Kinematics Problem Research Articles

Innovative Solutions for IK: PROA and Clonal Selection Algorithms Unveiled

Calculating joint angles for sequential manipulators consists of studying the correlation between Cartesian and joint variables. The problem-solving technique encounters two main hurdles described as direct and inverse kinematics. Matrix multiplications usually simplify the direct kinematic problem. However, inverse kinematic problems are harder as they require solving many nonlinear equations and eliminating variables a lot. In our work, we introduce two new methods of handling the complicated inverse kinematic problem for robotic manipulator arms; Poor and Rich Optimization Algorithm and Clonal Selection Algorithm (CSA). These advanced techniques enhance greatly the estimation of various joints in the arm which makes the solution more precise and efficient. To demonstrate the effectiveness, robustness, and potential benefits of these approaches for complicated kinematic problems we present extensive simulation results thereby enabling better performance of robots.

Tensor based approach for tooth contact analysis of planar and spatial gearing contact

This paper presents a new method for analyzing gear tooth contact, leveraging tensor notation and discrete differential geometry. Existing analytical and numerical methods often face challenges in convergence and computational efficiency. Our proposed approach involves defining a novel tensor notation and applying it to the gear tooth contact kinematics problem. By discretizing the tooth surfaces and using tensor operations, we can accurately determine the kinematics, path of contact, and transmission error of the gear pair. To validate our approach, we compared its results with those obtained from commercial software, KISSsoft and KiMOS. The results demonstrated high accuracy, with mean absolute errors below 0.08 for specific sliding, 0.003 for sliding factor, and 0.1μm for transmission error. Furthermore, we applied our method to analyze non-involute gear types, such as S-gears, pin gearing and cosine gears. Our findings revealed the kinematic performance and contact characteristics of these gear types, providing valuable insights for gear design and optimization. In conclusion, the proposed tensor-based approach offers a promising alternative for gear tooth contact analysis, providing accurate and efficient results for a wide range of gear types.

Leveraging Environmental Contact and Sensor Feedback for Precision in Robotic Manipulation.

This paper investigates methods that leverage physical contact between a robot's structure and its environment to enhance task performance, with a primary emphasis on improving precision. Two main approaches are examined: solving the inverse kinematics problem and employing quadratic programming, which offers computational efficiency by utilizing forward kinematics. Additionally, geometrical methods are explored to simplify robot assembly and reduce the complexity of control calculations. These approaches are implemented on a physical robotic platform and evaluated in real-time applications to assess their effectiveness. Through experimental evaluation, this study aims to understand how environmental contact can be utilized to enhance performance across various conditions, offering valuable insights for practical applications in robotics.

Upper limb exoskeleton rehabilitation robot inverse kinematics modeling and solution method based on multi-objective optimization

The inverse kinematics problem of exoskeleton rehabilitation robots is challenging due to the lack of a standard analytical model, resulting in a complex and varied solution process. This complexity is especially pronounced in redundant upper limb exoskeleton robots, where inefficient solutions hinder the robot’s ability to adapt to the kinematic shape of the upper limb. This paper proposes a modeling and solution method based on multi-objective optimization to address the inverse kinematics of upper limb exoskeleton robots. We analyzed and validated this method using a redundant upper limb exoskeleton rehabilitation robot system developed by ourselves. First, we established a multi-objective inverse kinematics solution model by defining the end-position function, joint motion comfort function, system energy consumption function, motion safety, and human-like constraints. Then, the solution was designed based on the Improved Equilibrium Optimization (IEO) algorithm and validated its computational performance in terms of optimization ability, accuracy, and robustness. Finally, we experimentally tested the inverse kinematics solution model with the IEO algorithm on discrete objectives and continuous training trajectories using a redundant upper limb exoskeleton rehabilitation robot system. The results show that by incorporating the joint comfort function, system energy consumption function, and human-like constraints into the inverse kinematics model, we can not only quickly solve the inverse kinematics of redundant upper limb exoskeleton robots but also significantly improve the robot’s motion shape. Furthermore, it has better solution accuracy and stronger robustness than other algorithms when solving this inverse kinematics model based on the IEO algorithm.

