scholarly journals A New Approach to the Solution of Robot Kinematics Based on Relative Transformation Matrices

Author(s):  
Mohammad Reza Elhami ◽  
Iman Dashti

In analyzing robot manipulator kinematics, we need to describe relative movement of adjacent linkages or joints in order to obtain the pose of end effector (both position and orientation) in reference coordinate frame. Denavit-Hartenberg established a method based on a 4×4 homogenous matrix so called “A” matrix. This method used by most of the authors for kinematics and dynamic analysis of the robot manipulators. Although it has many advantages, however, finding the elements of this matrix and link/joint’s parameters is sometimes complicated and confusing. By considering these difficulties, the authors proposed a new approach called ‘convenient approach’ that is developed based on “Relative Transformations Principle”. It provides a very simple and convenient way for the solution of robot kinematics compared to the conventional D-H representation. In order to clarify this point, the kinematics of the world known Stanford manipulator has been solved through D-H representation as well as convenient approach and the results are compared.


2011 ◽  
Vol 201-203 ◽  
pp. 1867-1872 ◽  
Author(s):  
Jian Ye Zhang ◽  
Chen Zhao ◽  
Da Wei Zhang

The pose accuracy of robot manipulators has long become a major issue to be considered in its advanced application. An efficient methodology to generate the end-effector position and orientation error model of robotic manipulator has been proposed based on the differential transformation matrix theory. According to this methodology, a linear error model that described the end-effector position and orientation errors due to robot kinematics parameters errors has been presented. A computer program to generate the error model and perform the accuracy analysis on any serial link manipulator has been developed in MATLAB. This methodology and software are applied to the accuracy analysis of a Phantom Desktop manipulator. The positioning error of the manipulator in its workspace cross section (XOZ) has been plotted as 3D surface graph and discussed.



2011 ◽  
Vol 697-698 ◽  
pp. 795-798
Author(s):  
Jian Ye Zhang ◽  
Chen Zhao ◽  
Da Wei Zhang

The Position and orientation accuracy of robot manipulator has long become a major issue to be considered in its advanced application. A linear error model that described the end-effector position and orientation errors of the master salve surgical robot system due to kinematics parameters errors has been presented. A computer program to perform the accuracy analysis has been developed in MATLAB. This methodology and software are applied to the accuracy analysis of a master-slave surgical robot system. The position error in its workspace cross section (XOZ) has been plotted as 3D surface graph and discussed.



2009 ◽  
Vol 21 (1) ◽  
pp. 104-112
Author(s):  
Daniela Vassileva ◽  
◽  
George Boiadjiev ◽  
Haruhisa Kawasaki ◽  
Tetsuya Mouri ◽  
...  

We proposed a new approach for redundant robots trajectories planning, based on the Null space (or Kernel) features. The Null space (Kernel) exists only in the case of redundant robots and it describes these joints motion which do not affect the robot end-effector motion in the sense of both position and orientation. Based on this “hidden motion” realized in the configuration space, which does not affect the motion in the working zone, we can control independently the robot end-effector position and orientation motions, or just maintain its state while some external force is applied to it. The proposed control strategy is simple, no additional penalty functions are used to restraint the end-effector motion as in the case of the conventional methods. No pseudo inverse kinematics calculations are required; the desired trajectories are generated directly in the configuration space. No complicated control schemes are introduced, the proposed method is based on solving algebraic systems of equations and finding eigenvectors and eigenvalues. In the paper the results from simulations and experiments based on the proposed method are presented and discussed.



ROTASI ◽  
2013 ◽  
Vol 15 (2) ◽  
pp. 37
Author(s):  
Munadi Munadi

An arm robot simulator has been developed, that capable in simulating a 5 degree of freedom robot manipulator, in which it was equipped with two-finger gripper mechanism at end-effector. This simulator is designed for educational purposes so that many students can easily understand when learning about robot manipulator. The simulator was developed using Ardiuno Uno with LabVIEW through the Firmata interface for controlling the actuators (servo motors). Ardiuno Uno was chosen because it can interact with LabVIEW that will be able to control the angular position of servo motor easily. Angular position errors that occur on the servo motor can be solved by using a numerical program functions and numerical multiply divided on LabVIEW. For analysis, this paper presents the forward kinematics problem which is concerned with the relationship between the individual joints of the arm robot simulator and the position and orientation of the tool or end-effector. The analysis result is carried out in MATLAB.



