scholarly journals Development a model of robot movement with five degrees of freedom for a warehouse

2021 ◽  
Vol 5 (1(61)) ◽  
pp. 12-17
Author(s):  
Volodymyr Shvets ◽  
Viktor Tkachov
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Emergent Behavior ◽  
Position Vector ◽  
Coordinate Systems ◽  
Robot Calibration ◽  
Initial State ◽  
The Matrix ◽  
Robot Position

The object of research is a mathematical model describing the movement of a robot with five degrees of freedom for a warehouse. The work was aimed at analyzing the kinematic structure of the manipulator, on the basis of which the base and local coordinate systems were selected, as well as further formalized recording of the kinematic equations in matrix form. It is noted that one of the most problematic places is that the algorithms for controlling the robot most often contain local rules for the interaction of robots between themselves and the external environment, and emergent behavior is manifested as a result of the application of these rules, which does not have a formal description. Therefore, it is important to modernize the models describing the motion of a robot with five degrees of freedom for a warehouse. Using the matrix method, the sequence of constructing coordinate systems is described and its mathematical description is given, which will make it possible to eliminate this drawback in the future. The computer implementation of the developed algorithms was carried out using methods for processing matrix data structures. The principle of constructing a kinematic model of a robot is presented, with the help of which the main coordinate transformation matrices are obtained for robot with five degrees of freedom, and the possibility of taking into account the size of the gaps in the joints is shown. The resulting model is obtained, which is proposed for use in building control algorithms for a robot with an automatic gap selection, as well as in robot calibration. This is due to the fact that the proposed model has a number of features, in particular, the basic coordinate system and the coordinate system of each link of robot with five degrees of freedom are taken into account. This makes it possible to obtain the values of the indicators for the projection of the robot position vector in the initial state, in the rotation of the fourth link at a well-defined angle and in the case of a vertically straightened manipulator. Compared to similar known studies, this provides advantages such as minimizing errors in position, speed and motion accuracy. The object of research is a mathematical model describing the movement of a robot with five degrees of freedom for a warehouse. The work was aimed at analyzing the kinematic structure of the manipulator, on the basis of which the base and local coordinate systems were selected, as well as further formalized recording of the kinematic equations in matrix form. It is noted that one of the most problematic places is that the algorithms for controlling the robot most often contain local rules for the interaction of robots between themselves and the external environment, and emergent behavior is manifested as a result of the application of these rules, which does not have a formal description. Therefore, it is important to modernize the models describing the motion of a robot with five degrees of freedom for a warehouse. Using the matrix method, the sequence of constructing coordinate systems is described and its mathematical description is given, which will make it possible to eliminate this drawback in the future. The computer implementation of the developed algorithms was carried out using methods for processing matrix data structures. The principle of constructing a kinematic model of a robot is presented, with the help of which the main coordinate transformation matrices are obtained for robot with five degrees of freedom, and the possibility of taking into account the size of the gaps in the joints is shown. The resulting model is obtained, which is proposed for use in building control algorithms for a robot with an automatic gap selection, as well as in robot calibration. This is due to the fact that the proposed model has a number of features, in particular, the basic coordinate system and the coordinate system of each link of robot with five degrees of freedom are taken into account. This makes it possible to obtain the values of the indicators for the projection of the robot position vector in the initial state, in the rotation of the fourth link at a well-defined angle and in the case of a vertically straightened manipulator. Compared to similar known studies, this provides advantages such as minimizing errors in position, speed and motion accuracy.

A Sensitivity Analysis Based Method for Robot Calibration

1992 ◽  
Author(s):  
S. Kaizerman ◽  
B. Benhabib ◽  
R. G. Fenton ◽  
G. Zak
Keyword(s):  
Sensitivity Analysis ◽  
Kinematic Model ◽  
Calibration Procedure ◽  
Inverse Kinematic ◽  
Model Parameters ◽  
Robot Calibration ◽  
Adjoint Sensitivity ◽  
Analysis Methods ◽  
The Matrix ◽  
Direct Sensitivity

Abstract A new robot kinematic calibration procedure is presented. The parameters of the kinematic model are estimated through a relationship established between the deviations in the joint variables and the deviations in the model parameters. Thus, the new method can be classified as an inverse calibration procedure. Using suitable sensitivity analysis methods, the matrix of the partial derivatives of joint variables with respect to robot parameters is calculated without having explicit expressions of joint variables as a function of task space coordinates (closed inverse kinematic solution). This matrix provides the relationship between the changes in the joint variables and the changes in the parameter values required for the calibration. Two deterministic sensitivity analysis methods are applied, namely the Direct Sensitivity Approach and the Adjoint Sensitivity Method. The new calibration procedure was successfully tested by the simulated calibrations of a two degree of freedom revolute-joint planar manipulator.

