scholarly journals Non-Linear Lumped-Parameter Modeling of Planar Multi-Link Manipulators with Highly Flexible Arms

Robotics ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 60 ◽  
Author(s):  
Ivan Giorgio ◽  
Dionisio Del Vescovo
Keyword(s):  
Control Strategy ◽  
Kinematic Chain ◽  
Rigid Bodies ◽  
Chain Model ◽  
Joint Angles ◽  
Lumped Parameter ◽  
Bending Resistance ◽  
Parabolic Trajectory ◽  
Lumped Parameter Modeling ◽  
Flexible Arms

The problem of the trajectory-tracking and vibration control of highly flexible planar multi-links robot arms is investigated. We discretize the links according to the Hencky bar-chain model, which is an application of the lumped parameters techniques. In this approach, each link is considered as a kinematic chain of rigid bodies, and suitable springs are added in order to model bending resistance. The control strategy employed is based on an optimal input pre-shaping and a feedback of the joint angles to treat the effects of undesired disturbances. Some numerical examples are given to show the potentialities of the proposed control, and a comparison with a standard collocated Proportional-Derivative (PD) control strategy is performed. In particular, we study the cases of a linear and a parabolic trajectory with a polynomial time law chosen to minimize the onset of possible vibrations.

Lumped-Parameter Modeling of Visco-Elastically Coupled Rigid Bodies Using Clifford’s Biquaternions

2000 ◽  
Author(s):  
Ernest D. Fasse
Keyword(s):  
Computer Simulation ◽  
Rigid Bodies ◽  
Elastic Coupling ◽  
Potential Utility ◽  
Dual Quaternions ◽  
Lumped Parameter ◽  
Lumped Parameter Modeling

Abstract This work considers the problem of modeling visco-elastically coupled rigid bodies, with application to modeling and computer simulation of spatial, flexural mechanisms. A method of modeling visco-elastic coupling based on Clifford’s biquaternions (dual quaternions) is presented. The potential utility of the method is demonstrated by simulating the behavior of a complex spatial, flexural mechanism.

Lumped Parameter Modeling of a Magnetorheological Fluid Clutch

2006 ◽  
Author(s):  
John C. Ulicny ◽  
Daniel J. Klingenberg ◽  
Anthony L. Smith ◽  
Zongxuan Sun
Keyword(s):  
Mathematical Model ◽  
Physical Properties ◽  
Magnetorheological Fluid ◽  
Input Current ◽  
Fluid Composition ◽  
Fluid Temperature ◽  
Temperature Range ◽  
Lumped Parameter ◽  
Lumped Parameter Modeling ◽  
Fan Speed

A lumped-parameter mathematical model of an automotive magnetorheological (MR) fluid fan clutch was developed. This model is able to describe the average fluid temperature, average clutch temperature, and output fan speed as a function of time, input current, and fluid composition. The model also reproduces numerous features of fan operation observed experimentally and revealed a mechanism for some observed cases of hysteresis. However, it fails to capture certain other features which lead us to conclude that phenomena which are not included in the model, e.g., sedimentation and re-suspension, are important to the clutch behavior. In addition, the results indicate that certain physical properties need to be measured over a larger temperature range in order for the model to better predict the clutch behavior.

Application of Center Manifold Theory to Regulation of a Flexible Beam

1997 ◽  
Vol 119 (2) ◽  
pp. 158-165 ◽  
Author(s):  
Amir Khajepour ◽  
M. Farid Golnaraghi ◽  
Kirsten A. Morris
Keyword(s):  
Control Strategy ◽  
Center Manifold ◽  
Flexible Beam ◽  
Trial And Error ◽  
Center Manifold Theory ◽  
Control Techniques ◽  
Lumped Parameter ◽  
The Stability ◽  
Frequency Relationship ◽  
Manifold Theory

