Inverse Kinematic Equations Research Articles

Mathematical Analysis and Motion Capture System Utilization Method for Standardization Evaluation of Tracking Objectivity of 6-DOF Arm Structure for Rehabilitation Training Exercise Therapy Robot.

A treatment method for suppressing shoulder pain by reducing the secretion of neurotransmitters in the brain is being studied in compliance with domestic and international standards. A robot is being developed to assist physical therapists in shoulder rehabilitation exercise treatment. The robot used for rehabilitation therapy enables the training of patients to perform rehabilitation exercises repeatedly. However, the biomechanical movement (or motion) of the shoulder joint should be accurately designed to enhance efficiency using a shoulder rehabilitation robot. Furthermore, safely treating patients by accurately evaluating biomechanical movements in compliance with domestic and international standards is a major task. Therefore, an in-depth analysis of shoulder movement is essential for understanding the mechanism of shoulder rehabilitation using robots. This paper proposes a method for analyzing shoulder movements. The rotation angle and range of motion (ROM) of the shoulder joint are measured by attaching a marker to the body and analyzing the inverse kinematics. The first motion is abduction and adduction, and the second is external and internal rotation. The location information of the marker is transmitted to an application software through an infrared camera. For the analysis using an inverse kinematics solution, five males and five females participated in the motion capture experiment. The subjects did not have any disability, and abduction and adduction were repeated 10 times. As a result, ROM of the abduction and adduction were 148° with males and 138.7° in females. Moreover, ROM of the external and internal rotation were 111.2° with males and 106° in females. Because this study enables tracking of the center coordinates of the joint suitably through a motion capture system, inverse kinematics can be accurately calculated. Additionally, a mathematical inverse kinematics equation will utilize follow-up study for designing an upper rehabilitations robot. The proposed method is assessed to be able to contribute to the definition of domestic and international standardization of rehabilitation robots and motion capture for objective evaluation.

2D Mapping of Mobile Robot Based on micro-ROS

This paper proposes micro-ROS-based mobile robot system development and 2D mapping. Micro-ROS uses the micro-XRCE-DDS middleware to communicate with ROS2 in an extremely resource-constrained microcontroller environment. The mobile robot control system adopts a layered control method. The x64 PC equipped with Ubuntu ROS foxy is used as the main control platform, the olimex-stm32-E407 equipped with micro-ROS is used as the motion control layer, and the stm32F103 microcontroller is the underlying driver core. The forward and inverse kinematic equations are obtained through the analysis of the robot kinematics model. Through the interaction between the ROS2 nodes in the micro-ROS environment and the ROS2 nodes on the PC side, the cartographer algorithm is used to verify the effectiveness of the micro-ROS-based mobile robot system.

Iterative weighted algorithm for 9-dof pose solution and its application

Nine-axis motion parameters need to be calculated according to the relative pose to be simulated when the precision calibration test of rendezvous and docking optical imaging sensor is carried out with nine-degree of freedom motion simulator. Based on the structural characteristics of the system and the principle of homogeneous coordinate transformation, the inverse kinematics equations are established in this paper, in order to improve the test efficiency and ensure the accuracy of pose simulation, the iterative algorithm with fixed degrees of freedom was adopted to approximate the solution results, at last, the nine-axis weighting algorithm was used to judge the end of iteration and obtain the solution results of relative pose optimization.

Zero Reaction Torque Trajectory Tracking of an Aerial Manipulator through Extended Generalized Jacobian

Aerial manipulators are used in industrial and service robotics tasks such as assembly, inspection, and maintenance. One of the main challenges in aerial manipulation is related to the motion of the UAV base caused by manipulator disturbance torques and forces, which jeopardize the precision of the robot manipulator. In this paper, we propose two novel inverse kinematic control methods used to track a trajectory with an aerial manipulator while also considering resultant UAV base motions. The first method is adapted from the generalized Jacobian formulation used in space robotics and includes the change in system momentum resulting from gravity and UAV control forces in the inverse kinematic control equation. This approach is simulated for a 2 and 3 degree-of-freedom aerial manipulator tracking trajectories with the end-effector. Although the end-effector position error is approximately zero throughout the simulated task, we see significant undesired UAV base motions of several centimeters in magnitude. To ameliorate this by exploiting the kinematic redundancy, we modify the generalized Jacobian by adding an additional task constraint which minimizes the reaction torques from the manipulator, to form the extended generalized Jacobian. While the second approach results in improved precision and reduced base motion by an order of magnitude as compared to the generalized Jacobian, a drawback is the reduction in the available workspace as the solution seeks to minimize the manipulator center of gravity translation. We also demonstrate and compare both approaches in a load picking task. All the algorithms are completed computationally faster than real time in the MATLAB simulations, illustrating their potential for application in real-world experiments.