Study of Neural-Kinematics Architectures for Model-Less Calibration of Industrial Robots

2021 ◽  
Vol 33 (1) ◽  
pp. 158-171
Author(s):  
Monica Tiboni ◽  
◽  
Giovanni Legnani ◽  
Nicola Pellegrini
Keyword(s):  
Degrees Of Freedom ◽  
Industrial Robot ◽  
Kinematic Model ◽  
Back Propagation ◽  
Simulated Data ◽  
Industrial Robots ◽  
Robot Calibration ◽  
Feed Forward Neural Network ◽  
Comparative Performance ◽  
Order Of Magnitude

Modeless industrial robot calibration plays an important role in the increasing employment of robots in industry. This approach allows to develop a procedure able to compensate the pose errors without complex parametric model. The paper presents a study aimed at comparing neural-kinematic (N-K) architectures for a modeless non-parametric robotic calibration. A multilayer perceptron feed-forward neural network, trained in a supervised manner with the back-propagation learning technique, is coupled in different modes with the ideal kinematic model of the robot. A comparative performance analysis of different neural-kinematic architectures was executed on a two degrees of freedom SCARA manipulator, for direct and inverse kinematics. Afterward the optimal schemes have been identified and further tested on a three degrees of freedom full SCARA robot and on a Stewart platform. The analysis on simulated data shows that the accuracy of the robot pose can be improved by an order of magnitude after compensation.

A Sensitivity Analysis Based Method for Robot Calibration

1994 ◽  
Vol 116 (2) ◽  
pp. 607-613 ◽  
Author(s):  
S. Kaizerman ◽  
G. Zak ◽  
B. Benhabib ◽  
R. G. Fenton
Keyword(s):  
Sensitivity Analysis ◽  
Kinematic Model ◽  
Calibration Procedure ◽  
Inverse Kinematic ◽  
Model Parameters ◽  
Robot Calibration ◽  
Adjoint Sensitivity ◽  
Analysis Methods ◽  
The Matrix ◽  
Direct Sensitivity

A new robot kinematic calibration procedure is presented. The parameters of the kinematic model are estimated through a relationship established between the deviations in the joint variables and the deviations in the model parameters. Thus, the new method can be classified as an inverse calibration procedure. Using suitable sensitivity analysis methods, the matrix of the partial derivatives of joint variables with respect to robot parameters is calculated without having explicit expressions of joint variables as a function of task space coordinates (closed inverse kinematic solution). This matrix provides the relationship between the changes in the joint variables and the changes in the parameter values required for the calibration. Two deterministic sensitivity analysis methods are applied, namely the Direct Sensitivity Approach and the Adjoint Sensitivity Method. The new calibration procedure was successfully tested by the simulated calibrations of a two-degree-of-freedom revolute-joint planar manipulator.

scholarly journals WRITING OUT OF FORMULAS FOR CALCULATING FORCES IN THE JOINTS OF MANIPULATORS IN STATICS

2021 ◽  
Vol 21 (3) ◽  
pp. 47-58
Author(s):  
S.G. Pudovkina ◽  
◽  
A.I. Telegin
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
Industrial Robots ◽  
Coordinate Systems ◽  
Systematic Analysis ◽  
Stationary Coordinate System ◽  
Reaction Forces ◽  
Vector Mechanics ◽  
Assembly Operations ◽  
Analytical Verification

