This document discusses algorithms for avoiding kinematic singularities in 6-DOF robotic manipulators controlled in real time using a teaching pendant. It proposes two algorithms: (1) non-redundancy avoidance using damped least squares to modify the inverse kinematic solution near singularities, and (2) redundancy avoidance using a potential function based on manipulability to incorporate singularity avoidance for redundant manipulators. The algorithms are experimentally tested on a DENSO VP-6242G robot to evaluate performance near shoulder and wrist singularities during teaching pendant controlled motion.
Solution of Inverse Kinematics for SCARA Manipulator Using Adaptive Neuro-Fuz...ijsc
Solution of inverse kinematic equations is complex problem, the complexity comes from the nonlinearity of joint space and Cartesian space mapping and having multiple solution. In this work, four adaptive neurofuzzy networks ANFIS are implemented to solve the inverse kinematics of 4-DOF SCARA manipulator. The implementation of ANFIS is easy, and the simulation of it shows that it is very fast and give acceptable
error.
Development of a quadruped mobile robot and its movement system using geometr...journalBEEI
As the main testbed platform of Artificial Intelligence, the robot plays an essential role in creating an environment for industrial revolution 4.0. According to their bases, the robot can be categorized into a fixed based robot and a mobile robot. Current robotics research direction is interesting since people strive to create a mobile robot able to move in the land, water, and air. This paper presents development of a quadruped mobile robot and its movement system using geometric-based inverse kinematics. The study is related to the movement of a four-legged (quadruped) mobile robot with three Degrees of Freedom (3 DOF) for each leg. Because it has four legs, the movement of the robot can only be done through coordinating the movements of each leg. In this study, the trot gait pattern method is proposed to coordinate the movement of the robot's legs. The end-effector position of each leg is generated by a simple trajectory generator with half rectified sine wave pattern. Furthermore, to move each robot's leg, it is proposed to use geometric-based inverse kinematic. The experimental results showed that the proposed method succeeded in moving the mobile robot with precision. Movement errors in the translation direction are 1.83% with the average pose error of 1.33 degrees, means the mobile robot has good walking stability.
PSO APPLIED TO DESIGN OPTIMAL PD CONTROL FOR A UNICYCLE MOBILE ROBOTJaresJournal
In this work, we propose a Particle Swarm Optimization (PSO) to design Proportional Derivative
controllers (PD) for the control of Unicycle Mobile Robot. To stabilize and drive the robot precisely with
the predefined trajectory, a decentralized control structure is adopted where four PD controllers are used.
Their parameters are given simultaneously by the proposed algorithm (PSO). The performance of the
system from its desired behavior is quantified by an objective function (SE). Simulation results are
presented to show the efficiency of the method. ).
The results are very conclusive and satisfactory in terms of stability and trajectory tracking of unicycle
mobile robot
Identification and Control of Three-Links Electrically Driven Robot Arm Using...Waqas Tariq
This paper uses a fuzzy neural network (FNN) structure for identifying and controlling nonlinear dynamic systems such three links robot arm. The equation of motion for three links robot arm derived using Lagrange’s equation. This equation then combined with the equations of motion for dc. servo motors which actuated the robot. For the control problem, we present the forward and inverse adaptive control approaches using the FNN. Computer simulation is performed to view the results for identification and control
Stabilization of Six-Legged Robot on Tilt Surface With 9 DOF IMU Based on Inv...IJRES Journal
Robot is a tool which is developed very fast. There are several types of robots, one of them is six-legged robot. One of the problems of this robot is when the robot walks on the tilt surface. This would result the movement of the robot could be late and the center of gravity is not balanced. In this research, stabilization of six-legged robot walking on tilt surface using nine degree of freedom (DOF) inertial measurement unit (IMU) sensor based on invers kinematic is designed. The IMU sensor comprises a gyroscope, a magnetometer, and three-axis accelerometer. This sensor works as the input of the tilt degree and heading of the robot, therefore they can be processed in fuzzy-pid controller to balance the body of the robot on tilt surface. The results show that the robot will move forward when the x-axis translation inverse changed from its original position, move aside when the y-axis translational modified and move up and down if the translation to the z-axis was changed. From the testing of IMU get the total of RMSE pitch is 1,73%, roll =1,67% and yaw = 1,24%. In controller fuzzy-pid get the good respon is on the value Kp have k1=0,5, k2=1 , k3 = 3 , Ki have k1=0,5 , k2=0,5, k3=0,5 and Kd have k1=0,25 , k2=0,35 dan k3=0,45.
Solution of Inverse Kinematics for SCARA Manipulator Using Adaptive Neuro-Fuz...ijsc
Solution of inverse kinematic equations is complex problem, the complexity comes from the nonlinearity of joint space and Cartesian space mapping and having multiple solution. In this work, four adaptive neurofuzzy networks ANFIS are implemented to solve the inverse kinematics of 4-DOF SCARA manipulator. The implementation of ANFIS is easy, and the simulation of it shows that it is very fast and give acceptable
error.
Development of a quadruped mobile robot and its movement system using geometr...journalBEEI
As the main testbed platform of Artificial Intelligence, the robot plays an essential role in creating an environment for industrial revolution 4.0. According to their bases, the robot can be categorized into a fixed based robot and a mobile robot. Current robotics research direction is interesting since people strive to create a mobile robot able to move in the land, water, and air. This paper presents development of a quadruped mobile robot and its movement system using geometric-based inverse kinematics. The study is related to the movement of a four-legged (quadruped) mobile robot with three Degrees of Freedom (3 DOF) for each leg. Because it has four legs, the movement of the robot can only be done through coordinating the movements of each leg. In this study, the trot gait pattern method is proposed to coordinate the movement of the robot's legs. The end-effector position of each leg is generated by a simple trajectory generator with half rectified sine wave pattern. Furthermore, to move each robot's leg, it is proposed to use geometric-based inverse kinematic. The experimental results showed that the proposed method succeeded in moving the mobile robot with precision. Movement errors in the translation direction are 1.83% with the average pose error of 1.33 degrees, means the mobile robot has good walking stability.
PSO APPLIED TO DESIGN OPTIMAL PD CONTROL FOR A UNICYCLE MOBILE ROBOTJaresJournal
In this work, we propose a Particle Swarm Optimization (PSO) to design Proportional Derivative
controllers (PD) for the control of Unicycle Mobile Robot. To stabilize and drive the robot precisely with
the predefined trajectory, a decentralized control structure is adopted where four PD controllers are used.
Their parameters are given simultaneously by the proposed algorithm (PSO). The performance of the
system from its desired behavior is quantified by an objective function (SE). Simulation results are
presented to show the efficiency of the method. ).
