMs software is used to simulate the mechanism. Findings: using inverse kinematic equations the results of displacements, velocities, and accelerations obtained for in-plane horizontal motion, and in-plane vertical motion s plotted. After checking the gripper performance, It is observed that the in-plane vertical transmission is better than the in-plane horizontal transmission. Based on the Energy Manipulation Index (EMI), the performance-to-effort ratio of the gripper object is calculated. It tells about the physical significance of energy transfer efficiency. If the energy occupied by the end-effector is higher than the 4-DOF Parallel Gripper achieves higher efficiency and possesses better manipulability performance. Maximum EMI is taken as an objective for optimization using GA. Simulation is carried out using ADAMS software to determine the driving forces or torques. Novelty/improvement: In this paper the performance index EMI is taken as objective to find the optimal dimensions of the 4-DOF of parallel gripper. Keywords: ­ DOF parallel gripper, In­hand manipulation, In­hand twisting, Driving force, Energy Manipulation Index (EMI)

Research on a Support-Free Five-Degree-of-Freedom Additive Manufacturing Method.

When using traditional 3D printing equipment to manufacture overhang models, it is often necessary to generate support structures to assist in the printing of parts. The post-processing operation of removing the support structures after printing is time-consuming and wastes material. In order to solve the above problems, a support-free five-degree-of-freedom additive manufacturing (SFAM) method is proposed. Through the homogeneous coordinate transformation matrix, the forward and inverse kinematics equations of the five-degree-of-freedom additive manufacturing device (FAMD) are established, and the joint variables of each axis are solved to realize the five-axis linkage of the additive manufacturing (AM) device. In this research work, initially, the layered curve is obtained through the structural lines of the overhang model, and a continuous path planning of the infill area is performed on it, and further, the part printing experiments are conducted on the FAMD. Compared with the traditional three-axis additive manufacturing (TTAM) method, the SFAM method shortens the printing time by 23.58% and saves printing materials by 33.06%. The experimental results show that the SFAM method realizes the support-free printing of overhang models, which not only improves the accuracy of the parts but also the manufacturing efficiency of the parts.

Computing The Kinematics Study of a 6 DOF Industrial Manipulator Prototype By Matlab

Since the mechanical parts in the robot are designed to do the movement, studying and analyzing the motion considered a primary issue that should be taken into consider when studying and designing the robot.
 In this research 6-DOF sample of the industrial manipulator based on ABB IRB 4400 model had been studied. The mathematical model of manipulator is established by DH (Denavait Hartenberg) method. The forward kinematics was done using DH Parameters in order to get the final transformation matrix. The inverse kinematics was done using geometrical and analytical methods in order to get the end effector final position and direction by calculate Euler angles values.
 Finally, the forward and inverse kinematics equations were computing by MATLAB to get angles, end effector, position, direction and Euler angles values.
 The kinematics study and the arm movement’s equations were compered with the practical measurements to make sure it fulfills the desired purpose.

Implementation of singularity-free inverse kinematics for humanoid robotic arm using Bayesian optimized deep neural network

This study presents the efficacy of deep learning techniques in controlling the arm of a humanoid robot without resorting to inverse kinematic analysis. Emphasizing real-time applicability, a straightforward deep neural network (DNN) structure is developed and optimized using hyperparameter Bayesian optimization. The Keras Bayesian Optimization Tuner with Gaussian process fine-tunes the DNN architecture. Utilizing a simulation environment and generating around 10 billion datasets, the optimized DNN is evaluated on both simulated and real robots. Impressively, the trained DNN exhibits a notable ability to predict robot control within a 25 ms timeframe, achieving a total Mean Absolute Error (MAE) of 0.02 for the xyz-axes. These results underscore the potential of deep learning-based approaches in humanoid robot arm control, eliminating the need for inverse kinematic equations and providing valuable insights for future robotic system development.

