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1

Singularity-robust inverse kinematics for serial manipulators

Dulęba Ignacy

Journal of Automation Mobile Robotics and Intelligent Systems

|

2023

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Vol. 17, No. 3

38--45

EN

This paper is a practical guideline on how to analyze and evaluate the literature algorithms of singularity- robust inverse kinematics or to construct new ones. Additive, multiplicative, and based on the Singularity Value Decomposition (SVD) methods are examined to retrieve well-conditioning of a matrix to be inverted in the Newton algorithm of inverse kinematics. It is shown that singularity avoidance can be performed in two different, but equivalent, ways: either via properly modified manipulability matrix or not allowing the decrease of the minimal singular value below a given threshold. It is discussed which method can always be used and which can only be used when some pre‐conditions are met. Selected methods are compared to with respect to the efficiency of coping with singularities based on a theoretical analysis as well as simulation results. Also, some questions important for mathematically and/or practically oriented roboticians are stated and answered.

2

Forward and inverse kinematics solution of a robotic manipulator using a multilayer feedforward neural network

Sharkawy Abdel-Nasser

Journal of Mechanical and Energy Engineering

|

2022

|

Vol. 6, No 2

1--17

EN

In this paper, a multilayer feedforward neural network (MLFFNN) is proposed for solving the problem of the forward and inverse kinematics of a robotic manipulator. For the forward kinematics solution, two cases are presented. The first case is that one MLFFNN is designed and trained to find solely the position of the robot end-effector. In the second case, another MLFFNN is designed and trained to find both the position and the orientation of the robot end-effector. Both MLFFNNs are designed considering the joints’ positions as the inputs. For the inverse kinematics solution, a MLFFNN is designed and trained to find the joints’ positions considering the position and the orientation of the robot end-effector as the inputs. For training any of the proposed MLFFNNs, data is generated in MATLAB using two different cases. The first case is that data is generated assuming an incremental motion of the robot’s joints, whereas the second case is that data is obtained with a real robot considering a sinusoidal joint motion. The MLFFNN training is executed using the Levenberg-Marquardt algorithm. This method is designed to be used and generalized to any DOF manipulator, particularly more complex robots such as 6-DOF and 7-DOF robots. However, for simplicity, this is applied in this paper using a 2-DOF planar robot. The results show that the approximation error between the desired output and the estimated one by the MLFFNN is very low and it is approximately equal to zero. In other words, the MLFFNN is efficient enough to solve the problem of the forward and inverse kinematics, regardless of the joint motion type.

3

Digital Twin: industrial robot kinematic model integration to the virtual reality environment

Kuts Vladimir, Cherezova Natalia, Sarkans Martins, Otto Tauno

Journal of Machine Engineering

|

2020

|

Vol. 20, No. 2

53--64

EN

Digital Twin (DT) concept nowadays is shown via the simulations of the manufacturing systems and included those production processes and parametric 3D models of the product. It is the primary method for planning, analysing and optimising the factory layout and processes. Moreover, work on management via the simulation in real-time is already done using Virtual Reality (VR) tools from a safe and remote environment. However, there is a list of limitation of such kind of digital systems, as connectivity speed and precision of the digital environment. The primary goal of this study is to access second listed limitation and on the example of the fully synchronised physical with its digital replica industrial robot, increase the level of precision of the developed DT environment. The proposed approach introduces transfer of the mathematical model to the virtual environment, thus creating a precise and scaled visual model of the Industrial Robot.

4

Projekt i wykonanie czterokołowego robota z wykorzystaniem kinematyki odwrotnej

Szywalski Patryk, Waindok Andrzej

Śląskie Wiadomości Elektryczne

|

2019

|

Nr 4 (126)

12--15

PL

W artykule opisano projekt oraz wykonanie robota czterokołowego. Do budowy urządzenia wykorzystano klocki Lego Technic. Do sterowania wykorzystano Raspberry Pi2 wraz z dołączonymi rozszerzeniami. Urządzenie zostało zbudowane w celu zdalnego monitoringu mieszkania. Pojazd posiada kamerę, której obraz rejestrowany jest na serwerze.

EN

A project and construction of a four-wheel robot were presented in the paper. Lego Technic bricks were used to build the device. The main controller is based on the Raspberry Pi2 board with additional modules. The device was built for remote monitoring of the flat. The device | has a camera whose video is registered on an external server.