The results are very conclusive and satisfactory in terms of stability and trajectory tracking of unicycle
mobile robot
Identification and Control of Three-Links Electrically Driven Robot Arm Using...Waqas Tariq
This paper uses a fuzzy neural network (FNN) structure for identifying and controlling nonlinear dynamic systems such three links robot arm. The equation of motion for three links robot arm derived using Lagrange’s equation. This equation then combined with the equations of motion for dc. servo motors which actuated the robot. For the control problem, we present the forward and inverse adaptive control approaches using the FNN. Computer simulation is performed to view the results for identification and control
Stabilization of Six-Legged Robot on Tilt Surface With 9 DOF IMU Based on Inv...IJRES Journal
Robot is a tool which is developed very fast. There are several types of robots, one of them is six-legged robot. One of the problems of this robot is when the robot walks on the tilt surface. This would result the movement of the robot could be late and the center of gravity is not balanced. In this research, stabilization of six-legged robot walking on tilt surface using nine degree of freedom (DOF) inertial measurement unit (IMU) sensor based on invers kinematic is designed. The IMU sensor comprises a gyroscope, a magnetometer, and three-axis accelerometer. This sensor works as the input of the tilt degree and heading of the robot, therefore they can be processed in fuzzy-pid controller to balance the body of the robot on tilt surface. The results show that the robot will move forward when the x-axis translation inverse changed from its original position, move aside when the y-axis translational modified and move up and down if the translation to the z-axis was changed. From the testing of IMU get the total of RMSE pitch is 1,73%, roll =1,67% and yaw = 1,24%. In controller fuzzy-pid get the good respon is on the value Kp have k1=0,5, k2=1 , k3 = 3 , Ki have k1=0,5 , k2=0,5, k3=0,5 and Kd have k1=0,25 , k2=0,35 dan k3=0,45.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Attitude Estimation And Compensation In Odometric Localization of Mobile Robo...Waqas Tariq
The paper introduces the attitude estimation and compensation in odometric localization of a differential drive indoor mobile robot. A mobile robot navigates through an inclined indoor environment, wherein localization using only wheel encoder is erroneous. The robot uses inertial sensors such as gyroscope, accelerometer and magnetometer to calculate its attitude and acquires a three degree of rotational data. It is observed that the attitude update using gyroscopes alone are prone to diverge and hence error needs to be eliminated. The advantage of MEMS sensors is less-cost while complementary filter algorithm is low complexity in implementation. The performance of the proposed complementary filter algorithm for attitude estimation and compensation in odometric localization are shown by experiment and analysis of results.
A NOVEL NAVIGATION STRATEGY FOR AN UNICYCLE MOBILE ROBOT INSPIRED FROM THE DU...JaresJournal
This paper deals with the design and the implementation of a novel navigation strategy for an unicycle
mobile robot. The strategy of navigation is inspired from nature (the duck walking) in the closed loop.
Therefore, a single sensor (gyroscope) is used to determine the pose of the robot, hence the proposed name
"gyroscopic navigation". A global presentation of the novel strategy and the robot and with its different
components are given. An experimental identification for the useful parameters are then exhibited.
Moreover, the controller design strategy and the simulation results are given. Finally, real time
experiments are accomplished to valid the simulation results.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Ziegler nichols pid controller for effective pay-load torque responses and ti...eSAT Journals
Abstract Robotic Technology is an imitation for human being’s. It is an electro mechanical modelling objects are important aspect of manipulator. A Manipulator is a machine able to drive the robot. This paper describes and investigates on effective pay-load torque responses, tip-vibrations. This paper presents modelling and simulation of the double link manipulator using the proposed PID Controller. Here the proposed Ziegler-Nichols proportional–integral–derivative controller (PID controller) initiates more advantageous in the view of better performance and flexible operation of manipulator. First, the electro mechanical object was modeled and simulated using State space technique. Here the torque responses and end tip vibrations are assigned by state space variables. The entire two link manipulator topology was investigated and modeled, simulated. The proposed control strategy carries a back –back feed forward controller can be used for flexible operation of manipulator. Here, the simulation was done by using M-File Technique in Control tool box of MATLAB. Keywords: Double Link Manipulator, Ziegler-Nichols PID Controller, Pay-Load Torque Responses, Tip-Vibrations, State space technique, back –back feed forward controller
Insect inspired hexapod robot for terrain navigationeSAT Journals
Abstract The aim of this paper is to build a sixlegged walking robot that is capable of basicmobility tasks such as walking forward, backward, rotating in place and raising orlowering the body height. The legs will be of a modular design and will have threedegrees of freedom each. This robot will serve as a platform onto which additionalsensory components could be added, or which could be programmed to performincreasingly complex motions. This report discusses the components that make up ourfinal design.In this paper we have selected ahexapod robot; we are focusing &developingmainly on efficient navigation method indifferent terrain using opposite gait of locomotion, which will make it faster and at sametime energy efficient to navigate and negotiate difficult terrain.This paper discuss the Features, development, and implementation of the Hexapod robot Index Terms:Biologically inspired, Gait Generation,Legged hexapod, Navigation.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
OPTIMAL TRAJECTORY OF ROBOT MANIPULATOR FOR ENERGY MINIMIZATION WITH QUARTIC ...cscpconf
In this paper, a different way to find the trajectory of the robot manipulators for energyoptimization is presented. In our method, the joint angles of the manipulator are set as quadratic polynomial functions. Then, with them taken into the variational function of energy consumption, Finite Element Modelling is employed to optimize the unknown parameters of the fourth order joint angles
Using Learning Automata in Coordination Among Heterogeneous Agents in a Compl...Waqas Tariq
This paper describes our use of Learning Automata as a reinforcement learning method in coordination among three heterogeneous teams of agents acting in RoboCup Rescue Simulation environment. We provide a brief introduction to Learning Automata and Cellular Learning Automata, the reinforcement machine learning methods that we have used in lots of parts of our agents’ development. Then we will describe the major challenges each team of agents should be concerned about in such a complex domain and for each challenge, we propose our approaches to develop cooperative teams. Finally, some results of using Learning Automata in coordinating these heterogeneous teams of agents that cooperate to mitigate the disastrous damages in a simulated city are evaluated.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Efficient robotic path planning algorithm based on artificial potential field IJECEIAES
Path planning is crucial for a robot to be able to reach a target point safely to accomplish a given mission. In path planning, three essential criteria have to be considered namely path length, computational complexity and completeness. Among established path planning methods are voronoi diagram (VD), cell decomposition (CD), probability roadmap (PRM), visibility graph (VG) and potential field (PF). The above-mentioned methods could not fulfill all three criteria simultaneously which limits their application in optimal and real-time path planning. This paper proposes a path PF-based planning algorithm called dynamic artificial PF (DAPF). The proposed algorithm is capable of eliminating the local minima that frequently occurs in the conventional PF while fulfilling the criterion of path planning. DAPF also integrates path pruning to shorten the planned path. In order to evaluate its performance, DAPF has been simulated and compared with VG in terms of path length and computational complexity. It is found that DAPF is consistent in generating paths with low computation time in obstacle-rich environments compared to VG. The paths produced also are nearly optimal with respect to VG.