Kinematic modeling and control of omnidirectional wheeled cellular conveyor

In this paper, kinematic modeling and control of an omnidirectional wheeled cellular conveyor are proposed. Two inverse kinematic models for the conveyor are compared: a Cell-Based – traditional one – and a Wheel-Based one proposed in this paper, Wheel kinematic constraints has been considered in the derivation of the inverse kinematic equations of motion for the proposed model. Cells/wheels selection methods based on the instantaneous position of the package is implemented. Each model provides the required velocities for the selected cells/wheels to control the package path. The system is simulated using the MATLAB© SIMULINK© platform to verify the accuracy of the derived equations. The simulations results are validated experimentally by using a small-scaled conveyor system. The Wheel-Based model shows better performance in terms of accuracy and is more energy efficient compared to the Cell-Based one.

AI-Based Posture Control Algorithm for a 7-DOF Robot Manipulator

With the rapid development of artificial intelligence (AI) technology and an increasing demand for redundant robotic systems, robot control systems are becoming increasingly complex. Although forward kinematics (FK) and inverse kinematics (IK) equations have been used as basic and perfect solutions for robot posture control, both equations have a significant drawback. When a robotic system is highly nonlinear, it is difficult or impossible to derive both the equations. In this paper, we propose a new method that can replace both the FK and IK equations of a seven-degrees-of-freedom (7-DOF) robot manipulator. This method is based on reinforcement learning (RL) and artificial neural networks (ANN) for supervised learning (SL). RL was used to acquire training datasets consisting of six posture data in Cartesian space and seven motor angle data in joint space. The ANN is used to make the discrete training data continuous, which implies that the trained ANN infers any new data. Qualitative and quantitative evaluations of the proposed method were performed through computer simulation. The results show that the proposed method is sufficient to control the robot manipulator as efficiently as the IK equation.

Kinematics and Trajectory Planning of the Masonry Robot

Abstract This paper proposes a mechanical system for a masonry robot comprising four parts: an omnidirectional mobile platform, a lifting platform, a six-degrees-of-freedom manipulator, and a grasping mechanism. The robot is specifically designed to carry out brick masonry on construction sites and is equipped to move bricks smoothly with slurry to their intended location. To prevent mortar from being shaken off the brick, the grasping mechanism is required to maintain optimal velocity and optimized acceleration. To implement online trajectory planning with velocity and acceleration constraints, the paper suggests an approach based on screw theory for resolving the inverse kinematics of the masonry robot. This method allows the inverse kinematic equations to be used to determine a unique solution for all joints of the redundant driver of the masonry robot. The approach and strategy are validated through numerical simulations of trajectory planning using a fifth-degree polynomial.

Verification of inverse kinematic equations for a five-axis machine tool with a spindle tilting configuration

In this paper, the methodology for verifying inverse kinematic equations is presented. Analysis of the kinematic structure of the machine is shown, which results in the kinematic equations needed for the configuration of the machine's postprocessor. The machine proposed in this paper is a five-axis machine tool with two rotating axes on the spindle. The machine's configuration is X'OYZBA. The derived equations are used to transform the CL data for a test model into a G code used on a virtual model of the machine tool. A simplified model of the machine is developed using the PTC Creo software, in which the initial testing of the equations was performed. The inverse kinematic equations were implemented in a postprocessing program using the Matlab software. Generated G-code for multi-axis machining process was tested on a virtual machine tool in the Vericut software.