Solving the inverse kinematics problem of discretely actuated hyper-redundant manipulators using a narrowing-down search algorithm

Solving the inverse kinematics problem of discretely actuated hyper-redundant manipulators using a narrowing-down search algorithm

Relaxation of the kinematic dynamo equations

We compute the exact relaxation and Λ \Lambda -convex hull of the kinematic dynamo equations and show that they coincide. We also find the relaxation in the stationary case and present applications to the infinite-time limit in the kinematic dynamo problem.

Improved Bald Eagle Search Optimization Algorithm for the Inverse Kinematics of Robotic Manipulators.

The inverse kinematics of robotic manipulators involves determining an appropriate joint configuration to achieve a specified end-effector position. This problem is challenging because the inverse kinematics of manipulators are highly nonlinear and complexly coupled. To address this challenge, the bald eagle search optimization algorithm is introduced. This algorithm combines the advantages of evolutionary and swarm techniques, making it more effective at solving nonlinear problems and improving search efficiency. Due to the tendency of the algorithm to fall into local optima, the Lévy flight strategy is introduced to enhance its performance. This strategy adopts a heavy-tailed distribution to generate long-distance jumps, thereby preventing the algorithm from becoming trapped in local optima and enhancing its global search efficiency. The experiments first evaluated the accuracy and robustness of the proposed algorithm based on the inverse kinematics problem of manipulators, achieving a solution accuracy of up to 10-18 m. Subsequently, the proposed algorithm was compared with other algorithms using the CEC2017 test functions. The results showed that the improved algorithm significantly outperformed the original in accuracy, convergence speed, and stability. Specifically, it achieved over 70% improvement in both standard deviation and mean for several test functions, demonstrating the effectiveness of the Lévy flight strategy in enhancing global search capabilities. Furthermore, the practicality of the proposed algorithm was verified through two real engineering optimization problems.

Robot inverse kinematics solution for center selection battle royale optimization algorithm

In order to solve the problems of high time complexity and insufficient global exploration ability of the battle royale optimization algorithm, this paper proposes an improved battle royale optimization algorithm based on chaos mapping, center selection and elite adaptive strategy. Through benchmark function testing, compared to particle swarm optimization algorithm, whale optimization algorithm, and the battle royale optimization algorithm, the improved algorithm significantly reduces time complexity and notably enhances convergence precision, speed, and stability. The improved algorithm is applied to the inverse kinematics problem of robots. The accuracy and The stability of the improved algorithm is better than those of the traditional battle royale optimization algorithm, it demonstrates superior solving precision and stability, proving its practicality and potential for development in solving robot inverse kinematics problems.

Inverse Kinematics of Robotic Manipulators Based on Hybrid Differential Evolution and Jacobian Pseudoinverse Approach

Robot manipulators play a critical role in several industrial applications by providing high precision and accuracy. To perform these tasks, manipulator robots require the effective computation of inverse kinematics. Conventional methods to solve IK often encounter significant challenges, such as singularities, non-linear equations, and poor generalization across different robotic configurations. In this work, we propose a novel approach to solve the inverse kinematics (IK) problem in robotic manipulators using a metaheuristic algorithm enhanced with a Jacobian step. Our method overcomes those limitations by selectively applying the Jacobian step to the differential evolution (DE) algorithm. The effectiveness and versatility of the proposed approach are demonstrated through simulations and real-world experimentation on a 5 DOF KUKA robotic arm.

Exploring artificial neural networks for the forward kinematics of a SCARA robotic manipulator using varied datasets and training optimizers

Abstract Although analytical methods are traditionally employed, the solution to the Forward Kinematics (FK) problem for Selective Compliance Assembly Robot Arm (SCARA) manipulator robots can prove intricate and computationally demanding. Recognizing this challenge, this study endeavors to introduce an intelligent approach by leveraging Artificial Neural Networks (ANNs) to address the FK problem specifically tailored for a four-degree-of-freedom (4-DoF) SCARA robot. To train the ANNs, we employ three distinct datasets, one with a fixed step size, one with a random step size, and one based on a sinusoidal signal. Moreover, the objective is to scrutinize the ANNs performance under the influence of three distinct training algorithms: Levenberg-Marquardt (LM), Bayesian Regularization (BR), and Scaled Conjugate Gradient (SCG). Through a systematic comparison of various ANN models, diverse training algorithms, and the three chosen datasets, the investigation reveals that optimal Mean Squared Error (MSE) results are achieved with random step size datasets for models with two hidden layers using the LM algorithm (MSE = 8.6099e-05). For the BR algorithm, the best MSE (8.0535e-05) was obtained with sinusoidal datasets and three hidden layers. For the SCG algorithm, the optimal MSE (1.1144e-04) was achieved with fixed step size datasets and one hidden layer. The accuracy of the ANN model is significantly influenced by the dataset, the choice of training optimizer, and the configuration of hidden layers. Consequently, further research could explore hybrid approaches that integrate evolutionary algorithms to leverage their respective strengths and improve overall ANN model performance.