Research and design a model of 2D profile generation system applied in laser welding technology using piezo linear actuators

The article introduces a method to create any 2D laser profiles applied in welding technology. This method allows for the creation of profiles that best suit the weld characteristics and material of the weld workpiece, thereby improving the quality, accuracy, and aesthetics of the weld and increasing laser welding efficiency. In the study, the authors proposed a model of a 2D laser profile generation system with a reflecting mirror and two piezoelectric linear actuators. The forward and inverse kinematic equations were completely solved, while a control algorithm was proposed to control the motion of linear actuators. The model is simulated on MATLAB with circular, sin-wave, and 8-figured profiles. The obtained results show that the control profiles are almost close to the desired ones (both shape and scan period). There is a displacement between them. With the given simulation parameters, the displacements of the above-mentioned profiles are 0.03 mm (1.5%), 0.05 mm (2.5%), and 0.05 mm (1.25%), respectively. This shifting can be reduced by increasing the number of samplings. The simulation results provide strong evidence for the feasibility of implementing a practical 2D laser profile generation system based on the proposed model.

Design, optimization, debugging, and simulation of an agricultural biomimetic hexapod robot

This paper comprehensively studies the model establishment, kinematic analysis, hardware design, software development, and agricultural applications of hexapod robot, laying a solid foundation for their practical application in the agricultural field and proposing prospects for future research and development. This article mainly conducts in-depth research on the mechanical design, kinematic analysis, hardware implementation, software development, and application in the agricultural field of hexapod robots. Firstly, a brief introduction to biomimetic robots will be provided, and a comparative analysis will be conducted on existing common legged robots. Afterwards, use solidworks-2021 for 3D modeling to draw the legs and main structure of the robot. In terms of kinematic analysis, by studying the mechanism structure and motion characteristics of hexapod robot, the forward and inverse kinematic equations are derived, and the gait planning and motion control algorithms of the robot are analyzed in detail. These analyses provide a theoretical basis for the robot's program and actual motion. In terms of hardware, a lightweight and high-performance hexapod robot hardware platform has been designed using mainstream controllers such as Borboardino and ultrasonic sensors. This hardware platform has excellent responsiveness and adaptability, and can efficiently move and operate in complex agricultural environments. In terms of software, a comprehensive control system has been developed, including motion planning, action execution, and obstacle avoidance modules. By integrating triangular gait technology and related algorithms, robot can achieve navigation and obstacle avoidance, and perform tasks such as crop planting and spraying in the agricultural field. The simulation file of the hexapod robot was established using CoppeliaSim software, achieving motion based on the robot body, six legs, and end effectors. Finally, a 3D-printer is used to print and assemble all components, and complete the design through debugging and verification. The hexapod robot is capable of autonomous cruising in farmland, completing tasks such as planting and watering crops, providing efficient and intelligent agricultural production solutions for farmers.

Simulation of Kinematic and Dynamic Model of Two Degrees of Freedom Robot Arm Using Simulink

The aim of this study is to realize the physical model of a robot arm with two degrees of freedom in the MATLAB Simulink environment, to show that the physical model of the robot arm matches the mathematical model and that the results of these models match. For this purpose, kinematic and dynamic modeling of a two-degree-of-freedom robotic arm is performed in the MATLAB Simulink environment. To ensure the accuracy of the physical model created in the MATLAB Simulink environment, mathematical equations are defined to a function within the physical model, in other words, a mathematical model is created. The kinematic equations of the robotic arm are examined in two steps as forward kinematics and inverse kinematics equations, and the geometric approach is used when obtaining the kinematic equations. The Lagrange-Euler method is used to obtain dynamic equations. The results obtained show that the mathematical kinematic and dynamic equations match the physical model in the MATLAB Simulink environment and reveal that the system is reliable.

2D of Robotic Arm Based on Inverse Kinematics Using Arduino

Abstract: The advancements and quick developments in the technology has made it possible to create a platform for the invention of new as well as great things. One of the concept that is being used lately to improve the technology is the concept of robotics. This project focuses on the implementation of inverse kinematics for a 2-DOF (two degrees of freedom) robot arm using an Arduino microcontroller. The inverse kinematics equations are derived and programmed to calculate the joint angles required to position the robot arm's end effector in a desired location within its workspace. The Arduino board is used to interface with the robot arm's actuators and control the movement of the arm. The Arduino programming aspect of the project involves developing a control algorithm that accepts target coordinates for the end effector and computes the necessary joint angles using inverse kinematics equations. Servo motors are manipulated through the Arduino Servo library to achieve the calculated angles, enabling the arm to reach the desired positions accurately and efficiently. To enhance the functionality and safety of the 2-DOF robotic arm, the project includes features such as calibration routines, testing procedures, and safety measures to avoid collisions and servo load. The project aims to demonstrate the application of inverse kinematics in controlling robotic manipulators for precise positioning tasks

