scholarly journals O(n) mass matrix inversion for serial manipulators and polypeptide chains using Lie derivatives

Robotica ◽  
2007 ◽  
Vol 25 (6) ◽  
pp. 739-750 ◽  
Author(s):  
Kiju Lee ◽  
Yunfeng Wang ◽  
Gregory S. Chirikjian
Keyword(s):  
Inverse Dynamics ◽  
Mass Matrix ◽  
Rotation Group ◽  
Rigid Bodies ◽  
Euclidean Group ◽  
Serial Manipulators ◽  
The Past ◽  
Polypeptide Chains ◽  
Serial Chains ◽  
And Robotics

SUMMARYOver the past several decades, a number of O(n) methods for forward and inverse dynamics computations have been developed in the multibody dynamics and robotics literature. A method was developed by Fixman in 1974 for O(n) computation of the mass-matrix determinant for a serial polymer chain consisting of point masses. In other of our recent papers, we extended this method in order to compute the inverse of the mass matrix for serial chains consisting of point masses. In the present paper, we extend these ideas further and address the case of serial chains composed of rigid-bodies. This requires the use of relatively deep mathematics associated with the rotation group, SO(3), and the special Euclidean group, SE(3), and specifically, it requires that one differentiates real-valued functions of Lie-group-valued argument.

A New O(n) Method for Inverting the Mass Matrix for Serial Chains Composed of Rigid Bodies

2005 ◽  
Author(s):  
Yunfeng Wang ◽  
Gregory S. Chirikjian
Keyword(s):  
Multibody Dynamics ◽  
Inverse Dynamics ◽  
Mass Matrix ◽  
Rotation Group ◽  
Rigid Bodies ◽  
Euclidean Group ◽  
The Past ◽  
Lumped Masses ◽  
Serial Chains ◽  
And Robotics

Over the past several decades a number of O(n) methods for forward and inverse dynamics computations have been developed in the multibody dynamics and robotics literature. In this paper, a method developed in 1973 by Fixman for O(n) computation of the mass-matrix determinant for a polymer chain consisting of point masses is adapted and modified. In other recent papers, we and our collaborators recently extended this method in order for Fixman’s results to be applicable to robotic manipulator models with lumped masses. In the present paper we extend these ideas further to the case of serial chains composed of rigid-bodies. This requires the use of relatively deep mathematics associated with the rotation group, SO(3), and the special Euclidean group, SE(3), and how to differentiate functions of group-valued argument.

Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices

1999 ◽  
Vol 66 (4) ◽  
pp. 986-996 ◽  
Author(s):  
S. K. Saha
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Kinematic Chain ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Orthogonal Complement ◽  
Forward Dynamics ◽  
Velocity Constraints

Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n—n being the degrees-of-freedom of the system at hand—inverse dynamics and order n3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system’s accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.

scholarly journals The impact of automation and robotics on motivation

2021 ◽  
Vol 11 (1) ◽  
pp. 41-49
Author(s):  
Péter Krecz ◽  
Andrea Herneczky ◽  
József Csernák ◽  
Aranka Baranyi
Keyword(s):  
Industrial Revolution ◽  
Employee Motivation ◽  
The Past ◽  
Long Run ◽  
The Social ◽  
The One ◽  
The Impact ◽  
Industrial Revolutions ◽  
And Robotics ◽  
Effective Contribution

Special attention should be paid to the human factors that influence the competitiveness of companies when analysing the correlations of economic processes. It is no longer controversial today that human capital is an important and crucial factor in a company's performance. The efficient, effective contribution of human resources to an organization's success depends to a large extent on how it can ensure employees' motivation in the long run. Robotics and automation are gaining more and more ground nowadays. In our study we explore how employee motivation is influenced by the rapid and widespread use of robotics. The industrial revolution that is still going on today is bringing enormous changes. The industrial revolutions that happened earlier in history have fundamentally changed the lives of people and have always posed serious challenges to various economic actors. Changes have had a dual impact in the past. On the one hand, industrial production has resulted in a change in the economy and, on the other hand, a huge change in the social structure. In recent years, mechanization has seemed extreme, but this phase must be seen today as a natural part of daily life.

A New Look to the Three Axes Theorem

2019 ◽  
Author(s):  
Juan Ignacio Valderrama-Rodríguez ◽  
José M. Rico ◽  
J. Jesús Cervantes-Sánchez ◽  
Fernando Tomás Pérez-Zamudio
Keyword(s):  
Lie Algebra ◽  
Historical Review ◽  
Kinematic Chain ◽  
Rigid Bodies ◽  
Bilinear Forms ◽  
General Version ◽  
Euclidean Group ◽  
Main Hypothesis ◽  
Spatial Mechanism ◽  
Form Part

Abstract This paper analyzes the well known three axes theorem under the light of the Lie algebra se(3) of the Euclidean group, SE(3) and the symmetric bilinear forms that can be defined in this algebra. After a brief historical review of the Aronhold-Kennedy theorem and its spatial generalization, the main hypothesis is that the general version of the Aronhold-Kennedy theorem is basically the application of the Killing and Klein forms to the equation that relates the velocity states of three bodies regardless if they are free to move in the space, independent of each other, or they form part of a kinematic chain. Two representative examples are employed to illustrate the hypothesis, one where the rigid bodies are free to move in the space without any connections among them and other concerning a RCCC spatial mechanism.

