scholarly journals On the Boundedness Property of the Inertia Matrix and Skew-Symmetric Property of the Coriolis Matrix for Vehicle-Manipulator Systems

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Pål Johan From ◽  
Ingrid Schjølberg ◽  
Jan Tommy Gravdahl ◽  
Kristin Ytterstad Pettersen ◽  
Thor I. Fossen
Keyword(s):  
Control Theory ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
State Variables ◽  
Boundedness Property ◽  
Inertia Matrix ◽  
Fixed Base ◽  
First Time ◽  
Symmetric Property ◽  
Future Reference

This paper addresses the boundedness property of the inertia matrix and the skew-symmetric property of the Coriolis matrix for vehicle-manipulator systems. These properties are widely used in control theory and Lyapunov-based stability proofs and thus important to identify. The skew-symmetric property does not depend on the system at hand but on the parameterization of the Coriolis matrix, which is not unique. It is the authors’ experience that many researchers take this assumption for granted without taking into account that several parameterizations exist. In fact, most researchers refer to references that do not show this property for vehicle-manipulator systems but for other systems such as single rigid bodies or fixed-base manipulators. As a result, the otherwise rigorous stability proofs fall apart. In this paper, we list some relevant references and give the correct proofs for some commonly used parameterizations for future reference. Depending on the choice of state variables, the boundedness of the inertia matrix will not necessarily hold. We show that deriving the dynamics in terms of quasi-velocities leads to an inertia matrix that is bounded in its variables. To the best of our knowledge, we derive for the first time the dynamic equations of vehicle-manipulator systems with non-Euclidean joints for which both properties are true.

scholarly journals Li–Yorke Chaos in Hybrid Systems on a Time Scale

2015 ◽  
Vol 25 (14) ◽  
pp. 1540024 ◽  
Author(s):  
Marat Akhmet ◽  
Mehmet Onur Fen
Keyword(s):  
Differential Equations ◽  
Hybrid Systems ◽  
Time Scales ◽  
Time Scale ◽  
Impulsive Differential Equations ◽  
Reduction Technique ◽  
Duffing Equation ◽  
Dynamic Equations ◽  
Definition Of ◽  
First Time

By using the reduction technique to impulsive differential equations [Akhmet & Turan, 2006], we rigorously prove the presence of chaos in dynamic equations on time scales (DETS). The results of the present study are based on the Li–Yorke definition of chaos. This is the first time in the literature that chaos is obtained for DETS. An illustrative example is presented by means of a Duffing equation on a time scale.

Simulation of Planar Dynamic Mechanical Systems With Changing Topologies: Part I — Characterization and Prediction of the Kinematic Constraint Changes

1987 ◽  
Author(s):  
B. J. Gilmore ◽  
R. J. Cipra
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
State Variables ◽  
Kinematic Constraint ◽  
Kinematic Constraints ◽  
Force Closure ◽  
Simulation Strategy ◽  
Reaction Forces ◽  
Discontinuous Equations

Abstract Due to changes in the kinematic constraints, many mechanical systems are described by discontinuous equations of motion. This paper addresses those changes in the kinematic constraints which are caused by planar bodies contacting and separating. A strategy to automatically predict and detect the kinematic constraint changes, which are functions of the system dynamics, is presented in Part I. The strategy employs the concepts of point to line contact kinematic constraints, force closure, and ray firing together with the information provided by the rigid bodies’ boundary descriptions, state variables, and reaction forces to characterize the kinematic constraint changes. Since the strategy automatically predicts and detects constraint changes, it is capable of simulating mechanical systems with unpredictable or unforeseen changes in topology. Part II presents the implementation of the characterizations into a simulation strategy and presents examples.

Cayley kinematics and the Cayley form of dynamic equations

2005 ◽  
Vol 461 (2055) ◽  
pp. 761-781 ◽  
Author(s):  
Andrew J. Sinclair ◽  
John E. Hurtado
Keyword(s):  
Euler Equations ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
Matrix Form ◽  
Dynamic Equations ◽  
Cayley Transform ◽  
Higher Dimensional ◽  
The Matrix ◽  
General Motion

The Cayley transform and the Cayley–transform kinematic relationships are an important and fascinating set of results that have relevance in N –dimensional orientations and rotations. In this paper these results are used in two significant ways. First, they are used in a new derivation of the matrix form of the generalized Euler equations of motion for N –dimensional rigid bodies. Second, they are used to intimately relate the motion of general mechanical systems to the motion of higher–dimensional rigid bodies. This approach can be used to describe an enormous variety of systems, one example being the representation of general motion of an N –dimensional body as pure rotations of an ( N + 1)–dimensional body.

scholarly journals Fault-Structure-Based Active Fault Diagnosis: A Geometric Observer Approach

Energies ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 4475
Author(s):  
Zhao Zhang ◽  
Xiao He
Keyword(s):  
Fault Diagnosis ◽  
Active Fault ◽  
Geometric Approach ◽  
Dynamic Equations ◽  
Fault Structure ◽  
Numerical Example ◽  
Input And Output ◽  
Incipient Faults ◽  
First Time ◽  
New Framework

Fault diagnosis techniques can be classified into passive and active types. Passive approaches only utilize the original input and output signals of the system. Because of the small amplitudes, the characteristics of incipient faults are not fully represented in the data of the system, so it is difficult to detect incipient faults by passive fault diagnosis techniques. In contrast, active methods can design auxiliary signals for specific faults and inject them into the system to improve fault diagnosis performance. Therefore, active fault diagnosis techniques are utilized in this article to detect and isolate incipient faults based on the fault structure. A new framework based on observer approach for active fault diagnosis is proposed and the geometric approach based fault diagnosis observer is introduced to active fault diagnosis for the first time. Based on the dynamic equations of residuals, auxiliary signals are designed to enhance the diagnosis performance for incipient faults that have specific structures. In addition, the requirements that auxiliary signals need to meet are discussed. The proposed method can realize the seamless combination of active fault diagnosis and passive fault diagnosis. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed approach, and it is indicated that the proposed method significantly improves the accuracy of the diagnosis for incipient faults.

