Inverse Dynamics of Flexible Robot Arms: Modeling and Computation for Trajectory Control

1990 ◽  
Vol 112 (2) ◽  
pp. 177-185 ◽  
Author(s):  
H. Asada ◽  
Z.-D. Ma ◽  
H. Tokumaru
Keyword(s):  
Efficient Algorithm ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Compact Form ◽  
Coordinate Systems ◽  
Flexible Robot ◽  
Rigid Link ◽  
Flexible Arm ◽  
Moving Coordinate ◽  
Virtual Coordinate Systems

The inverse dynamics of robot manipulators based on flexible arm models are considered. Actuator torques required for a flexible arm to track a given trajectory are formulated and computed by using special moving coordinate systems, called virtual rigid link coordinates. Dynamic deformations of the flexible arm can be represented in a simple and compact form with use of the virtual coordinate systems. This eliminates a number of terms involved in the equations of motion and significantly reduces complexity in the inverse dynamics computation. An efficient algorithm for computing the actuator torques is then presented on the basis of the simplified formulation, and applied to a two-link arm problem.

scholarly journals Method of applied direction of mathematics in the aviation institution of higher education

2021 ◽  
Vol 10 ◽  
pp. 13-19
Author(s):  
Olga BONDAR ◽  
◽  
Oksana ZADOROZHNA ◽  
Irina YAKUNINA ◽  
◽  
...  
Keyword(s):  
Higher Education ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Professional Activity ◽  
Coordinate Systems ◽  
Mathematical Concepts ◽  
Parallel Transfer ◽  
Moving Coordinate ◽  
Rotation Of Axes

The elements of the method of applied direction of mathematics in the aviation institution of higher education developed by us are considered. We use this technique in higher mathematics classes at the Flight Academy of the National Aviation University. Examples of a combination of fundamental mathematical concepts and practical methods of their application are given. We illustrate in detail the coordinate systems used in aviation. Among these systems are mobile and fixed coordinate systems. Problems of higher mathematics related to one or another coordinate system are indicated. For example, to record vector equations of motion in projections, moving coordinate systems are used, the beginning of which is located in the center of mass of the aircraft. Therefore, the study of the topic "Reflection of linear (vector) spaces" acquires a professional orientation. In particular, we present the formulas of coordinate transformations for parallel transfer and rotation of the axes. Note that the transformations of rectangular coordinate systems are used in aviation. Having considered aviation coordinate systems, the teacher is interested in students in the study of equations of motion, determination of accelerations, velocities and displacements. Methodical methods of formation of practical skills and abilities of future aviation specialists contribute to the implementation of the applied direction of mathematics. We have given some examples of methods of applied direction of mathematics in aviation in the sources that are currently published. The prospect of our research is to further improve practical approaches to solving problems of mathematical training of students of aviation institutions of higher education. This should help increase the level of methodological training of scientific and pedagogical staff of higher education institutions. At the same time, it should contribute to the improvement of methods of teaching mathematics in terms of its application. As a result, the graduate of the aviation institution of higher education must be ready for successful professional activity. Key words: applied direction of mathematics, coordinate systems in aviation, parallel transfer, rotation of axes, fundamental mathematical concepts in aviation.

On the Properties of a Dynamic Model of Flexible Robot Manipulators

1998 ◽  
Vol 120 (1) ◽  
pp. 8-14 ◽  
Author(s):  
Marco A. Arteaga
Keyword(s):  
Dynamic Model ◽  
Structural Properties ◽  
Robot Manipulators ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Control Design ◽  
Flexible Manipulator ◽  
Robot Dynamics ◽  
Flexible Link ◽  
Flexible Robot

Control design of flexible robot manipulators can take advantage of the structural properties of the model used to describe the robot dynamics. Many of these properties are physical characteristics of mechanical systems whereas others arise from the method employed to model the flexible manipulator. In this paper, the modeling of flexible-link robot manipulators on the basis of the Lagrange’s equations of motion combined with the assumed modes method is briefly discussed. Several notable properties of the dynamic model are presented and their impact on control design is underlined.