The Internet of Things and Beyond: Rise of the Non-Human Actors

2020 ◽  
pp. 1286-1297
Author(s):  
Arthur Tatnall ◽  
Bill Davey
Keyword(s):  
Internet Of Things ◽  
Science Fiction ◽  
Actor Network Theory ◽  
The Internet ◽  
The Past ◽  
Business Information ◽  
Healthcare It ◽  
Human Actors ◽  
The Internet Of Things ◽  
And Robotics

In the past, it was rare for non-humans to interact with each other without any involvement by humans, but this is changing. The Internet of Things (IoT) involves connections of physical things to the Internet. It is largely about the relationships between things, or non-humans actors. In other cases the ‘Things' seem to have inordinate power. The authors will ask: where does this leave humans? Are the things taking over? As a consideration of interactions like this must be a socio-technical one, in this article the authors will make use of Actor-Network Theory to frame the discussion. While the original applications for IoT technology were in areas such as supply chain management and logistics, now many more examples can be found ranging from control of home appliances to healthcare. It is expected that the ‘Things' will become active participants in business, information and social processes and that they will communicate among themselves by exchanging data sensed from the environment, while reacting autonomously. The Things will continue to develop identities and virtual personalities. In the past non-human actors have needed humans to interact with each other, but this is not the case anymore. In this perhaps provocative and rather speculative article we will look not just at the Internet of Things, but other related concepts such as artificial intelligence and robotics and make use of scenarios from science fiction to investigate the Rise of the Non-Human Actors and where this may lead in the future.

A Coordinate Invariant Formulation of the Dynamics of Cooperating Robot Systems

1996 ◽  
Author(s):  
Scott R. Ploen ◽  
Frank C. Park
Keyword(s):  
Mass Matrix ◽  
Equations Of Motion ◽  
Linear Operators ◽  
Closed Form Expression ◽  
Robot Dynamics ◽  
Euclidean Group ◽  
Closed Chain ◽  
Invariant Formulation ◽  
Robot Systems ◽  
Cooperating Robots

Abstract In this article we formulate the dynamics of cooperating robot systems using standard ideas and notation from the theory of Lie groups. Beginning with the coordinate-invariant formulation of robot dynamics introduced in Ploen and Park (1995), we extend these results to develop the equations of motion of a system of N cooperating robots manipulating a common workpiece. In the resulting dynamic equations the mass matrix, Jacobian, Coriolis, and gravity terms of the closed chain system admit concise block-triangular factorizations in terms of simple linear operators on se(3), the Lie algebra of the Euclidean group SE(3). A straightforward manipulation of the equations of motion and the kinematic constraints leads to a closed-form expression for the forces of constraint in which the robot parameters appear in a transparent manner.

Inverse dynamic analysis of milling machining robot, application in calibration of cutting force

2019 ◽  
Vol 57 (6) ◽  
pp. 773 ◽  
Author(s):  
Hai Ha Thanh
Keyword(s):  
Cutting Force ◽  
Cutting Forces ◽  
Inverse Dynamics ◽  
Milling Process ◽  
Machining Process ◽  
Empirical Formulas ◽  
Inverse Dynamic ◽  
Serial Manipulators ◽  
Machining Robot ◽  
Dynamics Problems

This article presents analysis of inverse dynamics of serial manipulators in milling process. Cutting forces and complicated motion involve to difficulties in solving dynamics problems of robots. In general, cutting forces are determined by using empirical formulas that lead to errors of cutting force values. Moreover, the cutting forces are changing and causing vibration during machining process. Errors of cutting force values affect to the accuracy of the dynamic model. This paper proposes an algorithm to compute the cutting forces based on the feedback values of the robot's motion.    

scholarly journals Robotics and Artificial Intelligence

2020 ◽  
Vol 10 (2) ◽  
pp. 57-78 ◽  
Author(s):  
Estifanos Tilahun Mihret
Keyword(s):  
Artificial Intelligence ◽  
At Risk ◽  
Human Beings ◽  
The Past ◽  
Near Future ◽  
And Robotics

Artificial intelligence and robotics are very recent technologies and risks for our world. They are developing their capacity dramatically and shifting their origins of developing intention to other dimensions. When humans see the past histories of AI and robotics, human beings can examine and understand the objectives and intentions of them which to make life easy and assist human beings within different circumstances and situations. However, currently and in the near future, due to changing the attitude of robotic and AI inventors and experts as well as based on the AI nature that their capacity of environmental acquisition and adaptation, they may become predators and put creatures at risk. They may also inherit the full nature of creatures. Thus, finally they will create their new universe or the destiny of our universe will be in danger.

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