Workspace and kinematic structure analysis of a 6-DOF Lambda parallel kinematic machine

This paper presents workspace and kinematic analysis of a parallel kinematic machine based on the Lambda mechanism. The considered parallel kinematic machine has six degrees of freedom (DOF), achievable with six actuated translation joints. The kinematic analysis includes the definition of every active part of the machine, as well as the definition of every active or passive joint used to connect machine parts. The mathematical model of the machine is created for the better understanding of the machine's operation. The proposed mathematical model of the machine includes inverse kinematic equations, whose solving presents the first step in workspace analysis. In this case, the offered parallel kinematic machine has six active-joint variables, and every active-joint variable is the result of one inverse kinematic equation. Verification of the inverse kinematic equations has been done analytically, using MatLab software and a CAD/CAM system. Workspace analysis, as one of the most important parameters of the parallel kinematic machine, presents the main topic of this paper. In this case two approaches to the workspace analysis are given. The first considered analysis is used to determine the achievable workspace of the machine, and the second analysis is used to determine the total orientation workspace of the machine. Polar coordinates are used to simplify the process of the workspace analysis.

Design, analysis and method of foot trajectory generation for quadruped robots in swing-stance phase

PurposeLegged walking robots have numerous advantages over the wheel or tracked robots due to their strong operational ability and exposure to the complex environment. This paper aims to present details about the mechanical formation and a new conceptual elliptical trajectory generation discussed throughout the paper of the quadruped robot.Design/methodology/approachInitially, a realistic CAD model of the four-legged robot is developed in Solidwork-2019. The proposed model’s forward and inverse kinematics equations are deduced using Denavit–Hartenberg parameters. Based on geometry and kinematics, manipulability and obstacle avoidance are investigated. A method of galloping trajectory is proposed for aiming the increase of upright direction impulse, which is produced by ground reaction force at each step frequency. Furthermore, the locomotion equation of the ellipse trajectory is derived by setting transition angle polynomial of free-fall phase, stance phase and swing phase and the constraints.FindingsFinally, a successive simulation on a 2D sagittal plane is performed to check and verify the usefulness of the proposed trajectory. Before the development of the full quadruped, a single prototype leg is generated for experimental verification of the dynamic simulations.Originality/valueThe proposed trajectory is novel in that it uses force tracking control, which is intended to improve the quadruped robot’s robustness and stability.

Design Optimization of 3-DOF Hybrid Manipulator

Studies related to reachable workspace, inverse kinematics, and best dimensions of 3-DOF Hybrid Manipulator (HM) are presented in this paper. This mechanism possesses both serial and parallel links. A third revolute joint is added in the five-linkage structure having two actuated revolute joints. The third revolute joint is added in such a way that its axis should pass through the axes of the two actuated revolute joints. This produces a structure called a hybrid mechanism consisting of parallel and serial links. The inverse kinematics analysis is implemented for obtaining the joint positions of the HM. The reachable workspace of the manipulator is found using inverse kinematic equations, and finally, the Global Conditioning Index (GCI) is used for optimization to find the optimal dimensions of the HM. The corresponding dimensions obtained based on the optimization by considering maximum GCI as an objective gives the best dimensions that are free from singularities. Here optimization is carried using Genetic Algorithms (GAs).

Kinematic Model and Redundant Space Analysis of 4-DOF Redundant Robot

The kinematics and redundant space analysis of redundant robots constitutes important research content. Currently, methods such as geometric method and iterative optimization method are relatively complicated and inconvenient for programming and practical control applications. Moreover, little research has been conducted on redundant space analysis. This paper takes the 4-DOF PowerCube redundant robot as the research object. The forward and inverse kinematics equation of the robot are established based on the D-H matrix method, projection and cosine theorem method, and vector coordinate method. Then, the redundant space of the robot is obtained and the redundant space range of the robot is analyzed. Finally, the simulation of kinematic and redundant space research is conducted. It is shown that the change of each joint angle of the robot is smooth without mutation, so it can ensure the stable motion of the robot. Additionally, the different position and redundant variable have a big influence on robotic configuration. The calculation amount is relatively small and convenient for programming application, and the path calculation data of the joints are obtained, which are conducive to the motion control of modular robots. The method used in this paper can be extended to the multi-DOF redundant robot. Finally, the motion optimization, control, and obstacle-avoidance of redundant robots are briefly studied. The results of this paper provide an important basis for these aspects of research.