SCARA TIPI 3D YAZICI TASARIMI VE İMALİ

This study designed and produced a Selective Compliance Assembly Robot Arm (SCARA)-type three-dimensional Fused Deposition Modelling (FDM) printer with three degrees of freedom based on kinematic and dynamic analyses. The dynamic capability of a SCARA robot and the FDM production method were combined, and a unique printer system was obtained by using open-source software. The Kinematic Calculations were achieved by analytical methods by using geometrical equations. An open-loop control system was created by inputting forward kinematic and inverse kinematic equations to the control software. The printing processes of the Cube and Prism samples were carried out with the SCARA-type three-dimensional printer. The data obtained from the analytical calculations and the results obtained from the experiments were compared, and the error rates in the desired and obtained prints and findings that were obtained based on print quality were shared. Academic studies on SCARA in the literature have usually focused on the dynamic calculations, design and control of SCARA robots, and especially in recent years, implementation of nature-inspired algorithms. A unique printer system was obtained by using open-source software. Prints were taken from cube and prism samples, and the samples were compared to the data obtained from the analytical results.This study implemented a form of a hybrid printer model where the movement capability of a SCARA robot was combined with FDM-type three-dimensional printer production technology. The SCARA-type three-dimensional printer was produced after making kinematic and kinetic calculations.

Kinematic Analysis of a New 3-DOF Parallel Wrist-Gripper Assembly with a Large Singularity-Free Workspace

This paper introduces a novel dexterous 3-DOF parallel wrist-gripper assembly with a large singularity-free range of motion. It consists of a zero-torsion 2-DOF parallel wrist and a 1-DOF parallel gripper. The wrist produces a 2-DOF sphere-on-sphere pure rolling motion. This large singularity-free 2-DOF sphere-on-sphere pure rolling motion of the wrist allows for smooth and precise manipulation of objects in various orientations, making it suitable for applications such as assembly, pick-and-place, and inspection tasks. Using a geometrical approach, analytical solutions for the inverse and forward kinematics problems of the wrist and gripper are derived. From the inverse kinematic equations, the Jacobian matrices are derived and it is shown that the whole workspace is free of type I and type II singularities. It is shown that with a proper choice of design variables, a large singularity-free range of motion can be obtained. The absence of singularities in the whole workspace of the wrist-gripper assembly is an important feature that enhances its reliability. Finally, the correctness of the derived equations for the wrist inverse and forward kinematics are verified using MSC Adams. These results confirm the feasibility and effectiveness of the proposed parallel wrist-gripper assembly. Overall, the novel parallel wrist-gripper assembly presented in this paper demonstrates great potential for improving the efficiency and flexibility of robotic manipulators in a variety of industrial and research applications.

Trajectory Smoothing Planning of Delta Parallel Robot Combining Cartesian and Joint Space

Delta parallel robots have been widely used in precision processing, handling, sorting, and the assembly of parts, and their high efficiency and motion stability are important indexes of their performance.Corners created by small line segments in trajectory planning cause abrupt changes in a tangential discontinuous trajectory, and the vibration and shock caused by such changes seriously affect the robot’s high-speed and high-precision performance. In this study, a trajectory-planning method combining Cartesian space and joint space is proposed. Firstly, the vector method and microelement integration method were used to establish the complete kinematic and dynamic equations of a delta parallel robot, and an inverse kinematic/dynamic model-solving program was written based on the MATLAB software R2020a. Secondly, the end-effector trajectory of the delta parallel robot was planned in Cartesian space, and the data points and inverse control points of the end effector’s trajectory were obtained using the normalization method. Finally, the data points and control points were mapped to the joint space through the inverse kinematic equation, and the fifth-order B-spline curve was adopted for quadratic trajectory planning, which allowed the high-order continuous smoothing of the trajectory planning to be realized. The simulated and experimental results showed that the trajectory-smoothing performance in continuous high-order curvature changes could be improved with the proposed method. The peak trajectory tracking error was reduced by 10.53%, 41.18%, and 44.44%, respectively, and the peak torque change of the three joints was reduced by 3.5%, 11.6%, and 1.6%, respectively.

