Kinematics Problem Research Articles

Dizajn i razvoj troškovno-efikasne robotske ruke sa robotskim kontrolerom baziranim na PLC-u

To develop a cost-efficient robot arm for a typical pick and place application that can applied in industry, this paper deployed a programmable logic controller (PLC) to control the rotation motion of the robot joints. The main tasks of the PLC controller are to calculate the kinematics, create high-speed pulse outputs for stepper motors, and implement sequence operations for a certain application. Functions are written into subprogram segments. When needed, the main program only turns on the corresponding flag for executing the subprogram. Using the pre-written subprograms, a logical sequence to implement the Pick and Place application is easily implemented and described in this paper. The PLC program is developed to control a SCARA robot with three rotation joins. Stepper motors drive the robot joints. The Delta DVPSV2 PLC is utilized to design the robot controller. This PLC series has four high-speed pulse output pins, which is suitable for this project. Synchronous motion of stepper motors is easily performed using high-speed pulse output commands built into the PLC program. Experimental results of robot arm control have demonstrated the efficiency and accuracy of the developed program. The robot arm's forward and inverse kinematics problems are verified using the simulator on the software. The robot's joints move synchronously as required to perform pick-and-place applications.

A Compact Set of Closed-form Equations for the Set of Dubins and Reeds-Shepp Paths

As the demand for robots and vehicles capable of autonomously navigating through obstacle-rich environments increases, so will the need for software capable of achieving such functionality. To find a collision-free trajectory through an obstacle-rich environment, the use of motion planning software may be necessary. When using the kinematic model of a car, the trajectories found by such software would ideally be composed of Dubins or Reeds-Shepp paths, depending on whether reversing is allowed or not. However, current methods for generating these paths tend to be rather verbose. This paper presents a compact set of closed-form equations that describe the set of Dubins and Reeds-Shepp paths. This set is compact in that the equations describe the set of Dubins and Reeds-Shepp path families as opposed to the set of Dubins and Reeds-Shepp path types, as defined in this paper, reducing the complexity of creating motion planning software when using the kinematic model of a car. These equations are derived by modelling the car as an underactuated system on the special Euclidean group in dimension 2 and then solving an associated set of inverse kinematics problems.

A Novel Method for Spatial Structural Kinematic Analysis

Kinematic analysis is the first task that needs to be solved for further real-life problems such as machine dynamics and durability, machine balancing, and optimization, chemistry, etc. Currently, there are many methods to analyze the kinematic problem, for instance: vector graphics method, vector-analytic method, or Dennavit-Hartenberg-Craig matrix method. Although each method has its advantages, they have mostly encountered difficulties in establishing equations associated with complicated spatial structures. This research proposed a novel method, entitled “'perpendicular projection method” to solve the problem of spatial structural kinematic analysis. This is an approximate solution method that combines the use of generalized coordinates and direction cosine matrices. With this method, the problem of kinematic analysis of spatial structures will be solved simply and easily by establishing connection equations as well as simulating the motion of spatial structures. This method was then applied in conducting the kinematic analysis of a spatial mechanism with 1 rotating joint (R), 1 ball joint (S), 1 translational joint (P), and one cylindrical joint (C). The calculated results, including the velocity, acceleration of generalized coordinates, angular velocity, angular acceleration of the links, velocity, and acceleration of the center of mass of the links, showed the efficiency of the proposed method.

Humanoid Motion Control using Auto Resonance Neural Network

It has been proven difficult to control robots with many mechanical joints due to a variety of problems, including redundant configurations, non-linear displacement, dynamic user surroundings, etc. Iterative computations have been applied to address inverse kinematic problems of industrial robots with up to six Degrees of Freedom (DoF). With one to three degrees of freedom in each of more than hundred joints used by humans for locomotion, the complexity is unfathomable. Consequently, in humanoid structures, algorithmic and heuristic approaches have failed. Numerous research fields that were earlier thought to be challenging to solve with computers have seen interest piqued by recent advancements in artificial intelligence and machine learning. One such domain is humanoid motion. This paper presents a novel kind of Artificial Neural Network named as Auto Resonance Neural Network (ARN). ARN uses the pull-relax mechanism applied by biological systems to control musculoskeletal motion. A variety of functions can be employed to build the pull-relax model, contingent on variables such as range, necessary coverage, and tunability. When employing ARN for joint control, inverse kinematics or some other kind of repetitive solution is not required. Its application is not influenced by the DoF or joint count. The network can use the learning methods like reinforcement learning or supervised or unsupervised learning.