Evolutionary multi-objective trajectory optimization for a redundant robot in Cartesian space considering obstacle avoidance

Abstract. A method of end-effector trajectory planning in Cartesian space based on multi-objective optimization is proposed in this paper to solve the collision problem during the motion of the redundant manipulator. First, a cosine polynomial function is used to interpolate the trajectory of the end effector, enabling it to reach the desired pose at a specific time. Then, the joint trajectory of the manipulator is solved by inverse kinematics, and the null space term is introduced as the joint limit constraint in the inverse kinematics equation. During the operation of the manipulator, the collision detection algorithm is employed to calculate the distance between the obstacle and each arm in real time. Finally, a multi-objective, multi-optimization model of trajectory that considers the obstacle avoidance, joint velocity, joint jerk and energy consumption is established and optimized with a multi-objective particle swarm optimization algorithm. The simulation results demonstrate that the proposed method can effectively accomplish the trajectory planning task and avoid obstacles; the joint trajectories obtained are smooth and meet the limit constraints; the joint jerk and energy consumption are well suppressed.

An Adaptive Nonsingular Fast Terminal Sliding Mode Controller for Dynamic Walking of a 5-Link Planar Biped Robot in Both Single and Double Support Phases

This paper aims to design an improved adaptive nonsingular fast terminal sliding mode controller for a fully actuated planar biped robot with five degrees of freedom in the single support (SSP) and double support (DSP) phases in the presence of external perturbation and uncertainties. A new sliding surface was proposed to avoid singularities and the chattering phenomenon. The proposed controller guarantees fast convergence of error signals in finite time. Unlike similar studies, the presented method considers a whole cycle of one step of walking, including SSP, double impact, and DSP phases. Also, the proposed approach does not require a predefined upper limit to estimate uncertainty using an adaptive law. Notably, dynamic walking was preferred over static walking to achieve more similarity to human walking. The designed trajectories were determined according to the position of the waist and swinging legs ankle, which could then be converted into the position of joints using inverse kinematics equations. The simulation results were used to approve the proposed controller's fast and robust tracking performance in the presence of external disturbances, mass, and inertia uncertainties without predefined knowledge of their upper bounds.

Position control for haptic device based on discrete-time proportional integral derivative controller

Haptic devices had known as advanced technology with the goal is creating the experiences of touch by applying forces and motions to the operator based on force feedback. Especially in unmanned aerial vehicle (UAV) applications, the position of the end-effector Falcon haptic sets the velocity command for the UAV. And the operator can feel the experience vibration of the vehicle as to the acceleration or collision with other objects through a forces feedback to the haptic device. In some emergency cases, the haptic can report to the user the dangerous situation of the UAV by changing the position of the end-effector which is be obtained by changing the angle of the motor using the inverse kinematic equation. But this solution may not accurate due to the disturbance of the system. Therefore, we proposed a position controller for the haptic based on a discrete-time proportional integral derivative (PID) controller. A Novint Falcon haptic is used to demonstrate our proposal. From hardware parameters, a Jacobian matrix is calculated, which combines with the force output from the PID controller to make the torque for the motors of the haptic. The experiment was shown that the PID has high accuracy and a small error position.

The Bees Algorithm Approach to Determining SMC Controller Parameters for the Position Control of a SCARA Robot Manipulator

In this study, position control of a SCARA robot manipulator is investigated using the sliding mode control (SMC) method based on parameter optimization using The Bees Algorithm. The modeling the SCARA manipulator is conducted in MSC Adams and the control implementation is carried out in MATLAB software. The numerical model of the SCARA manipulator is acquired by setting up a virtual prototype on MSC Adams software. In addition, the inverse kinematic equations of the SCARA manipulator are formed using Matlab/Simulink software in order to check the accuracy of the created virtual prototype. In addition, the SMC controller parameters are optimized with The Bees Algorithm to get better results. Then, the control performance of the system is examined on the virtual prototype using MSC Adams-MATLAB co-simulation. Moreover, Genetic Algorithm, another meta-heuristic method, is used for parameter optimization and the performance of The Bees Algorithm is compared with the results obtained. As a result, it has been observed that The Bees Algorithm can be used in studies related to the control of robotic systems.