5

An exoskeleton arm optimal configuration determination using inverse kinematics and genetic algorithm

Głowiński Sebastian, Błażejewski Andrzej

Acta of Bioengineering and Biomechanics

|

2019

|

Vol. 21, no. 1

45--53

EN

This paper deals with the kinematic modelling of an arm exoskeleton used for human rehabilitation. The biomechanics of the arm was studied and the 9 Degrees of Freedom model was obtained. The particular (optimal) exoskeleton arm configuration is needed, depending on patient abilities and possibility or other users activity. Methods: The model of upper arm was obtained by using Denavit–Hartenberg notation. The exoskeleton human arm was modelled in MathWorks package. The multicriteria optimization procedure was formulated to plan the motion of trajectory. In order to find the problem solution, an artificial intelligence method was used. Results: The optimal solutions were found applying a genetic algorithm. Two variants of motion with and the visualization of the change of joints angles were shown. By the use of genetic algorithms, movement trajectory with the Pareto-optimum solutions has been presented as well. Creating a utopia point, it was possible to select only one solution from Pareto-optimum results. Conclusions: The obtained results demonstrate the efficiency of the proposed approach that can be utilized to analyse the kinematics and dynamics of exoskeletons using the dedicated design process. Genetic algorithm solution could be implemented to command actuators, especially in the case of multi-criteria problems. Moreover, the effectiveness of this method should be evaluated in the future by real experiments.

6

Singularity robust trajectory generator for robotic manipulator based on genetic algorithm with dynamic encoding of solutions

Gierlak P.

Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika

|

2018

|

z. 90 [298], nr 4

465--480

EN

In this paper a singularity robust trajectory generator for robotic manipulators is presented. The generator contains the procedure of solving the inverse kinematics problem. This issue is defined as an optimization problem, where a genetic algorithm is used for optimizing the fitness function. In order to avoid singularity problem, the generator is based on the direct kinematics problem. The trajectory generator allows to obtain generalized coordinates, velocities and accelerations. Simulation results show that the procedure generates a trajectory of manipulator even in kinematics singularities.

PL

W niniejszym artykule przedstawiono generator trajektorii robota manipulacyjnego odporny na osobliwości kinematyki. Generator zawiera procedurę rozwiązywania zadania odwrotnego kinematyki. Problem ten jest zdefiniowany jako problem optymalizacyjny, w którym algorytm genetyczny służy do optymalizacji funkcji dopasowania opierającej się na błędzie rozwiązania zadania. Aby wyeliminować problem osobliwości, generator wykorzystuje zadanie proste kinematyki. Generator trajektorii umożliwia uzyskanie uogólnionych współrzędnych, prędkości i przyspieszeń manipulatora. Wyniki symulacji wskazują, że opracowana procedura generuje trajektorię manipulatora nawet w przypadku wystąpienia osobliwości kinematyki.

7

Badania symulacyjne robota mobilnego kroczącego po schodach

Sperzyński P., Szrek J., Muraszkowski A.

Modelowanie Inżynierskie

|

2018

|

T. 36, nr 67

58--65

PL

Roboty kołowo-kroczące są platformami hybrydowymi powstałymi z połączenia robotów kołowych i kroczących. Łączą wiele zalet obydwu typów lokomocji. Napęd jazdy pozwala na przemieszczanie się robota z dużymi prędkościami, natomiast, gdy robot napotka przeszkody uniemożliwiające ich ominięcie, może pokonać je, krocząc. W pracy przedstawiono symulację ruchu robota, podczas gdy napotyka na swojej drodze schody standardowych rozmiarów. Pokonanie takiej przeszkody jest trudne, ponieważ należy zachować stabilność platformy podczas podnoszenia kończyn. W celu analizy ruchu zbudowano model komputerowy robota w programie MSC Adams. Przedstawiona analiza pozwoli w przyszłości na zaplanowanie i wykonanie eksperymentu polegającego na wejściu robota na schody i dalszą analizę algorytmów kroczenia.

EN

Wheel-legged robots are hybrid platforms build upon combination of wheeled rovers and walking robots. Bonds many advantages of both kinds of locomotion. Wheel drive allows high speed maneuvers, when actuated limbs allows robot to overcome obstacles higher than wheel’s radius. In the paper, simulation of the robot climbing the stairs has been presented. Negotiating such obstacle brings many difficulties due to need of ensuring continuously stability of robot’s platform. In order to analyze robot motion, numerical model in MSC Adams has been created. In the future, presented analysis allows to prepare experiment and verify current result.