Trajectory Tracking of Underactuated Multibody Systems

2011 ◽  
Author(s):  
Stefan Reichl ◽  
Wolfgang Steiner
Keyword(s):  
Trajectory Tracking ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Feedforward Control ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Differential Algebraic Equations ◽  
State Variables ◽  
Algebraic Equations

This work presents three different approaches in inverse dynamics for the solution of trajectory tracking problems in underactuated multibody systems. Such systems are characterized by less control inputs than degrees of freedom. The first approach uses an extension of the equations of motion by geometric and control constraints. This results in index-five differential-algebraic equations. A projection method is used to reduce the systems index and the resulting equations are solved numerically. The second method is a flatness-based feedforward control design. Input and state variables can be parameterized by the flat outputs and their time derivatives up to a certain order. The third approach uses an optimal control algorithm which is based on the minimization of a cost functional including system outputs and desired trajectory. It has to be distinguished between direct and indirect methods. These specific methods are applied to an underactuated planar crane and a three-dimensional rotary crane.

Adding flexibility to the links of a rigid-link dynamic model of an articulated robot

Robotica ◽  
1989 ◽  
Vol 7 (2) ◽  
pp. 165-168 ◽  
Author(s):  
A. Bodner
Keyword(s):  
Computational Complexity ◽  
Dynamic Model ◽  
Euler Equations ◽  
Inverse Dynamics ◽  
Small Degree ◽  
End Effector ◽  
Rigid Link ◽  
Link Model ◽  
Articulated Robot ◽  
Special Case

SUMMARYA method was developed that takes into account flexibility of robot links in the inverse dynamics calculations. This method uses the Newton-Euler equations and is applicable for special case systems that allow for only a small degree of flexibility. Application of the method should improve the accuracy of the position of the end effector during motion of the robot.The results of this study show that the method can be based entirely on an existing rigid-link model with only minimal changes required as additions. The computational complexity of the method is discussed briefly as well and indicates an increase of computations of slightly more than a factor of two as compared to a rigid-link model for the same robot geometry.

scholarly journals The (A)symmetry between the Exterior and Interior of a Schwarzschild Black Hole

2018 ◽  
Author(s):  
Pawel Gusin ◽  
Andy Augousti ◽  
Filip Formalik ◽  
Andrzej Radosz
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Equations Of Motion ◽  
Coordinate Systems ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Spacetime ◽  
The Relationship

A black hole in a Schwarzschild spacetime is considered. A transformation is proposed that describes the relationship between the coordinate systems exterior and interior to an event horizon. Application of this transformation permits considerations of the (a)symmetry of a range of phenomena taking place on both sides of the event horizon. The paper investigates two distinct problems of a uniformly accelerated particle. In one of these, although the equations of motion are the same in the regions on both sides, the solutions turn out to be very different. This manifests the differences of the properties of these two ranges.

Inverse Dynamics Algorithm for Space Robots

1996 ◽  
Vol 118 (3) ◽  
pp. 625-629 ◽  
Author(s):  
Subir Kumar Saha
Keyword(s):  
Efficient Algorithm ◽  
Dynamic Models ◽  
Inverse Dynamics ◽  
Recursive Algorithm ◽  
Space Robot ◽  
Orthogonal Complement ◽  
Free Base ◽  
Space Robots ◽  
Primary Body ◽  
Kinematic Models

An efficient algorithm for the inverse dynamics of free-flying space robots, consisting of a serial manipulator mounted on a free-base, e.g., a spacecraft, is presented. The kinematic and dynamic models are based on the concepts of the Primary Body (PB) and the Natural Orthogonal Complement, respectively, reported elsewhere. In this paper, besides the efficiency, the usefulness of the PB in deriving different kinematic models and selecting an efficient one is pointed out. Moreover, it is shown that a recursive algorithm for the inverse dynamics of the space robot at hand can be developed even without the consideration of the momenta conservation principle.

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