Modeling and Control of Transverse and Torsional Vibrations in a Spherical Robotic Manipulator: Theoretical and Experimental Results

1997 ◽  
Vol 119 (3) ◽  
pp. 421-430 ◽  
Author(s):  
Liming Chen ◽  
Nabil G. Chalhoub
Keyword(s):  
Rigid Body ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Robotic Manipulator ◽  
Gain Scheduling ◽  
Torsional Vibrations ◽  
Flexible Link ◽  
Modeling And Control ◽  
Prismatic Joint ◽  
And Control

The present work addresses modeling and control issues pertaining to the positioning and orientating of rigid body payloads as they are being manipulated by flexible spherical robotic manipulators. A general approach, to systematically derive the equations of motion of the robotic manipulator, is used herein. The objective of the controller is to yield a desired rigid body response of the arm while damping out the transverse and torsional vibrations of the compliant link. Note that the control objective has to be achieved by solely relying on the existing joint actuators whose band-widths are far below the natural frequencies of the torsional modes. The current work demonstrates that, in spite of the physical limitations of the system, the controller can actively damp out the torsional vibrations by relying on the coupling terms between the torsional vibrations and the remaining degrees of freedom of the arm. Moreover, a gain scheduling procedure is introduced to continuously tune the controller to the natural frequencies of the flexible link whose length is varied by the prismatic joint. The digital simulation results demonstrate the capability of the “rigid and flexible motion controller (RFMC)” in drastically attenuating the transverse and torsional vibrations during point-to-point (PTP) maneuvers of the arm. Furthermore, the gain scheduling procedure is shown to significantly reduce the degradations in the RFMC performance that are brought about by having the flexible link connected to a prismatic joint. A limited experimental work has also been conducted to demonstrate the viability of the proposed approach.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

scholarly journals Modeling and control of a new robotic deburring system

Robotica ◽  
2005 ◽  
Vol 24 (2) ◽  
pp. 229-237 ◽  
Author(s):  
Jae H. Chung ◽  
Changhoon Kim
Keyword(s):  
Comparative Study ◽  
Decentralized Control ◽  
Control Method ◽  
Robotic Manipulator ◽  
Coordination Control ◽  
Pneumatic Actuators ◽  
Modeling And Control ◽  
Control Approach ◽  
Simulation Results ◽  
And Control

This paper discusses the modeling and control of a robotic manipulator with a new deburring tool, which integrates two pneumatic actuators to take advantage of a double cutting action. A coordination control method is developed by decomposing the robotic deburring system into two subsystems; the arm and the deburring tool. A decentralized control approach is pursued, in which suitable controllers were designed for the two subsystems in the coordination scheme. In simulation, three different tool configurations are considered: rigid, single pneumatic and integrated pneumatic tools. A comparative study is performed to investigate the deburring performance of the deburring arm with the different tools. Simulation results show that the developed robotic deburring system significantly improves the accuracy of the deburring operation.

Sensorless Modal Stabilization for Three-Link Robotic Arm With Elastic Wrist Drive Belt

2001 ◽  
Author(s):  
Martin Hosek
Keyword(s):  
Rigid Body ◽  
Robotic Manipulator ◽  
Vibration Damping ◽  
Rigid Body Dynamics ◽  
Limiting Factor ◽  
Direct Drive ◽  
Stability And Control ◽  
Body Dynamics ◽  
Improved Stability ◽  
And Control

Abstract A control system for a three-link direct-drive robotic manipulator with inherent structural flexibilities is presented. The structural flexibilities introduce undesirable vibration modes which may affect operation of the robot motion controller, resulting in destabilization of the closed-loop system. This represents a major limiting factor for implementation of a conventional controller designed solely for the rigid body dynamics of the robotic manipulator. The fundamental idea in the presented approach is to use a composite controller which consists of a trajectory-tracking section designed for the rigid-body dynamics and a vibration-damping compensator added for attenuation of the dominant flexible dynamics. The vibration damping compensator operates on estimated states of the dominant flexible dynamics obtained from a reduced-order state observer. A mechanism is implemented which allows the robotic manipulator to move through or hold in positions where the dominant flexible dynamics is unobservable and uncontrollable. Results of laboratory tests document that the presented approach leads to improved stability and control performance.

scholarly journals Natural Frequncies of Coupled Blade-Bending and Shaft-Torsional Vibrations

2007 ◽  
Vol 14 (1) ◽  
pp. 65-80 ◽  
Author(s):  
B.O. Al-Bedoor
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Coupled Model ◽  
Small Deformation ◽  
Torsional Vibrations ◽  
Reduced Order ◽  
Rotating Speed ◽  
Coupled Equations ◽  
Stiffening Effect

In this study, the coupled shaft-torsional and blade-bending natural frequencies are investigated using a reduced order mathematical model. The system-coupled model is developed using the Lagrangian approach in conjunction with the assumed modes method to discretize the blade bending deflection. The model accounts for the blade stagger (setting) angle, the system rotating speed and its induced stiffening effect. The coupled equations of motion are linearized based on the small deformation theory for the blade bending and shaft torsional deformation to enable calculation of the system natural frequencies for various combinations of system parameters. The obtained coupled eignvalue system is ready for use as a reference for comparison for larger size finite element simulations and for the use as a fast check on natural frequencies for the coupled blade bending and shaft torsional vibrations in the design and diagnostics processes. Some results on the predicted natural frequencies are graphically presented and discussed pertinent to the coupling controlling factors and their effects. In addition, the predicted coupled natural frequencies are validated using the Finite Element Commercial Package (Pro-Mechanica) where good agreements are found.

scholarly journals A unified approach to rigid body rotational dynamics and control

2011 ◽  
Vol 468 (2138) ◽  
pp. 395-414 ◽  
Author(s):  
Firdaus E. Udwadia ◽  
Aaron D. Schutte
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Equations Of Motion ◽  
Fundamental Equation ◽  
Rotational Dynamics ◽  
Constrained Motion ◽  
Dynamics And Control ◽  
Common Framework ◽  
The Stability ◽  
And Control

This paper develops a unified methodology for obtaining both the general equations of motion describing the rotational dynamics of a rigid body using quaternions as well as its control. This is achieved in a simple systematic manner using the so-called fundamental equation of constrained motion that permits both the dynamics and the control to be placed within a common framework. It is shown that a first application of this equation yields, in closed form, the equations of rotational dynamics, whereas a second application of the self-same equation yields two new methods for explicitly determining, in closed form, the nonlinear control torque needed to change the orientation of a rigid body. The stability of the controllers developed is analysed, and numerical examples showing the ease and efficacy of the unified methodology are provided.

Evolution of Rotations of a Rigid Body Under the Action of Restoring and Control Moments

2005 ◽  
Author(s):  
L. D. Akulenko ◽  
D. D. Leshchenko ◽  
T. A. Kozachenko
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
The Body ◽  
System Of Equations ◽  
Slow Time ◽  
Case Examples ◽  
First Approximation ◽  
Nutation Angle ◽  
Regular Precession ◽  
And Control

Perturbed rotations of a rigid body close to the regular precession in the Lagrangian case under the action of a restoring moment depending on slow time and nutation angle, as well as a perturbing moment slowly varying with time, are studied. The body is assumed to spin rapidly, and the restoring and perturbing moments are assumed to be small with a certain hierarchy of smallness of the components. A first approximation averaged system of equations of motion for an essentially nonlinear two-frequency system is obtained in the nonresonance case. Examples of motion of a body under the action of particular restoring, perturbing, and control moments of force are considered.

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