Study and Analysis of Design Optimization and Synthesis of Robotic ARMINFOGAIN PUBLICATION
A robot is a mechanical or virtual artificial agent, usually an electro-mechanical machine that is guided by a computer program or electronic circuitry. Robots can be autonomous or semi-autonomous. In this thesis, design optimization strategies and synthesis for robotic arm are studied. In the design process, novel optimization methods have been developed to reduce the mass of the whole robotic arm. The optimization of the robotic arm is conducted at three different levels, with the main objective to minimize the robot mass. At the first level, only the drive-train of the robotic arm is optimized. The design process of a robotic arm is decomposed into selection of components for the drive-train to reduce the weight At the second level, kinematic data is combined with the drive-train in the optimization. For this purpose, a dynamic model of the robot is required. Constraints are formulated on the motors, gearboxes and kinematic performance At the third level, a systematic optimization approach is developed, which contains design variables of structural dimensions, geometric dimensions and drive-train composes. Constraints are formulated on the stiffness and deformation. The stiffness and deformation of the arm are calculated through FEA simulation. The main objective of the thesis is to design optimization and synthesis analysis of robotic arm. The corresponding deflections, stresses and strains for that load will be find out by suing the method of finite element analysis.
This work presents the kinematics model of an RA-
02 (a 4 DOF) robotic arm. The direct kinematic problem is
addressed using both the Denavit-Hartenberg (DH) convention
and the product of exponential formula, which is based on the
screw theory. By comparing the results of both approaches, it
turns out that they provide identical solutions for the
manipulator kinematics. Furthermore, an algebraic solution of
the inverse kinematics problem based on trigonometric
formulas is also provided. Finally, simulation results for the
kinematics model using the Matlab program based on the DH
convention are presented. Since the two approaches are
identical, the product of exponential formula is supposed to
produce same simulation results on the robotic arm studied.
Keywords-Robotics; DH convention; product of exponentials;
kinematics; simulations
Kinematics modeling of six degrees of freedom humanoid robot arm using impro...IJECEIAES
The robotic arm has functioned as an arm in the humanoid robot and is generally used to perform grasping tasks. Accordingly, kinematics modeling both forward and inverse kinematics is required to calculate the end-effector position in the cartesian space before performing grasping activities. This research presents the kinematics modeling of six degrees of freedom (6-DOF) robotic arm of the T-FLoW humanoid robot for the grasping mechanism of visual grasping systems on the robot operating system (ROS) platform and CoppeliaSim. Kinematic singularity is a common problem in the inverse kinematics model of robots, but. However, other problems are mechanical limitations and computational time. The work uses the homogeneous transformation matrix (HTM) based on the Euler system of the robot for the forward kinematics and demonstrates the capability of an improved damped least squares (I-DLS) method for the inverse kinematics. The I-DLS method was obtained by improving the original DLS method with the joint limits and clamping techniques. The I-DLS performs better than the original DLS during the experiments yet increases the calculation iteration by 10.95%, with a maximum error position between the endeffector and target positions in path planning of 0.1 cm.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Attitude Estimation And Compensation In Odometric Localization of Mobile Robo...Waqas Tariq
The paper introduces the attitude estimation and compensation in odometric localization of a differential drive indoor mobile robot. A mobile robot navigates through an inclined indoor environment, wherein localization using only wheel encoder is erroneous. The robot uses inertial sensors such as gyroscope, accelerometer and magnetometer to calculate its attitude and acquires a three degree of rotational data. It is observed that the attitude update using gyroscopes alone are prone to diverge and hence error needs to be eliminated. The advantage of MEMS sensors is less-cost while complementary filter algorithm is low complexity in implementation. The performance of the proposed complementary filter algorithm for attitude estimation and compensation in odometric localization are shown by experiment and analysis of results.
A NOVEL NAVIGATION STRATEGY FOR AN UNICYCLE MOBILE ROBOT INSPIRED FROM THE DU...JaresJournal
This paper deals with the design and the implementation of a novel navigation strategy for an unicycle
mobile robot. The strategy of navigation is inspired from nature (the duck walking) in the closed loop.
Therefore, a single sensor (gyroscope) is used to determine the pose of the robot, hence the proposed name
"gyroscopic navigation". A global presentation of the novel strategy and the robot and with its different
components are given. An experimental identification for the useful parameters are then exhibited.
Moreover, the controller design strategy and the simulation results are given. Finally, real time
experiments are accomplished to valid the simulation results.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Ziegler nichols pid controller for effective pay-load torque responses and ti...eSAT Journals
Abstract Robotic Technology is an imitation for human being’s. It is an electro mechanical modelling objects are important aspect of manipulator. A Manipulator is a machine able to drive the robot. This paper describes and investigates on effective pay-load torque responses, tip-vibrations. This paper presents modelling and simulation of the double link manipulator using the proposed PID Controller. Here the proposed Ziegler-Nichols proportional–integral–derivative controller (PID controller) initiates more advantageous in the view of better performance and flexible operation of manipulator. First, the electro mechanical object was modeled and simulated using State space technique. Here the torque responses and end tip vibrations are assigned by state space variables. The entire two link manipulator topology was investigated and modeled, simulated. The proposed control strategy carries a back –back feed forward controller can be used for flexible operation of manipulator. Here, the simulation was done by using M-File Technique in Control tool box of MATLAB. Keywords: Double Link Manipulator, Ziegler-Nichols PID Controller, Pay-Load Torque Responses, Tip-Vibrations, State space technique, back –back feed forward controller
Insect inspired hexapod robot for terrain navigationeSAT Journals
Abstract The aim of this paper is to build a sixlegged walking robot that is capable of basicmobility tasks such as walking forward, backward, rotating in place and raising orlowering the body height. The legs will be of a modular design and will have threedegrees of freedom each. This robot will serve as a platform onto which additionalsensory components could be added, or which could be programmed to performincreasingly complex motions. This report discusses the components that make up ourfinal design.In this paper we have selected ahexapod robot; we are focusing &developingmainly on efficient navigation method indifferent terrain using opposite gait of locomotion, which will make it faster and at sametime energy efficient to navigate and negotiate difficult terrain.This paper discuss the Features, development, and implementation of the Hexapod robot Index Terms:Biologically inspired, Gait Generation,Legged hexapod, Navigation.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
OPTIMAL TRAJECTORY OF ROBOT MANIPULATOR FOR ENERGY MINIMIZATION WITH QUARTIC ...cscpconf