2010 ◽  
Vol 19 (03) ◽  
pp. 281-304 ◽  
Author(s):  
DIMITRIS ARISTOS ◽  
SPYROS TZAFESTAS

In many robotic applications it is required to manipulate a specific rigid object whose CAD model is known a priori, but its position and orientation in space are unknown. This category of tasks includes piercing, painting or iron welding on some specific points of the rigid object's surface. For this kind of tasks to become feasible the CAD data of the rigid object should be registered into the robot's workspace frame, so that the robot arm becomes aware of the position and orientation of the rigid body with reference to its own flange or base coordinate frame. In order to achieve this goal several techniques from the fields of image processing, 3D modeling and robot kinematics should be combined. This paper provides a convenient combination of such methods that can be used for the successful on-line registration of a rigid object's CAD data to the robot's workspace frame.



Author(s):  
Yong-Lin Kuo ◽  
Shih-Chien Tang

This paper presents a modified resolved acceleration control scheme based on deep regression of the convolutional neural network. The resolved acceleration control scheme can achieve precise motion control of robot manipulators by regulating the accelerations of the end-effector, and the conventional scheme needs the position and orientation of the end-effector, which are obtained through the direct kinematics of the robot manipulator. This scheme increases the computational loads and might obtain inaccurate position and orientation due to mechanical errors. To overcome the drawbacks, a camera is used to capture the images of the robot manipulator, and then a deep regression of convolutional neural network is imposed into the resolved acceleration control to obtain the position and orientation of the end-effector. The proposed approach aims to enhance the positioning accuracy, to reduce the computational loads, and to facilitate the deep regression in real-time control. In this study, the proposed approach is applied to a 3-DOF planar parallel robot manipulator, and the results are compared with those by the conventional resolved acceleration control and a visual servo-based control. The results show that those objectives are achieved. Furthermore, the robustness of the proposed approach is tested through only the partial image of the end-effector available, and the proposed approach still works functionally and effectively.



Robotica ◽  
2002 ◽  
Vol 20 (4) ◽  
pp. 359-366 ◽  
Author(s):  
Edward J. Park ◽  
Weihua Xu ◽  
James K. Mills

In multi-robot assembly of parts, for successful mating, the grasped parts must be located with sufficiently small position and orientation errors so that assembly can be achieved. This paper describes a new approach for determining the absolute three-dimensional spatial location of parts grasped by robots during assembly. Through a combination of robot pose calibration and part-sensor calibration, the robot, used to grasp the part, is calibrated to accurately position and orient parts to a designated mating location. First, by employing a robot pose measurement system, the 6 DOF robot pose errors relative to a reference coordinate frame are compensated. Second, with the implementation of a part pose measurement, the 6 DOF part pose errors, relative to the robot tool frame, are estimated in real time. An experimental verification of the proposed methodology using a single FANUC S–110 robot manipulating an automotive sheet metal part is described.





2018 ◽  
pp. 5-29 ◽  
Author(s):  
L. M. Grigoryev ◽  
V. A. Pavlyushina

The phenomenon of economic growth is studied by economists and statisticians in various aspects for a long time. Economic theory is devoted to assessing factors of growth in the tradition of R. Solow, R. Barrow, W. Easterly and others. During the last quarter of the century, however, the institutionalists, namely D. North, D. Wallis, B. Weingast as well as D. Acemoglu and J. Robinson, have shown the complexity of the problem of development on the part of socioeconomic and political institutions. As a result, solving the problem of how economic growth affects inequality between countries has proved extremely difficult. The modern world is very diverse in terms of development level, and the article offers a new approach to the formation of the idea of stylized facts using cluster analysis. The existing statistics allows to estimate on a unified basis the level of GDP production by 174 countries of the world for 1992—2016. The article presents a structured picture of the world: the distribution of countries in seven clusters, different in levels of development. During the period under review, there was a strong per capita GDP growth in PPP in the middle of the distribution, poverty in various countries declined markedly. At the same time, in 1992—2016, the difference increased not only between rich and poor groups of countries, but also between clusters.





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