The structural design and simulation of the tubing handling manipulator

The size of the oil pipes in the factory is relatively large, making them inconvenient to handle. There are few existing oil pipe handling devices, and a 2P2R four degree of freedom manipulator device has been innovatively designed to complete the oil pipe handling work. First, the three-dimensional model of the manipulator was established using SolidWorks software, and then the improved D-H method was used to carry out the kinematics modeling of the manipulator system, and the forward and Inverse kinematics equations were derived. Then, the MATLAB software was used to carry out the kinematics analysis of the manipulator, and the manipulator workspace was calculated. The movement trajectory, as well as the displacement, speed, and acceleration curves under the trajectory were obtained using the fifth order Polynomial interpolation method, Finally, the 3D model was imported into Adams software, and an Adams virtual prototype was established for dynamic analysis. The force and torque curves of each joint were obtained, laying the foundation for further design and research in the future.

COLOR AND SIZE SORTING SYSTEM WITH AN ESP32-BASED ROBOT ARM

Robotics has seen an explosive increase in usage in the past few decades owing to its abundance of benefits and automation capabilities. The use of robotics is especially prominent in industries where the demand for precise and automatic robots in order to increase production efficiency is high. One of the robots commonly used in these industries is the arm robot model, which is a machine designed specifically to mimic some of the human arm’s capabilities in order to execute certain tasks over and over again, either autonomously or not. This paper will discuss the design of a robotic arm with five degrees of freedom capable of picking up and placing objects with three different colors and sorting the objects based on their size, starting from the largest to the smallest. The inclusion of an additional degree of freedom allows the robot to adjust the rotation of its grip to properly grab rotated objects. With an ESP32-CAM acting as its eyes, the robot is aided by a Python program run remotely on a separate Laptop in order to analyze video stream uploaded by the camera to determine the coordinates, color, size, and rotation of objects placed within the Detection Zone. The implementation of inverse kinematics equations run on an ESP32 microcontroller allows the robot to reach arbitrary coordinates specified by the Python program. Testing revealed that the resulting robot is able to perform the tasks it was designed to, namely recognizing and sorting colored boxes of different colors and sizes, with an accuracy 100% in recognition tasks and an accuracy of 91.5% in sorting tasks.

Design and motion planning of a 7-DOF assembly robot with heavy load in spacecraft module

Currently, there is great demand for automated assembly of equipment inside spacecraft module, which would require an assembly robot with small size, large workspace, high load capacity, and high flexibility. To meet this demand, a redundant seven-degree-of-freedom (7-DOF) assembly robot with three prismatic joints and four rotating joints is proposed in this study. First, a kinematic model of the assembly robot is established, and the positional forward kinematics are derived. Then, the positional inverse kinematic equations are derived by using the fixed joint method and the coordinate inverse transformation method for the characteristics of the robot with redundant degrees of freedom. The inverse solution optimization model of the assembly robot is designed based on genetic algorithm, and B-spline interpolation algorithm is used for joint trajectory planning. Next, NSGA-2 algorithm is used to construct the trajectory optimization model, and the time-pulsation multi-objective Pareto optimal frontier is obtained. Finally, the joint simulation model of mechatronics and the prototype experiment are established to verify the effectiveness of the optimization results. Analysis shows that the proposed assembly robot has better load-bearing capacity and dynamic characteristics than similar existing assembly robots. Furthermore, the segmented trajectory optimization strategy for the assembly robot using inverse solution optimization, interpolation algorithm, and NSGA-2 based multi-objective optimization gets each motion joint to realize the trajectory tracking function quickly and stably, and the trajectory tracking error is small enough to meet the requirements of end positioning accuracy.