In this paper, a different way to find the trajectory of the robot manipulators for energyoptimization is presented. In our method, the joint angles of the manipulator are set as quadratic polynomial functions. Then, with them taken into the variational function of energy consumption, Finite Element Modelling is employed to optimize the unknown parameters of the fourth order joint angles
Using Learning Automata in Coordination Among Heterogeneous Agents in a Compl...Waqas Tariq
This paper describes our use of Learning Automata as a reinforcement learning method in coordination among three heterogeneous teams of agents acting in RoboCup Rescue Simulation environment. We provide a brief introduction to Learning Automata and Cellular Learning Automata, the reinforcement machine learning methods that we have used in lots of parts of our agents’ development. Then we will describe the major challenges each team of agents should be concerned about in such a complex domain and for each challenge, we propose our approaches to develop cooperative teams. Finally, some results of using Learning Automata in coordinating these heterogeneous teams of agents that cooperate to mitigate the disastrous damages in a simulated city are evaluated.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Efficient robotic path planning algorithm based on artificial potential field IJECEIAES
Path planning is crucial for a robot to be able to reach a target point safely to accomplish a given mission. In path planning, three essential criteria have to be considered namely path length, computational complexity and completeness. Among established path planning methods are voronoi diagram (VD), cell decomposition (CD), probability roadmap (PRM), visibility graph (VG) and potential field (PF). The above-mentioned methods could not fulfill all three criteria simultaneously which limits their application in optimal and real-time path planning. This paper proposes a path PF-based planning algorithm called dynamic artificial PF (DAPF). The proposed algorithm is capable of eliminating the local minima that frequently occurs in the conventional PF while fulfilling the criterion of path planning. DAPF also integrates path pruning to shorten the planned path. In order to evaluate its performance, DAPF has been simulated and compared with VG in terms of path length and computational complexity. It is found that DAPF is consistent in generating paths with low computation time in obstacle-rich environments compared to VG. The paths produced also are nearly optimal with respect to VG.
Study and Analysis of Design Optimization and Synthesis of Robotic ARMINFOGAIN PUBLICATION
A robot is a mechanical or virtual artificial agent, usually an electro-mechanical machine that is guided by a computer program or electronic circuitry. Robots can be autonomous or semi-autonomous. In this thesis, design optimization strategies and synthesis for robotic arm are studied. In the design process, novel optimization methods have been developed to reduce the mass of the whole robotic arm. The optimization of the robotic arm is conducted at three different levels, with the main objective to minimize the robot mass. At the first level, only the drive-train of the robotic arm is optimized. The design process of a robotic arm is decomposed into selection of components for the drive-train to reduce the weight At the second level, kinematic data is combined with the drive-train in the optimization. For this purpose, a dynamic model of the robot is required. Constraints are formulated on the motors, gearboxes and kinematic performance At the third level, a systematic optimization approach is developed, which contains design variables of structural dimensions, geometric dimensions and drive-train composes. Constraints are formulated on the stiffness and deformation. The stiffness and deformation of the arm are calculated through FEA simulation. The main objective of the thesis is to design optimization and synthesis analysis of robotic arm. The corresponding deflections, stresses and strains for that load will be find out by suing the method of finite element analysis.
This work presents the kinematics model of an RA-
02 (a 4 DOF) robotic arm. The direct kinematic problem is
addressed using both the Denavit-Hartenberg (DH) convention
and the product of exponential formula, which is based on the
screw theory. By comparing the results of both approaches, it
turns out that they provide identical solutions for the
manipulator kinematics. Furthermore, an algebraic solution of
the inverse kinematics problem based on trigonometric
formulas is also provided. Finally, simulation results for the
kinematics model using the Matlab program based on the DH
convention are presented. Since the two approaches are
identical, the product of exponential formula is supposed to
produce same simulation results on the robotic arm studied.
Keywords-Robotics; DH convention; product of exponentials;
kinematics; simulations
Kinematics modeling of six degrees of freedom humanoid robot arm using impro...IJECEIAES
The robotic arm has functioned as an arm in the humanoid robot and is generally used to perform grasping tasks. Accordingly, kinematics modeling both forward and inverse kinematics is required to calculate the end-effector position in the cartesian space before performing grasping activities. This research presents the kinematics modeling of six degrees of freedom (6-DOF) robotic arm of the T-FLoW humanoid robot for the grasping mechanism of visual grasping systems on the robot operating system (ROS) platform and CoppeliaSim. Kinematic singularity is a common problem in the inverse kinematics model of robots, but. However, other problems are mechanical limitations and computational time. The work uses the homogeneous transformation matrix (HTM) based on the Euler system of the robot for the forward kinematics and demonstrates the capability of an improved damped least squares (I-DLS) method for the inverse kinematics. The I-DLS method was obtained by improving the original DLS method with the joint limits and clamping techniques. The I-DLS performs better than the original DLS during the experiments yet increases the calculation iteration by 10.95%, with a maximum error position between the endeffector and target positions in path planning of 0.1 cm.
Simulation design of trajectory planning robot manipulatorjournalBEEI
Robots can be mathematically modeled with computer programs where the results can be displayed visually, so it can be used to determine the input, gain, attenuate and error parameters of the control system. In addition to the robot motion control system, to achieve the target points should need a research to get the best trajectory, so the movement of robots can be more efficient. One method that can be used to get the best path is the SOM (Self Organizing Maps) neural network. This research proposes the usage of SOM in combination with PID and Fuzzy-PD control for finding an optimal path between source and destination. SOM Neural network process is able to guide the robot manipulator through the target points. The results presented emphasize that a satisfactory trajectory tracking precision and stability could be achieved using SOM Neural networking combination with PID and Fuzzy-PD controller.The obtained average error to reach the target point when using Fuzzy-PD=2.225% and when using PID=1.965%.
Trajectory reconstruction for robot programming by demonstration IJECEIAES
The reproduction of hand movements by a robot remains difficult and conventional learning methods do not allow us to faithfully recreate these movements because it is very difficult when the number of crossing points is very large. Programming by Demonstration gives a better opportunity for solving this problem by tracking the user’s movements with a motion capture system and creating a robotic program to reproduce the performed tasks. This paper presents a Programming by Demonstration system in a trajectory level for the reproduction of hand/tool movement by a manipulator robot; this was realized by tracking the user’s movement with the ArToolkit and reconstructing the trajectories by using the constrained cubic spline. The results obtained with the constrained cubic spline were compared with cubic spline interpolation. Finally the obtained trajectories have been simulated in a virtual environment on the Puma 600 robot.