8

A comparison of methods solving repeatable inverse kinematics for robot manipulators

Duleba I., Karcz-Duleba I.

Archives of Control Sciences

|

2018

|

Vol. 28, No. 1

5--18

EN

In this paper two recent methods of solving a repeatable inverse kinematic task are compared. The methods differ substantially although both are rooted in optimization techniques. The first one is based on a paradigm of continuation methods while the second one takes advantage of consecutive approximations. The methods are compared based on a quality of provided results and other quantitative and qualitative factors. In order to get a statistically valuable comparison, some data are collected from simulations performed on pendula robots with different paths to follow, initial configurations and a degree of redundancy.

9

Sterowanie awatarem człowieka przez aproksymację pozy osoby zanurzonej w środowisku wirtualnym za pomocą systemu wizyjnego i kinematyki odwrotnej

Welenc H., Jankowski J.

Przegląd Mechaniczny

|

2017

|

nr 9

62--64

PL

Projektowanie wysokiej jakości środowisk wirtualnych przeznaczonych do edukacji w zakresie bezpieczeństwa pracy wymaga uwzględnienia aspektu bezpiecznego poruszania się w obrębie symulowanego stanowiska. Do osiągnięcia tego celu niezbędne jest stworzenie numerycznego modelu ludzkiego ciała, który naśladuje ruchy osoby szkolonej w wirtualnym świecie. W opracowaniu zostanie przedstawiona technika przechwytywania przybliżonej pozy człowieka i jej przenoszenia na wirtualny model ciała ludzkiego, optymalna dla szkolenia wielu osób jednocześnie.

EN

The design of high-quality VR environments concerned about the issue of labour safety requires considering the aspect of safe moving within the simulated workstation. To achieve this creation of numeric model of the human body that mimics the motion of a person trained within a virtual world is mandatory. In this paper a technique, that concerns the acquisition of approximated pose of a human body and transfering said pose into the virtual model of a human body, optimal for training many people simultaneously, will be presented

10

Applied inverse kinematics for bipedal characters moving on the diverse terrain

Burdka Ł., Rohleder P.

Machine Graphics and Vision

|

2017

|

Vol. 26, No. 1/4

3--11

EN

A solution to the problem of adjusting the pose of an animated video game character to the diverse terrain and surroundings is proposed. It is an important task in every modern video game where there is a focus on animated characters. Not addressing this issue leads to major visual glitches such as legs hovering above the ground surface, or penetrating the obstacles while moving. As presented in this work, the described problem can be effectively solved by examining the surroundings in real-time and applying Inverse Kinematics (IK) as a procedural post process to the currently used animation.

11

Suboptimal approximations in repeatable inverse kinematics for robot manipulators

Duleba I., Karcz-Duleba I.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2017

|

Vol. 65, nr 2

209--217

EN

In this paper a repeatable inverse kinematic task was solved via an approximation of a pseudo-inverse Jacobian matrix of a robot manipulator. An entry configuration to the task was optimized and a task-dependent definition of an approximation region, in a configuration space, was utilized. As a side effect, a relationship between manipulability and optimally augmented forward kinematics was established and independence of approximation task solutions on rotations in augmented components of kinematics was proved. A simulation study was performed on planar pendula manipulators. It was demonstrated that selection of an initial configuration to the repeatable inverse kinematic task heavily impacts solvability of the task and its quality. Some remarks on a formulation of the approximation task and its numerical aspects were also provided.

12

An inverse kinematic algorithm for the human leg

Głowiński S., Krzyżyński T.

Journal of Theoretical and Applied Mechanics

|

2016

|

Vol. 54 nr 1

53--61

EN

In this article, a 3-link kinematic model of a human leg is defined and analyzed with focus on optimizing the manipulability. The forward kinematics for the leg is used to define quantitative measures of the manipulability and workspace in a sagittal plane. Analytical results for different manipulability indices are derived. Using numerical optimization in Matlab package, the manipulability measure is optimized under different constraints. The range of motion and joint comfort zones of every joint is defined. The algorithm for redundant chain, based on analytical equations, is proposed in inverse kinematics.

13

A New Approach for Handling Element Accessibility Problems Faced by Persons with a Wheelchair

Saidi Sief A., Pruski A., Bennia A.