The problem of bulkiness of mathematical models of manipulative systems of industrial robots is solved. Here we consider formulas for calculating static reactions in joints and formulas for active forces that balance the forces of gravity acting on the manipulator's bodies in its stationary state. The manipulator can be in such a state when it is before capturing the object of manipulation and releasing it, or when it is performing some assembly operations, or it is during spot welding and in slow (quasi-static) arc-welding and painting processes. Aim. The aim is to derive general recur-rence and finite formulas for calculating the reaction forces in joints and their projections to the ax-es of the coordinate system rigidly connected with the selected body. Express the formulas of force projections in terms of guiding cosines and justify their optimality in terms of the minimum of arithmetic operations. Derive general inverse recurrence formulas for writing out the guide cosines of the axes associated with the moving bodies of the coordinate system with respect to the stationary coordinate system. Research methods. The methods of research relate to vector mechanics and sys-tems analysis, and the algorithmization of calculations by reducing them to the use of recurrent formulas. Results. A systematic analysis of general formulas, in which all possible regular expres-sions are highlighted which are corresponding unambiguously to the kinematic parameters of ma-nipulators, is performed. These regular expressions are used in software for analytical modeling of manipulator, in particular, for the analytical solution of problems of statics of a manipulator. The method of analytical verification of the prescribed formulas is described. The tasks of writing out optimal formulas for calculating the projections of static reaction forces in joints have been solved. And the tasks of writing out optimal formulas for calculating active forces in progressive joints of universal manipulators with six degrees of freedom, operating in Cartesian, cylindrical, spherical and angular coordinate systems, have been solved also. Analytical verification of the derived equations of stat-ics is performed. Examples of the reuse of the derived formulas for manipulators with the same kin-ematic schemes of their subsystems. Conclusion. Expressions of the equations of statics of manipu-lators through the guide cosines of the axes of the associated coordinate systems of their bodies al-low us to write these equations through the known parameters of body orientation. The recurrent formulas for calculating directional cosines allows to use recursive functions in their software im-plementation, i.e. to increase the computational efficiency of the software.

scholarly journals A coordinate-system-independent method for comparing joint rotational mobilities

2020 ◽  
Vol 223 (18) ◽  
pp. jeb227108
Author(s):  
Armita R. Manafzadeh ◽  
Stephen M. Gatesy
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Rotational Mobility ◽  
Coordinate Systems ◽  
Map Projection ◽  
Fold Reduction ◽  
Euler Space ◽  
Rotational Degrees Of Freedom ◽  
Alternative Spaces

ABSTRACTThree-dimensional studies of range of motion currently plot joint poses in a ‘Euler space’ whose axes are angles measured in the joint's three rotational degrees of freedom. Researchers then compute the volume of a pose cloud to measure rotational mobility. However, pairs of poses that are equally different from one another in orientation are not always plotted equally far apart in Euler space. This distortion causes a single joint's mobility to change when measured based on different joint coordinate systems and precludes fair comparison among joints. Here, we present two alternative spaces inspired by a 16th century map projection – cosine-corrected and sine-corrected Euler spaces – that allow coordinate-system-independent comparison of joint rotational mobility. When tested with data from a bird hip joint, cosine-corrected Euler space demonstrated a 10-fold reduction in variation among mobilities measured from three joint coordinate systems. This new quantitative framework enables previously intractable, comparative studies of articular function.

Reference Coordinate System Requirements for Geophysics

1975 ◽  
Vol 26 ◽  
pp. 87-92
Author(s):  
P. L. Bender
Keyword(s):  
Coordinate System ◽  
Polar Motion ◽  
Main Part ◽  
Measurement Techniques ◽  
Reference Points ◽  
Angular Motion ◽  
Coordinate Systems ◽  
Axis Of Rotation ◽  
The Earth ◽  
Fixed System