Mathematical modeling and kinematic analysis of 5 degrees of freedom serial l...IJECEIAES
Modeling and kinematic analysis are crucial jobs in robotics that entail identifying the position of the robot’s joints in order to accomplish particular tasks. This article uses an algebraic approach to model the kinematics of a serial link, 5 degrees of freedom (DOF) manipulator. The analytical method is compared to an optimization strategy known as sequential least squares programming (SLSQP). Using an Intel RealSense 3D camera, the colored object is picked up and placed using vision-based technology, and the pixel location of the object is translated into robot coordinates. The LOBOT LX15D serial bus servo controller was used to transmit these coordinates to the robotic arm. Python3 programming language was used throughout the entire analysis. The findings demonstrated that both analytical and optimized inverse kinematic solutions correctly identified colored objects and positioned them in their appropriate goal points.
Fractional-order sliding mode controller for the two-link robot arm IJECEIAES
This study presents a control system of the two-link robot arm based on the sliding mode controller with the fractional-order. Firstly, the equations of the two-link robot arm are analyzed, then the author proposes the controller for each joint based on these equations. The controller is a sliding mode controller with its order is not an integer value. The task of the control system is controlling the torques acted on the joints so that the response angle of each link equal to the desired angle. The effectiveness of the proposed control system is demonstrated through Matlab-Simulink software. The robot model and controller are built for investigating the efficiency of the system. The result shows that the system quality is very good: there is not the chattering phenomenon of torques, the response angle of two links always follow the desired angle with the short transaction time and the static error of zero.
Integral Backstepping Approach for Mobile Robot ControlTELKOMNIKA JOURNAL
This paper presents the trajectory tracking problem of a unicycle-type mobile robots. A robust output tracking controller for nonlinear systems in the presence of disturbances is proposed, the approach is based on the combination of integral action and Backstepping technique to compensate for the dynamic disturbances. For desired trajectory, the values of the linear and angular velocities of the robot are assured by the kinematic controller. The control law guarantees stability of the robot by using the lyapunov theorem. The simulation and experimental results are presented to verify the designed trajectory tracking control.
A fuzzy logic controllerfora two link functional manipulatorIJCNCJournal
This paper presents a new approach for designing a Fuzzy Logic Controller "FLC"for a dynamically multivariable nonlinear coupling system. The conventional controller with constant gains for different operating points may not be sufficient to guarantee satisfactory performance for Robot manipulator. The Fuzzy Logic Controller utilizes the error and the change of error as fuzzy linguistic inputs to regulate the system performance. The proposed controller have been developed to simulate the dynamic behavior of A
Two-Link Functional Manipulator. The new controller uses only the available information of the input-output for controlling the position and velocity of the robot axes of the motion of the end effectors
Adaptive synchronous sliding control for a robot manipulator based on neural ...IJECEIAES
Robot manipulators have become important equipment in production lines, medical fields, and transportation. Improving the quality of trajectory tracking for
robot hands is always an attractive topic in the research community. This is a
challenging problem because robot manipulators are complex nonlinear systems
and are often subject to fluctuations in loads and external disturbances. This
article proposes an adaptive synchronous sliding control scheme to improve trajectory tracking performance for a robot manipulator. The proposed controller
ensures that the positions of the joints track the desired trajectory, synchronize
the errors, and significantly reduces chattering. First, the synchronous tracking
errors and synchronous sliding surfaces are presented. Second, the synchronous
tracking error dynamics are determined. Third, a robust adaptive control law is
designed,the unknown components of the model are estimated online by the neural network, and the parameters of the switching elements are selected by fuzzy
logic. The built algorithm ensures that the tracking and approximation errors
are ultimately uniformly bounded (UUB). Finally, the effectiveness of the constructed algorithm is demonstrated through simulation and experimental results.
Simulation and experimental results show that the proposed controller is effective with small synchronous tracking errors, and the chattering phenomenon is
significantly reduced.
ROBOTICS-ROBOT KINEMATICS AND ROBOT PROGRAMMINGTAMILMECHKIT
Forward Kinematics, Inverse Kinematics and Difference; Forward Kinematics and Reverse Kinematics of manipulators with Two, Three Degrees of Freedom (in 2 Dimension), Four Degrees of freedom (in 3 Dimension) Jacobians, Velocity and Forces-Manipulator Dynamics, Trajectory Generator, Manipulator Mechanism Design-Derivations and problems. Lead through Programming, Robot programming Languages-VAL Programming-Motion Commands, Sensor Commands, End Effector commands and simple Programs
Kineto-Elasto Dynamic Analysis of Robot Manipulator Puma-560IOSR Journals
Current industrial robots are made very heavy to achieve high Stiffness
which increases the accuracy of their motion. However this heaviness limits the robot speed and in masses the
required energy to move the system. The requirement for higher speed and better system performance makes it
necessary to consider a new generation of light weight manipulators as an alternative to today's massive
inefficient ones. Light weight manipulators require Less energy to move and they have larger payload abilities
and more maneuverability. However due to the dynamic effects of structural flexibility, their control is much
more difficult. Therefore, there is a need to develop accurate dynamic models for design and control of such
systems.This project presents the flexibility and Kineto - Elasto dynamic analysis of robot manipulator
considering deflection. Based on the distributed parameter method, the generalized motion equations of robot
manipulator with flexible links are derived. The final formulation of the motion equations is used to model
general complex elastic manipulators with nonlinear rigid-body and elastic motion in dynamics and it can be
used in the flexibility analysis of robot manipulators and spatial mechanisms. Manipulator end-effector path
trajectory, velocity and accelerations are plotted. Joint torques is to be determined for each joint trajectory
(Dynamics) .Using joint torques, static loading due to link’s masses, masses at joints, and payload, the robot
arms elastic deformations are to be found by using ANSYS-12.0 software package. Elastic compensation is
inserted in coordinates of robotic programming to get exact end-effectors path. A comparison of paths
trajectory of the end-effector is to be plotted. Also variation of torques is plotted after considering elastic
compensation. These torque variations are included in the robotic programming for getting the accurate endeffect
or’s path trajectory
Solution of Inverse Kinematics for SCARA Manipulator Using Adaptive Neuro-Fuz...ijsc
Solution of inverse kinematic equations is complex problem, the complexity comes from the nonlinearity of joint space and Cartesian space mapping and having multiple solution. In this work, four adaptive neurofuzzy networks ANFIS are implemented to solve the inverse kinematics of 4-DOF SCARA manipulator. The implementation of ANFIS is easy, and the simulation of it shows that it is very fast and give acceptable error.
Manipulability index of a parallel robot manipulatorIAEME Publication
The manipulability index is used to quantify manipulators velocity transmission capabilities or the dexterity of robot. The index is a measure of manipulating ability of robotic echanisms in positioning and orienting the end effectors. The index allows to quantify the proximity of the robot to a singularity, which is ideal for identifying paths of welding with continuous and soft movements at the robot joints.