Journal of Automation Mobile Robotics and Intelligent Systems

|

2016

|

Vol. 10, No. 4

27--39

EN

The built environment accessibility evaluation is required if the person physical capacities no longer correspond to the habitat requirements, which generally occur after an accident. For the person with disabilities, the inner accessibility of habitat is a highly important factor that allows him to live and work independently. This paper presents a new approach to determine the accessibility of handling elements like doors, windows, etc. inside the habitat for the wheelchair user. Thus, allowing housing professionals to assess the needed changes in terms of accessibility. The idea is to involve a new computer approach to evaluating the performance of these elements against wheelchair user capacity. The presented approach simulated wheelchair user behavior when he/ she is operating a handling element in order to determine the dimensions/positions of wheelchair clearance space and handle grip optimal heights while considering wheelchair arrival direction and respecting joint limits constraints of person upper body and wheelchair nonholonomy constraints.

14

Quaternions – alternative for Euler angles in kinematic analysis of machine mechanisms

Czyżewski T.

Czasopismo Techniczne. Mechanika

|

2015

|

Y. 112, iss. 2-M

19--26

EN

The article presents some types of problems that can occur during solving the inverse kinematics and the steps to prevent them. These problems concern the numerical singularities which occur when Euler angles are used to describe the orientation of the mechanism links in space. This paper proposes to eliminate the mentioned numerical singularities by replacing Euler angles with quaternions. The discussed issues were shown on the example of a backhoe excavator equipment system.

PL

W artykule przedstawiono pewien typ problemów, jakie mogą wystąpić podczas rozwiązywania zadania odwrotnego kinematyki oraz kroki pozwalające na ich zapobieganie. Problemy te dotyczą osobliwości numerycznych powstałych w wyniku stosowania kątów Eulera do opisu orientacji członów mechanizmu w przestrzeni. Poniższa praca proponuje wyeliminowanie wspomnianych osobliwości numerycznych poprzez zastąpienie katów Eulera kwaternionami. Poruszane zagadnienia przedstawiono na przykładzie osprzętu roboczego koparki podsiębiernej.

15

Reference trajectory tracking for a multi-DOF robot arm

Krasňanský R., Valach P., Soós D., Zarbakhsh J.

Archives of Control Sciences

|

2015

|

Vol. 25, no. 4

513--527

EN

This paper presents the problem of tracking the generated reference trajectory by the simulation model of a multi-DOF robot arm. The kinematic transformation between task space and joint configuration coordinates is nonlinear and configuration dependent. To obtain the solution of the forward kinematics problem, the homogeneous transformation matrix is used. A solution to the inverse kinematics is a vector of joint configuration coordinates calculated using of pseudoinverse Jacobian technique. These coordinates correspond to a set of task space coordinates. The algorithm is presented which uses iterative solution and is simplified by considering stepper motors in robot arm joints. The reference trajectory in Cartesian coordinate system is generated on-line by the signal generator previously developed in MS Excel. Dynamic Data Exchange communication protocol allows sharing data with Matlab-Simulink. These data represent the reference tracking trajectory of the end effector. Matlab-Simulink software is used to calculate the representative joint rotations. The proposed algorithm is demonstrated experimentally on the model of 7-DOF robot arm system.

16

Design of inverse kinematics algorithms: extended Jacobian approximation of the dynamically consistent Jacobian inverse

Ratajczak J.

Archives of Control Sciences

|

2015

|

Vol. 25, no. 1

35--50

EN

The paper presents the approximation problem of the inverse kinematics algorithms for the redundant manipulators. We introduce the approximation of the dynamically consistent Jacobian by the extended Jacobian. In order to do that, we formulate the approximation problem and suitably defined approximation error. By the minimization of this error over a certain region we can design an extended Jacobian inverse which will be close to the dynamically consistent Jacobian inverse. To solve the approximation problem we use the Cholesky decomposition and the Ritz method. The computational example illustrates the theory.

17

Prototyp manipulatora do zadań specjalnych

Świstak Ł., Szrom D., Szlachta A.

Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej

|

2014

|

Nr 38

69--72

PL

W pracy opisano prototyp manipulatora przeznaczonego do pracy w warunkach szkodliwych. Przedstawiono strukturę oraz funkcjonalność manipulatora. Przedstawiany w artykule prototyp manipulator pozwala studentom zapoznać się z zagadnieniami kinematyki odwrotnej oraz konfiguracji osobliwej Prototyp manipulatora został wykonany w skali 1:5. Opracowany system składa się z konstrukcji manipulatora, wraz ze sterownikiem i modułem Bluetooth oraz aplikacją do obsługi robota.