Computational Thinking Skills to Solve Kinematics Problems at High Cognitive Level Cases

Problems of kinematics of rectilinear motion in high-level cognitive level problems often display complexity in their solutions. This research aims to describe the use of computational thinking (CT) methods in helping students solve linear motion kinematics problems designed at a high cognitive level (analysis, evaluation, and creation). This research uses a descriptive quantitative method by using skills observation sheets and analysis of performance results as data collection instruments. The sample was 14 students from the Natural Sciences Tadris study program in introductory physics courses. This research's data analysis technique uses an interpretation of student performance results in solving linear motion kinematics questions at a high cognitive level using the performance stages of the CT method. Significant findings show that the average student cannot solve cases at a high cognitive level using CT skills. Students can only complete and pass the stages of computational thinking skills in the temporary decomposition and abstraction phases but have difficulties in the visualization and design stages at the analysis, evaluation, and creation levels.

STUDYING THE PHYSICAL CHARACTERISTICS OF THE SNAKE ROBOT MOTION BASED ON THE “BIOLOID PREMIUM KIT” CONSTRUCTION

This article examines the physical characteristics of the movement of a snake robot. The main purpose of this work is to develop an algorithm based on the study of the physical characteristics of the movement of a snake robot, which will allow movement in various environmental conditions, both an industrial robot manipulator and a mobile robot. In the course of the work, the equations of motion of the snake robot on various surfaces were obtained. It is established that the snake robot is an open kinematic chain, the elements of which are interconnected by five or more kinematic nodes of rotation based on solving direct and inverse kinematics problems and calculating the position of the robot block in a given orientation. Basedon the study of the physical movements of snakes, a proprietary algorithm for the movement of a snake robot has been developed. A prototype snake robot based on the ROBOTIS BIOLOID Premium Kit was assembled and tested on seven different surfaces. The created high-speed prototype consists of eleven blocks and a CM-530 controller without wheels and ensures high smoothness of movement compared to analogues thanks to the use of the developed algorithm.

Fast Convergent Ali Baba and Forty Thieves Algorithm for Inverse Kinematic Solution of 7-DOF Robotic Manipulator

Inverse kinematics is a crucial topic in robotics, enabling robots to calculate the joint angles required to achieve the desired end effector position and orientation. Solving the inverse kinematics problem quickly with high accuracy is vital for robot manipulators. If sufficient speed is provided, the real-time motion planning task of robot manipulators can be achieved. Real-time motion planning of complex robot manipulators is not possible with classical mathematical methods. Overcoming this problem will provide many benefits in the design and control of robot manipulators. In contemporary research, metaheuristic approaches have become widely employed for addressing the inverse kinematics problem. This investigation utilizes the efficient and simple Ali Baba and the Forty Thieves (AFT) algorithm to resolve the inverse kinematics problem. To increase convergence speed of AFT, a parameter has been used in early iterations of the algorithm to prevent thieves from randomly searching within the search area to find Ali Baba when they realized they had been deceived. Additionally, an approach has been proposed regarding the accuracy of the information brought by the Marjaneh. Finally, the inverse kinematics solution of the 7-DOF robot manipulator was carried out comparatively.

Direct positional kinematics problem of the RRRRT manipulator in the maple software environment

This article presents the direct positional problem of the RRRRT manipulator created by the authors of the 3D model and its movement using the Maple software environment. In this paper, the positional kinematics problem of this manipulator is studied in detail. To find the kinematic characteristics of the manipulator, the Denavit-Hartenberg and Newton-Euler methods were rationally used. The results were obtained in the Maple software environment, which allows you to obtain the results of kinematic characteristics in the form of 3D graphs. Such graphs allow you to visually see how the modules and directions of the given parameters of the manipulator in the graphs change in space, depending on the position of the manipulator in space.