Design, modeling and kinematic analysis of a multi-configuration dexterous hand with integrated high-dimensional sensors

PurposeThis study aims to introduce a multi-configuration, three-finger dexterous hand with integrated high-dimensional sensors and provides an analysis of its design, modeling and kinematics.Design/methodology/approachA mechanical design scheme of the three-finger dexterous hand with a reconfigurable palm is proposed based on the existing research on dexterous hands. The reconfigurable palm design enables the dexterous hand to achieve four grasping modes to adapt to multiple grasping tasks. To further enhance perception, two six-axis force and torque sensors are integrated into each finger. The forward and inverse kinematics equations of the dexterous hand are derived using the D-H method for kinematics modeling, thus providing a theoretical model for index analysis. The performance is evaluated using three widely applied indicators: workspace, interactivity of fingers and manipulability.FindingsThe results of kinematics analysis show that the proposed hand has excellent dexterity. Additionally, three different experiments are conducted based on the proposed hand. The performance of the dexterous hand is also verified by fingertip force, motion accuracy test, grasping and in-hand manipulation experiments based on Feix taxonomy. The results show that the dexterous hand has good grasping ability, reproducing 82% of the natural movement of the human hand in daily grasping activities and achieving in-hand manipulations such as translation and rotation.Originality/valueA novel three-finger dexterous hand with multi-configuration and integrated high-dimensional sensors is proposed. It performs better than the previously designed dexterous hand in actual experiments and kinematic performance analysis.

Five-axis parallel mechanism system (PMS) CNC partial link control system based on modified inverse kinematic of 6-DOF UPS parallel manipulator

This paper presents a control system algorithm for a five-axis parallel mechanism system (PMS) CNC milling machine based on a 6-DOF Stewart platform parallel manipulator with a universal-prismatic-spherical (UPS) configuration. The control system reads the G-Code commands as standard CNC machine language, then extract data points and interpolates them to generate the robot trajectory patterns as motion references. Then, the control system uses the modified inverse kinematic equation to determine the length of each link to move the end effector to track the trajectory patterns from the previous G-code extraction process. The inverse kinematic equation is modified especially for the five-axis PMS CNC milling machine by including machine-offset and tools-offset parameters so it will be easier for the control system to implement the kinematic equation. As expected, the system simulation results successfully followed the G-Code program moving commands. The average error of the length control system is 0,1 mm, while the average error of the length change rate control system is 1,8 mm/s. The maximum error is 26.9 mm was caused by the system's inability to follow the motion profile in transient. It can be concluded that 6-DOF Stewart platform parallel structures,which provide better performance than serial structures, can be implemented as a new concept for the motion mechanism of five-axis CNC milling machines. The five-axis PMS CNC milling machine also promises better performance than conventional five-axis gantry structures CNC.

Kinematic Modeling and Simulation of a New Robot for Wingbox Internal Fastening Application

At present, the fastener installation in a wingbox facing a narrow space must be performed manually. Using a robot is an appropriate solution for automatic assembly. However, the existing robots cannot meet the internal fastening requirements. A new robot with a prismatic joint and four revolute joints (1P4R) was developed to perform the positioning and operation in the wingbox. A compact arm link was designed, and mechanical frame structures were set up. The control system was also set up for the robot’s motion. Then, the forward kinematic model was carried out with the matrix transformation method, and in the analysis the workspace entirely covered the wingbox. The inverse kinematic model was established using the geometric method, and through calculation and simulation, the inverse kinematic equations were verified and refined.

Razvoj SCARA robotske ruke za aplikacije za paletizaciju zasnovane na kompjuterskom vidu

This paper develops a computer vision system integrated with a SCARA robot arm to pick and place objects. A novel method to calculate the 3D coordinates of the objects from a camera is proposed. This method helps simplify the camera calibration process. It requires no knowledge of camera modeling and mathematical knowledge of coordinate transformations. The least square method will predate the Equation describing the relationship between pixel coordinates and 3D coordinates. An image processing algorithm is presented to detect objects by color or pixel intensity (thresholding method). The pixel coordinates of the objects are then converted to 3D coordinates. The inverse kinematic Equation is applied to find the joint angles of the SCARA robot. A palletizing application is implemented to test the accuracy of the proposed method. The kinematic Equation of the robot arm is presented to convert the 3D position of the objects to the robot joint angles. So, the robot moves exactly to the required positions by providing suitable rotational movements for each robot joint. The experiment results show that the robot can pick and place 27 boxes on the conveyor to the pallet with an average time of 2.8s per box. The positions of the boxes were determined with an average error of 0.5112mm and 0.6838mm in the X and Y directions, respectively.