Direct and inverse kinematics solutions of a particular type of 3-PSP parallel manipulator

Abstract In this paper, the direct and inverse kinematics problems for a particular type of 3-DOF, 3-PSP parallel manipulator are considered. The proposed direct kinematics solution is based on an existing one in the literature, but with an alternative, simplified second stage in the solution’s formulation. An explicit analytical solution of the inverse kinematics problem is also proposed for one of the manipulator’s operational modes, requiring one pass through the direct kinematics solution. The proposed solutions can be seamlessly extended to the inverted parallel structure.

Fusion IK: Solving inverse kinematics using a hybridized deep learning and evolutionary approach

Inverse kinematics is a core aspect of robot manipulation. This paper presents an approach to solving Inverse Kinematics (IK) for robots, including articulated industrial ones, combining deep learning with an evolutionary algorithm. Fusion IK passes the manipulator’s target and current joint values into a neural network, the results of which are then used to seed an evolutionary algorithm, Bio IK, to complete the solution of the inverse kinematics problem. Fusion IK allows for solving the position and orientation of the robot while attempting to minimize joint movement times. Comparisons between Fusion IK and its underlying algorithm Bio IK are tested on a six-degree-of-freedom articulated industrial robot as well as a 20-degree-of-freedom robot to explore the move times that Fusion IK produces. The comparisons show that the variations of the Fusion IK algorithm show comparable results to its underlying evolutionary Bio IK algorithm on a six-degrees-of-freedom articulated robot and improvements on a 20-degree-of-freedom robot without any additional hyperparameter tuning. The results show that Fusion IK could be of real value regarding the movement time and the quality of the obtained solutions upon further research, especially with higher degree-of-freedom robots.

Linking Traditional Teaching to Innovative Approaches: Student Conceptions in Kinematics

This study delves into the problem-solving approaches of students who attend classes with traditional teaching methods in university physics education with innovative curriculum materials. This research, conducted with university physics and engineering students, focused on applying research-based curriculum materials in solving kinematic problems. The study analyzes the impact of student knowledge and the distinction between rote learning and scientific practices on conceptual understanding. Student responses are categorized based on the depth of knowledge demonstrated, the skill type utilized, and the degree to which responses indicate a logical progression. These, together with demographic data, are analyzed to determine any patterns. Findings reveal that students use intuitive and mathematical skills to solve a graphical question. However, students employ qualitative and mathematical skill types when they are required to design an experiment. Notably, gender disparity appears to influence the approach to graphical questions, but the design-based question shows no significant relationship between males and females. Gender was likely to contribute to knowledge and logical progression levels, but grades might not show a positive relationship with knowledge level. This study aims to contribute to developing physics education at the university level by highlighting the gap between innovative course materials and their enactment.

Adaptive ANN-BFO Hybrid Method for Solving the Forward Kinematics Problem of a Hexa Parallel Robot

Adaptive ANN-BFO Hybrid Method for Solving the Forward Kinematics Problem of a Hexa Parallel Robot

Inverse kinematic solution and singularity avoidance using a deep deterministic policy gradient approach

<p>The robotic arm emerges as a subject of paramount significance within the industrial landscape, particularly in addressing the complexities of its kinematics. A significant research challenge lies in resolving the inverse kinematics of multiple degree of freedom (M-DOF) robotic arms. The inverse kinematics of M-DOF robotic arms pose a challenging problem to resolve, thus it involves consideration of singularities which affect the arm robot movement. This study aims a novel approach utilizing deep reinforcement learning (DRL) to tackle the inverse kinematic problem of the 6-DOF PUMA manipulator as a representative case within the M-DOF manipulator. The research employs Jacobian matrix for the kinematics system that can solve the singularity, and deep deterministic policy gradient (DDPG) as the kinematics solver. This chosen technique offers enhancing speed and ensuring stability. The results of inverse kinematic solution using DDPG were experimentally validated on a 6-DOF PUMA arm robot. The DDPG successfully solves inverse kinematic solution and avoids the singularity with 1,000 episodes and yielding a commendable total reward of 1,018.</p>