Neural Network Method of Controlling Self-Collisions of Multilink Manipulators Based on the Solution of the Classification Problem

The problem of self-collisions of manipulators with several links installed on a robot can arise when they work together in one zone. To prevent self-collisions, it is necessary to develop methods for their detection and their subsequent inclusion in control algorithms. This paper proposes an approach for determining the occurrence of self-collisions of manipulators using the Artificial Neural Networks approach. In contrast to the regression problem, this article proposes a classification approach. The effectiveness of the proposed approach was tested on robots with multilink manipulators “Ichtiandr” and SAR-401 and their simulators. Self-collision detection using the proposed method is much faster than using the traditional approach of solving the inverse kinematics problem without loss of accuracy. The problem was solved by constructing various Artificial Neural Networks and then checking the accuracy of the solution. A comparative analysis of Artificial Neural Networks was carried out and as a result, the Artificial Neural Networks approach showing the best accuracy was selected. The problem was solved for a robot with two manipulators. The resulting solution can be extended to a larger number of manipulators installed on the robot.

Linear perturbations of the Bloch type of space-periodic magnetohydrodynamic steady states. III. Asymptotics of branching

The previous paper of this series presented the results of a numerical investigation of the dependence of the dominant growth rates of Bloch eigenmodes on the diffusivity parameters (the molecular viscosity ν and molecular magnetic diffusivity η) in three linear stability problems: the kinematic dynamo problem, and the hydrodynamic and MHD stability problems for steady spaceperiodic flows and MHD states. The dominant eigenmodes (i.e., the stability modes, whose growth rates are maximum over the wave vector q of the planar wave involved in the Bloch modes) comprise branches. In some branches, the dominant growth rates are attained for constant half-integer q. In all the three stability problems for parity-invariant steady states, offshoot branches, stemming from the branches of this type, were found, in which the dominant growth rates are attained for q depending on ν and/or η. We consider now such a branching of the dominant magnetic modes in the kinematic dynamo problem, where an offshoot stems from a branch of neutral eigenmodes for q = 0, and construct power series expansions for the offshoots and the associated eigenvalues of the magnetic induction operator near the point of bifurcation. We show that the branching occurs for the molecular magnetic diffusivities, for which the two eigenvalues of the eddy diffusivity operator become imaginary, and magnetic field generation by the mechanism of the negative eddy diffusivity ceases. The details of branching in the other linear stability problems under consideration are distinct.

РОЗРОБКА МАНІПУЛЯТОРА ДЛЯ ПОВНОЇ АВТОМАТИЗАЦІЇ ПРОЦЕСУ ЗАРЯДЖАННЯ ЕЛЕКТРОМОБІЛЕЙ

Electric cars are gradually gaining popularity both in the world and in Ukraine. But in order for them to be freely used throughout the country, an appropriate infrastructure is needed. Unlike traditional cars with internal combustion engines, electric cars can be refuelled anywhere there is access to an electrical outlet. The main problems of electric cars during their operation over long distances are related to the duration of the journey on one charge and the low development of the infrastructure for them. Systems of automated charging stations are also gradually developing. There are already terminals of charging stations with payment by bank card and other payment systems, but they work on the principle of self-service. For full automation of the charging process, connecting the charging station to the electric car without human intervention is not enough. Wireless charging can solve this problem, but at this stage of development, the power transferred in this way is not always enough. To solve this problem, a combination of a manipulator arm and a typical charging station was proposed. The manipulator will determine the vehicle's position and insert the charging station's socket into the car's plug using sensors and machine vision. As part of this work, we made a conceptual project of a manipulator that will automatically connect the connector of the charging station to the car. Also, for this charging complex, a system of monitoring and protection of the electrical connection of the charger with the consumer against short circuit, overheating, sparking and arcing connector was developed, taking into account various interchangeable connectors. When developing the manipulator's arms, the following tasks were taken into account: ensuring sufficient kinematic freedom of movement to cover the working area of the charging station service and maximally simplifying the design. To reliably ensure access to any point of the working space, a kinematic scheme with two translational and three rotational links was used. Next, to determine the position of the manipulator in the workspace, the direct and inverse kinematics problems for this scheme were solved. The physical model of the manipulator along with servomotors, PID controllers and control system based on the equations of kinematics problems was simulated in the Matlab application software package. The implementation of a machine vision system and a switching device protection system is proposed for a full-fledged control system of the automated charging station. The resulting design of the automated charging station is experimental and does not have many analogues in the world. The modularity of the design ensures the versatility of its use at other types of charging stations, as well as the possibility of its modernization.