EN

The work describes a prototype manipulator designed to work under harmful conditions. The prototype of manipulator enables students to familiarize with problems of inverse kinematics and singular configuration was presented. Developed manipulator has been built at a scale of 1:5. The article presents the structure and functionality of the manipulator. The developed system consists of wireless communication by Bluetooth and control system. The application window, which was written in C #, is dedicated to communicate with the manipulator. Control of manipulator is carried out in three modes of operation.

18

Position Project to Study Selected Characteristics of the Optoelectronic Heads in RobotStudio

Kaczmarek W., Panasiuk J.

Problemy Mechatroniki : uzbrojenie, lotnictwo, inżynieria bezpieczeństwa

|

2014

|

Vol. 5, Nr 3 (17)

7-22

EN

In the article, a project of robotized positions to study optoelectronic heads in the RobotStudio environment was presented. The authors suggested to use industrial robots in order to simulate movement of the head holder as well as tracked objects. Modern RobotStudio programming environment application with virtual controller technology allowed for accurate reflection of the research position functionality. As a part of the carried out works, the control programs were drawn up in RAPID language.

19

Aproksymacja algorytmu jakobianu dynamicznie zgodnego algorytmem typu jakobianu rozszerzonego

Ratajczak J.

Prace Naukowe Politechniki Warszawskiej. Elektronika

|

2014

|

z. 194, t. 2

649--658

PL

Praca przedstawia metodę aproksymacji algorytmu jakobianu dynamicznie zgodnego algorytmem typu jakobianu rozszerzonego. Rozwiązanie zadania aproksymacji sprowadza się do znalezienia optymalnej funkcji rozszerzającej minimalizującej błąd aproksymacji. W celu wyznaczenia optymalnego przybliżenia posłużymy się metodą bezpośrednią rachunku wariacyjnego, jaką jest metoda Ritza. Wywody teoretyczne poparte są badaniami symulacyjnymi robota o czterech stopniach swobody.

EN

The paper presents the approximation problem of the inverse kinematics algorithms for the redundant manipulators. We focus on the approximation of the dynamically consistent Jacobian by the extended Jacobian. For this aim we formulate the approximation problem with suitably defined approximation error. By the minimization of this error over a certain region we can design an extended Jacobian inverse which will be close to the dynamically consistent Jacobian. To solve the approximation problem we use the Ritz method. Theoretical considerations are supported by numerical simulations.

20

Integracja czujników inercyjnych z konstrukcją robota humanoidalnego cz. II

Świątek-Brzeziński P., Kosiński P.

Pomiary Automatyka Kontrola

|

2013

|

R. 59, nr 1

47--50

PL

W niniejszym artykule przedstawiono algorytmy sterowania robotem humanoidalnym firmy Futaba. Zaprezentowano wykorzystanie sztucznych sieci neuronowych, jako alternatywnego sposobu obliczenia kinematyki odwrotnej oraz wykorzystanie środowiska Microsoft Robotics Developer Studio do tworzenia złożonych, wielowątkowych aplikacji szeroko stosowanych w robotyce. Ponadto pokazano zastosowanie środowiska symulacyjnego VSE (Visual Simulation Environment) w procesie prototypowania algorytmów sterujących.

EN

This paper presents a control system for a Futaba humanoid robot [1]. It is equipped with a controller board based on a microcontroller with an ARM7TDMI core, a full set of inertial sensors and a 2.4 GHz wireless communication module. The controller uses the wireless communication module to send information about the robot state to a PC on which the controlling application is run. This paper focuses on the software part of the presented system (the hardware part has been presented in the first part of this paper). In order to develop a controlling algorithm, an analysis of robot kinematics was made and equations for direct kinematics were derived in consistency with the Denavit-Hartenberg convention. To eliminate the necessity of designating equations for inverse kinematics, which can be very complex due to the kinematic redundancy of the robot, an artificial neural network was used (Fig. 2). The application was written using the Microsoft Robotics Developer Studio designed for creating complex, multithread, distributed and scalable applications used in robotics. The application uses the data acquired by radio to implement the walking and balance-keeping algorithms. For visualization of the robot movement, testing and development of the algorithms without the risk of damaging the robot, a simulation in the Visual Simulation Environment, a part of the Microsoft Robotics Developer Studio, was created. A 3D model of the robot was used in this simulation (Fig. 4).