The Geometry of Virtual Work Dynamics in Screw Space

1992 ◽  
Vol 59 (2) ◽  
pp. 411-417 ◽  
Author(s):  
Steven Peterson
Keyword(s):  
Tangent Space ◽  
Screw Theory ◽  
Virtual Work ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Coordinate Space ◽  
Dynamical Equations ◽  
Least Action ◽  
System Of Rigid Bodies ◽  
Configuration Manifold

In this paper, screw theory is employed to develop a method for generating the dynamic equations of a system of rigid bodies. Exterior algebra is used to derive the structure of screw space from projective three space (homogeneous coordinate space). The dynamic equation formulation method is derived from the parametric form of the principle of least action, and it is shown that a set of screws exist which serves as a basis for the tangent space of the configuration manifold. Equations generated using this technique are analogs of Hamilton’s dynamical equations. The freedom screws defining the manifold’s tangent space are determined from the contact geometry of the joint using the virtual coefficient, which is developed from the principle of virtual work. This results in a method that eliminates all differentiation operations required by other virtual work techniques, producing a formulation method based solely on the geometry of the system of rigid bodies. The procedure is applied to the derivation of the dynamic equations for the first three links of the Stanford manipulator.

A Unified Framework for Dynamics and Lyapunov Stability of Holonomically Constrained Rigid Bodies

2005 ◽  
Vol 9 (4) ◽  
pp. 387-394 ◽  
Author(s):  
Khoder Melhem ◽  
◽  
Zhaoheng Liu ◽  
Antonio Loría ◽  
◽  
...  
Keyword(s):  
System Dynamics ◽  
Lyapunov Stability ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Minimal Realization ◽  
State Variables ◽  
Unified Framework ◽  
Constrained System ◽  
And Control

A new dynamic model for interconnected rigid bodies is proposed here. The model formulation makes it possible to treat any physical system with finite number of degrees of freedom in a unified framework. This new model is a nonminimal realization of the system dynamics since it contains more state variables than is needed. A useful discussion shows how the dimension of the state of this model can be reduced by eliminating the redundancy in the equations of motion, thus obtaining the minimal realization of the system dynamics. With this formulation, we can for the first time explicitly determine the equations of the constraints between the elements of the mechanical system corresponding to the interconnected rigid bodies in question. One of the advantages coming with this model is that we can use it to demonstrate that Lyapunov stability and control structure for the constrained system can be deducted by projection in the submanifold of movement from appropriate Lyapunov stability and stabilizing control of the corresponding unconstrained system. This procedure is tested by some simulations using the model of two-link planar robot.

scholarly journals First record of Enoplometopus callistus (Crustacea: Decapoda: Nephropidae) in the Cape Verde Islands

2003 ◽  
Vol 83 (6) ◽  
pp. 1233-1234 ◽  
Author(s):  
Sonia Elsy Merino ◽  
J. Alistair Lindley
Keyword(s):  
First Record ◽  
Cape Verde ◽  
East Atlantic ◽  
Cape Verde Islands ◽  
By Catch ◽  
First Time ◽  
Existing Data ◽  
Future Reference

Enoplometopus callistus is reported for the first time from the Cape Verde Islands. In January 2001 two specimens were captured in depths of 100–150  m as by-catch in the lobster fisheries. One of them was dissected and kept in alcohol for future reference, the second one was put into an aquarium. The existing data on the distributions of the two Atlantic species of this genus, E. antillensis and E. callistus, indicate that the latter is restricted to the waters of the East Atlantic.

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.

Position Analysis in Analytical Form of the 3-PSP Mechanism

1999 ◽  
Vol 123 (1) ◽  
pp. 51-55 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Vincenzo Parenti-Castelli
Keyword(s):  
Nonlinear Equations ◽  
Parallel Mechanism ◽  
Analytical Form ◽  
Rigid Bodies ◽  
The Other ◽  
Kinematic Chains ◽  
Position Analysis ◽  
Fixed Base ◽  
Inverse Position Analysis ◽  
Movable Platform

In this paper the direct and the inverse position analysis of a 3-dof fully-parallel mechanism, known as 3-PSP mechanism, is addressed and solved in analytical form. The 3-PSP mechanism consists of two rigid bodies, one movable (platform) and the other fixed (base), connected to each other by means of three equal serial kinematic chains (legs) of type PSP, P and S standing for prismatic and spherical pair respectively. Both the direct and the inverse position analysis of this mechanism lead to nonlinear equations that are difficult to solve. In particular, the inverse position analysis comprises different subproblems which need specific solution techniques. Finally a numerical example is reported.

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