Impact analysis of actuator torque degradation on the IRB 120 robot performan...IJECEIAES
Actuators in a robot system may become faulty during their life cycle. Locked joints, free-moving joints, and the loss of actuator torque are common faulty types of robot joints where the actuators fail. Locked and free-moving joint issues are addressed by many published articles, whereas the actuator torque loss still opens attractive investigation challenges. The objectives of this study are to classify the loss of robot actuator torque, named actuator torque degradation, into three different cases: Boundary degradation of torque, boundary degradation of torque rate, and proportional degradation of torque, and to analyze their impact on the performance of a typical 6-DOF robot (i.e., the IRB 120 robot). Typically, controllers of robots are not pre-designed specifically for anticipating these faults. To isolate and focus on the impact of only actuator torque degradation faults, all robot parameters are assumed to be known precisely, and a popular closed-loop controller is used to investigate the robot’s responses under these faults. By exploiting MATLAB-the reliable simulation environment, a simscape-based quasi-physical model of the robot is built and utilized instead of an actual expensive prototype. The simulation results indicate that the robot responses cannot follow the desired path properly in most fault cases.
Dynamics and control of a robotic arm having four linksAmin A. Mohammed
Abstract The manipulator control is an important problem
in robotics. To work out this problem, a correct dynamic
model for the robot manipulator must be in hand. Hence, this
work first presents the dynamic model of an existing 4-DOF
robot manipulator based on the Euler–Lagrange principle,
utilizing the body Jacobian of each link and the generalized
inertia matrix. Furthermore, essential properties of the
dynamic model are analyzed for the purpose of control. Then,
a PID controller is designed to control the position of the
robot by decoupling the dynamic model. To achieve a good
performance, the differential evolution algorithm is used for
the selection of parameters of the PID controller. Feedback
linearization scheme is also utilized for the position and trajectory
tracking control of the manipulator. The obtained
results reveal that the PID control coupled with the differential
evolution algorithm and the feedback linearization
control enhance the performance of the robotic manipulator.
It is also found out that increasing masses of manipulator
links do not affect the performance of the PID position control,
but higher control torques are required in these cases.
Keywords Robot control · PID · Differential evolution ·
Feedback linearization
Output feedback trajectory stabilization of the uncertainty DC servomechanism...ISA Interchange
This work proposes a solution for the output feedback trajectory-tracking problem in the case of an uncertain DC servomechanism system. The system consists of a pendulum actuated by a DC motor and subject to a time-varying bounded disturbance. The control law consists of a Proportional Derivative controller and an uncertain estimator that allows compensating the effects of the unknown bounded perturbation. Because the motor velocity state is not available from measurements, a second-order sliding-mode observer permits the estimation of this variable in finite time. This last feature allows applying the Separation Principle. The convergence analysis is carried out by means of the Lyapunov method. Results obtained from numerical simulations and experiments in a laboratory prototype show the performance of the closed loop system.
2. Fig. 2. Workflow of teaching-playback manipulator system
given prior, so that the singularity-free path can be planned.
However, in the teaching-playback robot manipulator system,
the robot does not know where the next position will be until
the user presses the button on the teaching pendant.
The purpose of this study is to design a teaching-playback
robot manipulator system with automatic singularity
avoidance that allows the user to control the robot manipulator
to move smoothly from point-to-point by using teaching
pendant (shown in Fig. 1(b)). The challenging point of this
study is considering how to avoid kinematic singularities
during the controlling of the robot manipulator using a
teaching pendant in real time. Two novel singularity
avoidance algorithms for a teaching-playback robot
manipulator system will be proposed and compared through
an experiment in this paper.
The paper is organized as follows: The next section
describes the formulation of the problem. Proposed algorithms
are explained in Section III. Section IV discusses the
specification of the robot manipulator and experimental setup.
Some experiment results are presented in Section V, and
conclusions follow in Section VI.
II. PROBLEM FORMULATION
A. Assumption, Input, and Output Parameters
We assume that an initial position and orientation (P&O)
and a final P&O are given in a task. P&O are indicated in task
configuration , which included position X, Y, Z, and
orientation R_ X , R_ Y , R_ Z . The user needs to use a
teaching pendant to control the end-effector from initial P&O
to final P&O, and the teaching pendant will read the input
based on any change in the end-effector’s task configuration
∆ ∆X, ∆Y, ∆Z, ∆R_ X , ∆R_ Y , ∆R_ Z set by user,
while the robot manipulator is moving based on the changing
of joint configuration ∆ until the end-effector arrives at the
desired end-effector task configuration set by the user. From
here, we can see that the input of end-effector’s task
configuration ∆ is changing, and the output of the joint
configuration ∆ is changing. We can even define the velocity
of joints ∆ /∆t, and the velocity of the end-effector
∆ /∆t, where ∆t is the changing of time.
B. Jacobian and Kinematic Singularity
The velocity relationship between the joints and the
end-effector is determined by the manipulator Jacobian matrix
[15]:
where ∈ is the end-effector velocity vector, and ϵ
is the vector representing the joint velocities. is the
manipulator Jacobian matrix with dimension m n. For
non-redundant manipulators, m = n, while for redundant
manipulators, m < n. The inverse kinematics of a manipulator
at the velocity level from the above relation [10] is:
Non-redundant manipulator:
Redundant manipulator: #
,
where is the inverse, and #
is the pseudo-inverse of the
manipulator Jacobian. Kinematic singularity occurs when the
rank of Jacobian, rank , is not the full rank and determinant
of Jacobian, det 0. Hence, we can utilize measure of
manipulability [16] to check the existence of kinematic
singularity. The movement of the robot manipulator can be
kept away from singular configuration by ensuring the value
of the measure of manipulability, ω, is always greater than
zero, as
ω det 0
The measure of manipulability (4) is non-negative and
becomes zero only at singular points. Hence, it can be
considered as a kind of distance from singular points.
The overall workflow of the teaching-playback
manipulator system is shown in Fig. 2. First, the P&O of the
end-effector need to be initialized and set as HOME P&O.
Next, the user will give the input ∆ by pressing the button on
the teaching pendant. In a normal teaching-playback robot
manipulator system, which does not have singularity
avoidance, the output ∆ will be obtained via (2) for a
non-redundant manipulator and (3) for a redundant
manipulator. In singularity avoidance, the value of is
modified so that det 0. More detail will be discussed in
the next section. The loop will keep going until the user stops
to give input; in other words, the robot manipulator will not
move without input ∆ from the user. The ultimate goal in
this paper is to minimize the completion time T for moving the
end-effector from initial P&O to final P&O by using the
teaching pendant.