AbstractFive important geodynamical quantities which are closely linked are: 1) motions of points on the Earth’s surface; 2)polar motion; 3) changes in UT1-UTC; 4) nutation; and 5) motion of the geocenter. For each of these we expect to achieve measurements in the near future which have an accuracy of 1 to 3 cm or 0.3 to 1 milliarcsec.From a metrological point of view, one can say simply: “Measure each quantity against whichever coordinate system you can make the most accurate measurements with respect to”. I believe that this statement should serve as a guiding principle for the recommendations of the colloquium. However, it also is important that the coordinate systems help to provide a clear separation between the different phenomena of interest, and correspond closely to the conceptual definitions in terms of which geophysicists think about the phenomena.In any discussion of angular motion in space, both a “body-fixed” system and a “space-fixed” system are used. Some relevant types of coordinate systems, reference directions, or reference points which have been considered are: 1) celestial systems based on optical star catalogs, distant galaxies, radio source catalogs, or the Moon and inner planets; 2) the Earth’s axis of rotation, which defines a line through the Earth as well as a celestial reference direction; 3) the geocenter; and 4) “quasi-Earth-fixed” coordinate systems.When a geophysicists discusses UT1 and polar motion, he usually is thinking of the angular motion of the main part of the mantle with respect to an inertial frame and to the direction of the spin axis. Since the velocities of relative motion in most of the mantle are expectd to be extremely small, even if “substantial” deep convection is occurring, the conceptual “quasi-Earth-fixed” reference frame seems well defined. Methods for realizing a close approximation to this frame fortunately exist. Hopefully, this colloquium will recommend procedures for establishing and maintaining such a system for use in geodynamics. Motion of points on the Earth’s surface and of the geocenter can be measured against such a system with the full accuracy of the new techniques.The situation with respect to celestial reference frames is different. The various measurement techniques give changes in the orientation of the Earth, relative to different systems, so that we would like to know the relative motions of the systems in order to compare the results. However, there does not appear to be a need for defining any new system. Subjective figures of merit for the various system dependon both the accuracy with which measurements can be made against them and the degree to which they can be related to inertial systems.The main coordinate system requirement related to the 5 geodynamic quantities discussed in this talk is thus for the establishment and maintenance of a “quasi-Earth-fixed” coordinate system which closely approximates the motion of the main part of the mantle. Changes in the orientation of this system with respect to the various celestial systems can be determined by both the new and the conventional techniques, provided that some knowledge of changes in the local vertical is available. Changes in the axis of rotation and in the geocenter with respect to this system also can be obtained, as well as measurements of nutation.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

SCREW KINEMATIC MODEL FOR ROBOT CALIBRATION WITH PC-ROBOT COMMUNICATION OVERVIEW

2017 ◽  
Author(s):  
Lucas Kato ◽  
Tiago Pinto ◽  
Henrique Simas ◽  
Daniel Martins
Keyword(s):  
Kinematic Model ◽  
Robot Calibration ◽  
Robot Communication

Technique for relation global reference system and local realization of global reference system by continuously operated reference stations

2020 ◽  
Vol 962 (8) ◽  
pp. 24-37
Author(s):  
V.E. Tereshchenko
Keyword(s):  
Coordinate System ◽  
Russian Federation ◽  
Reference System ◽  
Main Part ◽  
Precise Point Positioning ◽  
Global Coordinate System ◽  
Coordinate Systems ◽  
Novosibirsk Region ◽  
The Russian Federation

The article suggests a technique for relation global kinematic reference system and local static realization of global reference system by regional continuously operated reference stations (CORS) network. On the example of regional CORS network located in the Novosibirsk Region (CORS NSO) the relation parameters of the global reference system WGS-84 and its local static realization by CORS NSO network at the epoch of fixing stations coordinates in catalog are calculated. With the realization of this technique, the main parameters to be determined are the speed of displacement one system center relativly to another and the speeds of rotation the coordinate axes of one system relatively to another, since the time evolution of most stations in the Russian Federation is not currently provided. The article shows the scale factor for relation determination of coordinate systems is not always necessary to consider. The technique described in the article also allows detecting the errors in determining the coordinates of CORS network in global coordinate system and compensate for them. A systematic error of determining and fixing the CORS NSO coordinates in global coordinate system was detected. It is noted that the main part of the error falls on the altitude component and reaches 12 cm. The proposed technique creates conditions for practical use of the advanced method Precise Point Positioning (PPP) in some regions of the Russian Federation. Also the technique will ensure consistent PPP method results with the results of the most commonly used in the Russian Federation other post-processing methods of high-precision positioning.

scholarly journals A New Approach of Soft Joint Based on a Cable-Driven Parallel Mechanism for Robotic Applications

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1468
Author(s):  
Luis Nagua ◽  
Carlos Relaño ◽  
Concepción A. Monje ◽  
Carlos Balaguer
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Experimental Tests ◽  
Humanoid Robots ◽  
Inverse Kinematic ◽  
Element Analysis ◽  
New Approach ◽  
Flexible Polymer ◽  
The Mathematical Model

A soft joint has been designed and modeled to perform as a robotic joint with 2 Degrees of Freedom (DOF) (inclination and orientation). The joint actuation is based on a Cable-Driven Parallel Mechanism (CDPM). To study its performance in more detail, a test platform has been developed using components that can be manufactured in a 3D printer using a flexible polymer. The mathematical model of the kinematics of the soft joint is developed, which includes a blocking mechanism and the morphology workspace. The model is validated using Finite Element Analysis (FEA) (CAD software). Experimental tests are performed to validate the inverse kinematic model and to show the potential use of the prototype in robotic platforms such as manipulators and humanoid robots.

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