Development and simulation of the Feed Pusher Robot software and hardware system for the maintenance of the feed table at livestock facilities

BACKGROUND: Analysis of trends in the development of industrial technologies in the field of agriculture showed that manufacturers of technological equipment used on farms turn to robotics to exclude human labor when performing labor-intensive cyclical operations that are accompanied by a high degree of tension. To perform operations for the preparation and distribution of feed on a farm, maintenance of the feed table, as well as for manure harvesting, it is necessary to use a wheeled robotic platform with an automatic positioning system.
 AIMS: Development and testing of the software and hardware system of the Feed Pusher robot for the autonomous execution of operations for the maintenance of the feed table at livestock facilities.
 METHODS: Wheeled robot motion simulation, as well as a mathematical description of the kinematic and dynamic properties of the wheeled robot motion was carried out using the MATLAB software and the Simscape library and the Simulink application. The Figma graphic design software was used to develop layouts of mobile software interfaces for the wheeled robot remote control.
 RESULTS: During the wheeled robot motion simulation, direct and inverse kinematics problems were solved, consisting in finding theω1,ω2, vectors with the input parameters x0,y0,φ0,x,y,φ, as well as the final angle of the path (relative to the horizontal). Layouts of the robot remote control software interfaces have been developed, as well as the frontend and backend development of the program adapted to the use at a smartphone has been carried out. The testing of the wheeled robot was carried out at a livestock facility, during the maintenance of the feed table and the simultaneous execution of operations to push the feed to the fence and dosing of feed additives.
 CONCLUSIONS: The practical value of the research lies in the possibility of using the results of the wheeled robot motion simulation to adjust the operation of the automatic positioning system. At the same time, the farmer using the proposed Feed Pusher robot will ensure an increase in the technological efficiency of cattle keeping, in particular dairy cattle, with an increase in milk yields up to 1 liter per day per head, which was determined during the tests on the farm.

Underwater manipulator that imitates the movements of the human arm

In this paper, the design of a five degrees of freedom (5DoF) underwater manipulator system is presented and discussed. The forward and inverse kinematics problem are solved and shown. Additionally, a system that mimics the human arm movements using a manipulator is proposed. In order to imitate the movement of the human arm, the layout diagram of the IMU sensors and the method of first calibration were presented. The work also presents a device with a simple haptic feedback used to facilitate control of the gripper. The presented approach to the design of a robot control system is dedicated to an underwater robot with the main assumption of reducing the complexity of the system. Taking into account the authors’ knowledge, this approach distinguishes the presented system from solutions known from the literature.

Formative Assessment Strategies by Monitoring Science Students’ Problem-Solving Skill Development

To be able to support students’ competence development in solving physics problems over the course of a lesson series effectively, teachers need a proper appreciation of students’ deficiencies. As teachers commonly assess students’ competence by means of written tests, teachers are challenged to interpret students’ work on these tests and to intervene when some students fail to understand the proper application of solution methods in different contexts. This paper evaluates a formative assessment practice where teachers have been instructed to pinpoint students’ level of understanding of kinematics problems by means of a cognitive diagnostic instrument and to provide personalized hints that match students’ current level of understanding. The study is novel in this sense that the assessment of written tests results of students’ problem solving is not expressed in grades and pass rates, but in terms of cognitive level of understanding. The results show that teachers can determine and monitor shifts of performance of students’ cognitive level of understanding by using this instrument. Second, the results indicate that among students with low initial results, the group that received sufficient feedback via sticky notes made significantly more progress in solving problems than the group that did not receive feed forward on sticky notes. Third, the timing of feedback in the form of sticky notes did not affect on students’ progress in achieving mastery at the end of the instruction period. Our conclusion of this study is: Cognition develops through levels and tiers and support is essential to move to the Zone of Proximal Development. Subsequently, we evaluate group and subgroup implications for didactic interventions and propose suggestions for further investigations.

Using Lie Derivatives with Dual Quaternions for Parallel Robots

We introduce the notion of the Lie derivative in the context of dual quaternions that represent rigid motions and twists. First we define the wrench in terms of dual quaternions. Then we show how the Lie derivative helps understand how actuators affect an end effector in parallel robots, and make it explicit in the two cases case of Stewart Platforms, and cable-driven parallel robots. We also show how to use Lie derivatives with the Newton-Raphson Method to solve the forward kinematic problem for over constrained parallel actuators. Finally, we derive the equations of motion of the end effector in dual quaternion form, which include the effect of inertia from the actuators.

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.