III. PROPOSED ALGORITHM
Many methods of singularity avoidance have been
discussed in previous studies, especially in regard to the
motion-planning problem. Basically, all the methods
mentioned are discussed mainly in two directions:
non-redundancy and redundancy singularity avoidance. In this
paper, non-redundancy singularity avoidance means the
manipulator will avoid the kinematic singularity by
considering 6 task configurations that include position
X, Y, Z, and orientation R_ X , R_ Y , R_ Z together
with 6 degrees of freedom (DOF) manipulator, which means
Y
Robot Move
START
Initialization
Singularity
Avoidance
Task
Finished?
END
Input: ∆
Output: ∆
N
Input
454
3. Fig. 3. Flowchart of non-redundancy singularity avoidance Fig. 4. Flowchart of redundancy singularity avoidance
m = n = 6, while redundancy singularity avoidance means the
manipulator will avoid the kinematic singularity by
considering 3 task configurations that include only position
X, Y, Z, together with 6 DOF manipulator, which means m
< n, since m = 3 and n = 6.
A. Non-redundancy: Damped Least Squares (DLS) Inverse
Kinematic
An effective strategy that allows motion control of a
non-redundant manipulator in the neighborhood of kinematic
singularities is the damped least squares (DLS) technique
proposed in [8]. The method corresponds to solve the
equation:
λ
where λ is a damping factor, and I is a (6 x 6) identity matrix.
It can be easily shown that the solution to (5) can be formally
written as:
λ
Note that when λ 0, equation (1) becomes identical to
(5) and the damped least squares solution reduces to a regular
matrix inversion which is ill-conditioned close to singularity.
An effective choice is to adjust λ as a function of some
measure of closeness to the singularity at the current
configuration of the manipulator; the measure of
manipulability [15] or smallest singular value [16] can be
adopted for this purpose.
A singular region can be defined on the basis of the
estimate of the smallest singular value of . Outside the region,
the origin solution (2) is used, while inside the region, a
configuration-varying damping factor is introduced to obtain
the desired approximate solution. The factor must be chosen
so that continuity of joint velocity is ensured in the
transition at the border of the singular region. The damping
factor is selected according to the following law [8]:
λ
0 when σ ε
1 λ otherwise,
Here, the size of singular region ε and value of λ are set by
the user to suitably shape the solution in the neighborhood of a
singularity. Fig. 3 shows the flowchart of non-redundancy
singularity avoidance with a DLS inverse kinematic.
B. Redundancy: Potential Function
By using a potential function as the second manipulation
variable, we can utilize redundancy to avoid mechanical
constraint of the redundant manipulator. The potential
approach [15] is described by
# #
k
where k is a positive constant. The measure of manipulability
(4) is used as a potential function for avoiding singularity [15,
17] as below:
p det
Choosing equation (9) as a potential function is expected
to keep a manipulator away from singularity. Note that
minimizing the potential function implies not only avoiding
the singularity but also maintaining the kinematic ability of the
manipulator as much as possible [16]. Fig. 4 shows the
flowchart of redundancy singularity avoidance with potential
function.
IV. EXPERIMENT SETUP
The experiment is implemented using DENSO VP-6242G,
which is a six-revolute-joint (6R) manipulator manufactured
by DENSO WAVE. The Denavit-Hartenberg parameters and
velocity limits and joint limits of the manipulator are reported
in Table I and Table II, respectively.
Three typical singularities are commonly seen for a 6R
manipulator in factories including shoulder, elbow, and wrist
singularities [18]. However, due to the limitation of joint 3 of
VP-6242G, only shoulder singularity and wrist singularity can
be tested in this experiment.
A.Shoulder Singularity Test
During the shoulder singularity test, the user needs to
control the end-effector from initial P&O to final P&O by
Subroutine
Singularity Avoidance
Return
σ ε ?
λ 1
σ
ε
λ
λ
∂
∂
N
Y
Return
Subroutine
Singularity Avoidance
∂
∂
σ ε ?
# #
k
N
Y
455
4. (a) Before starting the test (b) After completing the test
Fig. 6 Wrist singularity test
(a) Before starting the test
(b) After completing the test
Fig. 5. Shoulder singularity test
TABLE I. DENSO VP-6242G ROBOT MANIPULATOR:
DENAVIT-HARTENBERG PARAMETERS
Link θ rad d [m] a [m] α [rad]
1 0.280 0 π/2
2 0 0.210 0
3 0 0.075 π/2
4 0.210 0 π/2
5 0 0 π/2
6 0.070 0 0
TABLE II. DENSO VP-6242G ROBOT MANIPULATOR:
JOINT LIMITS AND VELOCITY LMITS
Joint Motion Range [rad] Max Velocity [rad/s]
1 2.79 ~ 2.79 4.36
2 2.09 ~ 2.09 3.26
3 0.33 ~ 2.79 4.36
4 2.79 ~ 2.79 5.24
5 2.09 ~ 2.09 5.24
6 6.28 ~ 6.28 5.24
TABLE III. SETTING VALUE TEST IN WRIST
SINGULARITY AVOIDANCE
Computational time, Tc (s)
λ2
max
1.000 × × × × ×
0.500 × × × × ×
0.100 × × × × ×
0.050 × 227.222 × × ×
0.010 × 12.864 × × ×
0.005 × × × × ×
0.001 × × × × ×
0.001 0.005 0.010 0.050 0.100
ε
(a) Setting value test for non-redundancy singularity avoidance
Computational time, Tc (s)
k
10.000 × 10.392 11.251 18.517 ×
5.000 × 10.420 11.228 18.464 ×
1.000 × 10.404 11.188 18.516 ×
0.500 × 10.341 11.264 18.547 ×
0.100 × 10.410 11.159 18.504 ×
0.050 × 10.484 11.247 18.490 ×
0.010 × 10.363 11.205 18.456 ×
0.001 0.005 0.010 0.050 0.100
ε
(b) Setting value test for redundancy singularity avoidance
Notes:
×
Cannot complete the task due to the final destination
being inside the singular region, ε set by user.
× Cannot escape from singularity region.
using a teaching pendant (as shown in Fig. 5(a)). The
judgment for completing the test is shown in Fig. 5(b).
B. Wrist Singularity Test
During wrist singularity test, the user needs to control the
end-effector from initial P&O to final P&O by using a
teaching pendant (as shown in Fig. 6(a)). The judgment for
completing the test is shown in Fig. 6(b).
C. Algorithm-Setting Parameter
Several combinations of the settings had been tried in
wrist singularity tests beforehand in order to arrive at the
setting values from the best combination based on the shortest
computational time Tc for robot manipulator moves from
initial P&O to final P&O (as shown in Table III). Overall, the
smaller the value of singular region is, the closer the
end-effector is to the singular point. In contrast, the larger the
value of singular region is, the more area the end-effector
cannot reach, or the completion time T is increased due to the
manipulator avoiding the singularity from far away.