In this paper we consider the problem of regulation of a flexible lumped parameter beam. The controller is an active/passive mass-spring-dashpot mechanism which is free to slide along the beam. In this problem the plant/controller equations are coupled and nonlinear, and the linearized equations of the system have two uncontrollable modes associated with a pair of pure imaginary eigenvalues. As a result, linear control techniques as well as most conventional nonlinear control techniques can not be applied. In earlier studies Golnaraghi (1991) and Golnaraghi et al. (1994) a control strategy based on Internal resonance was developed to transfer the oscillatory energy from the beam to the slider, where it was dissipated through controller damping. Although these studies provided very good understanding of the control strategy, the analytical method was based on perturbation techniques and had many limitations. Most of the work was based on numerical techniques and trial and error. In this paper we use center manifold theory to address the shortcomings of the previous studies, and extend the work to a more general control law. The technique is based on reducing the dimension of system and simplifying the nonlinearities using center manifold and normal forms techniques, respectively. The simplified equations are used to investigate the stability and to develop a relation for the optimal controller/plant natural frequencies at which the maximum transfer of energy occurs. One of the main contributions of this work is the elimination of the trial and error and inclusion of damping in the optimal frequency relationship.

Improving Techniques in Statically Equivalent Serial Chain Modeling for Center of Mass Estimation

2014 ◽  
Author(s):  
Bingjue Li ◽  
Andrew P. Murray ◽  
David H. Myszka
Keyword(s):  
Center Of Mass ◽  
Original System ◽  
Rigid Bodies ◽  
Joint Angles ◽  
Practical Applications ◽  
Serial Chain ◽  
System Of Rigid Bodies ◽  
Final Development ◽  
Data Error ◽  
Insight Into

Any articulated system of rigid bodies defines a Statically Equivalent Serial Chain (SESC). The SESC is a virtual chain that terminates at the center of mass (CoM) of the original system of bodies. A SESC may be generated experimentally without knowing the mass, CoM, or length of each link in the system given that its joint angles and overall CoM may be measured. This paper presents three developments toward recognizing the SESC as a practical modeling technique. Two of the three developments improve utilizing the technique in practical applications where the arrangement of the joints impacts the derivation of the SESC. The final development provides insight into the number of poses needed to create a usable SESC in the presence of data collection errors. First, modifications to a matrix necessary in computing the SESC are proposed. Second, the problem of generating a SESC experimentally when the system of bodies includes a mass fixed in the ground frame are presented and a remedy is proposed for humanoid-like systems. Third, an investigation of the error of the experimental SESC versus the number of data readings collected in the presence of errors in joint readings and CoM data is conducted. By conducting the method on three different systems with various levels of data error, a general form of the function for estimating the error of the experimental SESC is proposed.

scholarly journals A Recursive Algorithm for the Forward Kinematic Analysis of Robotic Systems Using Euler Angles

Robotics ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 15
Author(s):  
Fernando Gonçalves ◽  
Tiago Ribeiro ◽  
António Fernando Ribeiro ◽  
Gil Lopes ◽  
Paulo Flores
Keyword(s):  
Recursive Algorithm ◽  
Kinematic Chain ◽  
Robotic Systems ◽  
Mobile Manipulator ◽  
Euler Angles ◽  
Joint Angles ◽  
Main Research ◽  
Kinematic Chains ◽  
Research Fields ◽  
Forward Kinematic

Forward kinematics is one of the main research fields in robotics, where the goal is to obtain the position of a robot’s end-effector from its joint parameters. This work presents a method for achieving this using a recursive algorithm that builds a 3D computational model from the configuration of a robotic system. The orientation of the robot’s links is determined from the joint angles using Euler Angles and rotation matrices. Kinematic links are modeled sequentially, the properties of each link are defined by its geometry, the geometry of its predecessor in the kinematic chain, and the configuration of the joint between them. This makes this method ideal for tackling serial kinematic chains. The proposed method is advantageous due to its theoretical increase in computational efficiency, ease of implementation, and simple interpretation of the geometric operations. This method is tested and validated by modeling a human-inspired robotic mobile manipulator (CHARMIE) in Python.

Sign in / Sign up

Export Citation Format

Share Document