Geometric approach to solving inverse kinematics of six DOF robot with spherical joints

Inverse kinematics is a fundamental concept in robotics that plays a crucial role in a robot’s ability to perform tasks. In this contribution, we propose a novel geometric approach based on vector calculus to solve the inverse kinematics problem. The primary advantage of this approach originates from the solutions, which exhibit a linear form and uncoupled equations. To validate the effectiveness and correctness of our proposed method, we constructed a six-degrees-of-freedom robot. This robot is controlled by an Arduino Mega 2650 on which we have implemented the inverse kinematics algorithm. The validation process involved considering various desired trajectories of the end-effector, which were simulated in Matlab and then performed by the physical robot. Importantly, our findings confirm that the end-effector successfully tracks the predefined trajectories. Furthermore, we conducted a comparative analysis between Paul’s method and the results obtained from joint angles using our proposed approach. Interestingly, our study reveals a significant similarity between the two sets of results, reaffirming the accuracy and validity of the approach presented in this study.

PhyNRnet: Physics-informed Newton-Raphson Network for Forward Kinematics Solution of Parallel Manipulators

Abstract Despite significant performance advantages, the intractable forward kinematics have always restricted the application of parallel manipulators to small posture spaces. Traditional analytical method and Newton-Raphson method usually cannot solve this problem well due to lack of generality or latent divergence. To address this issue, this study employs recent advances in deep learning to propose a novel physics-informed Newton-Raphson network (PhyNRnet) to rapidly and accurately solve this forward kinematics problem for general parallel manipulators. The main strategy of PhyNRnet is to combine the Newton-Raphson method with the neural network, which helps to significantly improve the accuracy and convergence speed of the model. In addition, to facilitate the network optimization, semi-autoregression, hard imposition of initial/boundary conditions (I/BCs), batch normalization, etc. are developed and applied in PhyNRnet. Unlike previous data-driven paradigms, PhyNRnet adopts the physics-informed loss functions to guide the network optimization, which gives the model clear physical meaning and helps improve generalization ability. Finally, the performance of PhyNRnet is verified by three parallel manipulator paradigms with large postures, where the Newton-Raphson method has generally diverged. Besides, the efficiency analysis shows that PhyNRnet consumes only a small amount of time at each time step, which meets the real-time requirements.

The dynamic factor particle swarm optimization (DFPSO) to inverse kinematics of CMOR based on pose decomposition strategy

The Chinese Fusion Engineering Testing Reactor (CFETR) is a superconducting Tokamak device, whose components would get gradually damaged by being susceptible to high temperature, strong magnetic field, radiation, and so on, and should be maintained regularly. The CFETR Multipurpose Overload Robot (CMOR) is a redundant robot designed as a macro-micro arm structure for a gigantic workspace in the blanket and diverter of CFETR's maintenance. Due to the macro-micro arm structure, the robot has a high degree of freedom, and its serial DOF is up to 16 so the traditional algorithm is low efficient for the robot's kinematics. Hence, in this paper, a kinematic decomposition strategy is proposed to allocate or decouple the position aim. Besides, a novel particle swarm optimization (PSO) with dynamic accuracy called dynamic factor particle swarm optimization (DFPSO) is designed to accelerate solving the high-dimensional nonlinear kinematic problem and to improve accuracy. The results of the research show the validation and efficiency of DFPSO in the CMOR system's kinematics. Moreover, it's also a universal kinematic algorithm for all high-DOF robots.

A two-step solution for robot-world calibration made intelligible by implementing Chasles’ motion decomposition in Ad(SE(3))

As a typical kinematic problem, an important criterion for the accuracy of robot-world calibration is whether the rotational and translational parts are calculated separately or not. Solving the kinematic equation separately increases the interest into the decomposition mode of the equation. This paper provides a decomposition mode for Ad(SE(3)) with embedded Chasles’ motion, providing a new decomposition mode for the robot-world equation. Firstly, the Lie algebra ad(se(3)) for Chasles’ rotational and translational motions are constructed and mapped exponentially to the Lie group Ad(SE(3)) separately, thus implementing the Chasles’ motion decomposition of Ad(SE(3)). Subsequently, the robot-world equation in Ad(SE(3)) is derived based on joint kinematics. A new decomposition mode for robot-world equation is proposed through the Chasles’ motion decomposition, and a two-step method based on point set matching is proposed. Finally, the effect of coordinate invariants on the calibration accuracy is discussed, and the superiority of the proposed method is verified with simulation and experimental tests.