Distributed Path Planning Classification with Web-based 3D Visualization using Deep Neural Network for Internet of Robotic Things

Internet of Robotic Things (IoRT) distributes heterogeneous intelligences among devices and platforms. A distributed control of a three-degree-of-freedom (3-DOF) robot manipulator is integrated with web-based 3D visualization. An asynchronous protocol was utilized to broadcast kinematic data of a 3-DOF robot manipulator between platforms. However, kinematic data computed using inverse kinematic equations directly cannot identify the singularity issue of robot manipulator. Singularity avoidance required to prevent robot component or joint from damage. Therefore, this study proposed a deep neural network approach as a classification-based of manipulator robot path planning to avoid singularity issues. Deep neural network (DNN) was trained in 12 minutes, 52 seconds in 500 iterations. Training accuracy measured with value 96,23 percent, validation accuracy measured with value 96,13 percent, and testing accuracy measured with value 96,48 percent Additionally, 3 DOF manipulator robot web-based 3D visualization was made using Web Graphics Library (WebGL). The distributed platform was tested successfully and can distribute and classify 2352 motions per second.

End effector position calculation with the ANN for tapping machine

Nowadays, manufacturers give importance to the production of machines that allow for faster production, reduce labor costs, and minimize operation errors to meet the increasing demand. The search for such machines leads the manufacturing sector to automation. In this study, an automation-supported tapping machine prototype was manufactured. Kinematic equations were used for determining the location of the end effector in Cartesian space, whereas inverse kinematic equations were used for angular positions in joint space relative to positions in Cartesian space. Based on the results of the kinematic equations, the data obtained in certain positions were taught to the system through ANN. The position values for the angles known through the artificial intelligence algorithm were taught to the system. Then, the position coordinates to be reached by this manipulator, which has four degrees of freedom, for the intermediate position coordinate values through artificial neural networks (ANN) have been obtained. It is expected that the device controlled by artificial intelligence will not be affected by the variables in parameter or force changes requiring high working performance. With the control of the positions through ANN, it has been ensured that the position control of the tapping robot manipulator is predicted based on artificial intelligence techniques depending on the angle values of the limbs, and the robot is prevented from going to a position that is on a different trajectory. Accordingly, the robot arm has been made controllable with ANN techniques. With ANN modelling, the position of the end point to perform the tapping process was estimated with high reliability. For future research, a rough simulation was made to see whether the end point would go to a different position in space.

Utilization of multilayer perceptron for determining the inverse kinematics of an industrial robotic manipulator

Inverse kinematic equations allow the determination of the joint angles necessary for the robotic manipulator to place a tool into a predefined position. Determining this equation is vital but a complex work. In this article, an artificial neural network, more specifically, a feed-forward type, multilayer perceptron (MLP), is trained, so that it could be used to calculate the inverse kinematics for a robotic manipulator. First, direct kinematics of a robotic manipulator are determined using Denavit–Hartenberg method and a dataset of 15,000 points is generated using the calculated homogenous transformation matrices. Following that, multiple MLPs are trained with 10,240 different hyperparameter combinations to find the best. Each trained MLP is evaluated using the R 2 and mean absolute error metrics and the architectures of the MLPs that achieved the best results are presented. Results show a successful regression for the first five joints (percentage error being less than 0.1%) but a comparatively poor regression for the final joint due to the configuration of the robotic manipulator.

DDPG Algoritmasında Bulunan Ornstein–Uhlenbeck Gürültüsünün Standart Sapmasının Araştırılması

Reinforcement learning is a learning method that many creatures often unwittingly use to gain abilities such as eating and walking. Inspired by this learning method, machine learning researchers have reduced this learning method to subheadings as value learning and policy learning. In this study, the noise standard deviation of the deep deterministic policy gradient (DDPG) method, which is one of the policy learning algorithms, was examined to solve inverse kinematics of a 2 degrees-of-freedom planar robot. For this examination, 8 different functions were determined depending on the maximum value of the output of the action artificial neural network. Created artificial neural networks were trained by using these functions in 1000 iterations with 200 steps in each iteration. After the training, the statistical difference between the groups was examined and it was found that there was no statistical difference between the three best groups. For this reason, the best three groups were retrained 2500 iterations and 200 steps and tested for 100 different test scenarios after the training. After testing, the inverse kinematic equation of the 2 degrees-of-freedom planar robot with minimal errors was obtained with the help of artificial neural networks. In the light of the results, the importance of the choice of the standard deviation of noise and the correct range of selection was presented for researchers who will work in this field.