Inverse kinematics of six degrees of freedom robot manipulator based on improved dung beetle optimizer algorithm

Inverse kinematics is a basic problem in robotics, which aims to solve the robot’s joint angles according to the end effector’s position and orientation. This paper proposed an improved spiral search multi-strategy dung beetle optimizer (DBO) algorithm for solving the inverse kinematics problem. The improved DBO algorithm considers not only the error between the target value and the current value but also the previous position of the robot to ensure minimum displacement during the movement. To solve the end position error and orientation error of the robot end effector more accurately, the quaternion is introduced as a penalty factor in the optimization objective function, which is of great significance for reducing the orientation error. Through the improved DBO algorithm, the position error is still accurate, and the orientation error is reduced from 9.5901 to 1.8718. Experimental results show that the proposed algorithm outperforms other swarm-intelligent algorithms in terms of accuracy and convergence speed. Overall, the proposed spiral search multi-strategy DBO algorithm provides an effective and efficient solution to the inverse kinematics problem in robotics.

PPLICATION OF KINEMATIC APPROACHES IN GEOMETRIC PROBLEMS

This work is devoted to the use of kinematic methods in the process of solving geometric problems. The first part of the work is devoted to solving geometric problems by considering the movements of some image points. The minimum knowledge required to apply the kinematic method in elementary geometry is briefly outlined. Then a solution to a generalized version of a well-known geometric problem is presented. The importance of studying elements of operator calculus from an interdisciplinary perspective is also presented. The next part of the article examines problems selected according to the principle of gradual complication, from high school to bachelor’s degree. In these problems, the radius of curvature at various points is determined by kinematic way. Using the result of solving a kinematic problem about a body thrown in a horizontal direction, the expression for the radius of curvature of a parabola is determined. One physical method for determining the radius of curvature of a cycloid is presented. The problem of motion, which generates the equations of an ellipse and a hyperbola, is considered, and a kinematic version of determining the radii of curvature at the points of intersection of these curves and axes of symmetry is presented. The main methodological novelty of the work lies in the development, generalization and systematic presentation of kinematic problems that bring geometric results. Some methodological guidelines and arguments are also given to substantiate the importance of the discussed kinematic approaches to solving geometric problems.

Noise suppression zeroing neural network for online solving the time-varying inverse kinematics problem of four-wheel mobile manipulators with external disturbances

A novel noise suppression zeroing neural network (NSZNN) is presented for the trajectory tracking problem on a four Mecanum wheeled mobile manipulator (FMWMM) by solving its time-varying inverse kinematics (TVIK) problem. The holistic kinematic model of the FMWMM is developed, which can receive synergistic control of the mobile manipulator. Different from the situation without external interference addressed in our previous work, this paper considers a variety of common time-varying interferences by studying the basic principles of various noises, and proves the NSZNN model’s of the validity and superiority, which solves the TVIK problem of the FMWMM with external disturbances through theoretical analyses. Compared with the existing gradient neural network (GNN) and the traditional zeroing neural network (ZNN), the most representative hybrid noise is selected to conduct a large number of experiments to substantiate the high efficiency and robustness of the NSZNN model. Finally, the NSZNN model is verified on the FMWMM via a robot operating system (ROS) by a successful execution of the trajectory tracking task.

Kinematic Modelling of Humanoid Robot Based on Vectorial Approach

The present work is dedicated to the study of the inverse kinematics solution of a humanoid bipedal robot with 30 degrees of freedom using a newly approach based on vectors that generated from the geometric space of the robot. The solutions of the inverse kinematics problem for all joints articulations are carried out through a simple and linear equations. Finally, simulations of results are performed through harmonization of trajectories of end effectors of the robot's members.

Closed-Form Kinematics Solutions for Redundant Medical Robots with Joint Limits and Singularity Avoidance

Closed-form forward and inverse position, velocity and acceleration kinematics problems solutions are developed for a redundant medical robot family. Developed solutions allow one to choose a specific joint as a set one. Solutions work in constant time, suitable for real-time operation. Methods for joint limit and singularity avoidance are proposed. Simulation experiments are performed on simulated KUKA MED 14 r820 robot.