In the algorithm of non-redundancy singularity avoidance
(NRSA), the smaller the value of is, the higher the
joints velocity, hence the lower computational time for the
end-effector to move from initial P&O to final P&O (as
shown in Table III(a)). In the algorithm of redundancy
singularity avoidance (RSA), the value of k does not greatly
affect joint velocity (as shown in Table III(b)). The setting for
the algorithm of NRSA is 0.005 and 0.010;
while the setting for RSA is 0.005 and 0.500, which
are the best combination according to the observation from
Table III. This setting is mainly focused on point-to-point
tasks such as pick-and-place or assembly tasks in industry.
Final Position
and Orientation
Initial Position
and Orientation
Final Position
and OrientationInitial Position
and Orientation
456
5. (a) No singularity avoidance
(b) Non-redundancy singularity avoidance
(c) Redundancy singularity avoidance
Fig. 7. Trajectory of end-effector moves from initial point to final point
in shoulder singularity test using teaching pendant
Z
X
Z
X
0.026m
Z
X
0.014m
TABLE IV. RESULT OF SHOULDER SINGULARITY TEST
User Completion Time T (s)
NSA NRSA RSA
A 113.5 73.8 ×
B × 51.3 46.4
C × 41.0 45.1
D × 66.9 45.1
E × 46.0 48.0
F × 38.1 49.5
G × 42.9 59.1
Note: ×means user cannot complete the test due to the singularity
TABLE V. RESULT OF WRIST SINGULARITY TEST
User Completion Time T (s)
NSA NRSA RSA
A × × 75.3
B × 54.7 25.0
C × 37.8 33.3
D × 33.3 34.4
E × 69.1 23.6
F × 58.4 28.2
G × 59.4 42.0
Note: ×means user cannot complete the test due to the singularity
D. Participants
Seven people participated in this experiment, and the age
range is between 21 and 32. All of them are healthy, both
physically and mentally.
E. Data Collection and Analysis
First, simple instruction about how to control the
manipulator is given to fresh users; then they are to try to
manipulate the robot within 10 minutes. In this 10 minutes,
the user just needs to be familiar with the function of + and –
on each button of X, Y, Z, RX, RY, and RZ. After that, three
trials will be done on each singularity test, and each trial
represents each tested condition, which includes:
① No singularity avoidance (NSA),
② Non-redundancy singularity avoidance (NRSA), and
③ Redundancy singularity avoidance (RSA).
Each user will have a different sequence of tested condition,
e.g., user A will try the sequence of ○1 → ○2 → ○3 , user B
will try the sequence of ○2 → ○1 → ○3 , etc.
The evaluation method for this experiment is recording
the completion time T when the user is moving the
end-effector from initial P&O to final P&O by using a
teaching pendant. Differences in completion times for
different conditions are compared using Student’s two-tailed
t-test. A p-value < 0.05 is considered significant.
V. EXPERIMENT RESULT
The movement results can be referred to video attached.
Table IV shows the result of the shoulder singularity test, and
we can see that all users were unable to avoid the shoulder
singularity under the condition of NSA except for user A; and
even so, user A took a long time to complete the test. There is
no significant difference between NRSA and RSA (p-value >
0.84) in the t-test (excluding user A). The average time
(excluding user A) to accomplish the test under the condition
of NRSA is 47.7s, and 48.9s for RSA. The difference of
average time for both methods is 1.2s, which also means there
is not much difference between these methods.
Fig. 7 shows the trajectory of end-effector moves from
initial P&O to final P&O in the shoulder singularity test using
a teaching pendant. When the end-effector is close to the
shoulder singular region, very high joint velocities and large
deviations occur under the NSA condition (as shown in Fig.
7(a)). Meanwhile, NRSA and RSA will lead the end-effector
to move in the +Z direction to avoid the singular region (as
shown in Fig. 7(b) and Fig. 7(c)). We can also observe that
when only the +X button is pressed continuously from initial
P&O until position X = 0.068m from base, which is near the
final position, the position Z of the end-effector in RSA (Fig.
7(c)) is 0.012m higher than in NRSA (Fig. 7(b)). This means
that for those users who move the end-effector in the +Z
direction before the +X direction, they need more time to
adjust the end-effector in order to reach the final position.
Table V shows the result of the wrist singularity test.
Clearly, all users were unable to avoid the wrist singularity
under the condition of NSA. The p-value between NRSA and
457
6. (a) No singularity avoidance (b) Non-redundancy singularity avoidance (c) Redundancy singularity avoidance
Fig. 8. Trajectory of end-effector moves from initial point to final point in wrist singularity test using teaching pendant
Z
X
Z
X
Z
X
0.071m 0.016m
RSA is less than 0.04 in t-test (excluding user A), leading to a
probability of greater than 96% that there is a significant
difference between NRSA and RSA. The average time
(excluding user A) for accomplishing the test under the
condition of NRSA is 52.1s, and 31.1s for RSA. The method
RSA is significantly faster than NRSA.
Fig. 8 shows the trajectory of end-effector moves from the
initial P&O to final P&O in the wrist singularity test using a
teaching pendant. When the end-effector is close to wrist
singular region, very high joint velocities and large deviations
occur under the condition of NSA (we can see that the word
“DENSO” is backward in Fig. 8(a) compared with the
previous movement). Meanwhile, NRSA and RSA will lead
the end-effector to move in the +X direction to avoid the
singular region (as shown in Fig. 8(b) and Fig. 8(c)). We can
also observe that when only the –Z button is pressed
continuously from initial P&O until position Z = 0.040m
from the base, which is near the final position, the position X
of the end-effector in RSA (Fig. 8(c)) is 0.055m closer than in
NRSA (Fig. 8(b)) from the final position. This is because
RSA is only concerned with position, while NRSA is
concerned with both position and orientation. If position is
preferred, the error of RSA is smaller than that of NRSA.
However, if orientation is preferred, the error of RSA is
bigger than that of NRSA. In the case of taking position as
priority, the trajectory of RSA is shorter than that of NRSA,
and so the completion time is shorter as well.
VI. CONCLUSION
A teaching-playback robot manipulator system with
automatic singularity avoidance had been designed to allow
the user to control the robot manipulator using a teaching
pendant without worrying about the kinematic singularities of
the robot manipulator. In the shoulder singularity test, there is
no significant difference between NRSA and RSA, while RSA
is averagely 67.5% faster than NRSA in the wrist singularity
test. In future work, more experiments will be done under
different circumstances to compare the two methods of
singularity avoidance. Some questionnaires might be collected
in order to understand what users think about when the P&O
of the end-effector is different from their controlling due to the
singularity avoidance.
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