Impedance control of a two degree-of-freedom planar flexible link manipulator using singular perturbation theory

Robotica ◽  
2005 ◽  
Vol 24 (2) ◽  
pp. 221-228 ◽  
Author(s):  
G. R. Vossoughi ◽  
A. Karimzadeh
Keyword(s):  
Singular Perturbation ◽  
Sliding Mode ◽  
Impedance Control ◽  
Singular Perturbation Theory ◽  
Flexible Link ◽  
Singular Perturbation Method ◽  
Flexible Links ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Flexible Link Robots

In this article, impedance control of a two link flexible link manipulators is addressed. The concept of impedance control of flexible link robots is rather new and is being addressed for the first time by the authors. Impedance Control provides a universal approach to the control of flexible robots, in both constrained and unconstrained maneuvers. The initial part of the paper concerns the use of Hamilton's principle to derive the mathematical equations governing the dynamics of joint angles, vibration of the flexible links and the constraining forces. The approximate elastic deformations are then derived by means of the Assumed-Mode-Method (AMM). Using the singular perturbation method, the dynamic of the manipulator is decomposed into fast and slow subsystems. The slow dynamic corresponds to the rigid manipulator and the fast dynamic is due to vibrations of flexible links. The sliding mode control (SMC) theory has been used as the means to achieve the 2nd order target impedance for the slow dynamics. A controller based on state feedback is also designed to stabilize the fast dynamics. The composite controller is constructed by using the slow and fast controllers. Simulation results for a 2-DOF robot in which only the 2nd link is flexible confirm that the controller performs remarkably well under various simulation conditions.

Impedance Control of a Two Degree-of-Freedom Flexible Link Manipulator Using Singular Perturbation and Sliding Mode Control Theory

Volume 1 ◽  
2004 ◽  
Author(s):  
A. Karimzadeh ◽  
G. R. Vossoughi
Keyword(s):  
Singular Perturbation ◽  
Sliding Mode Control ◽  
Sliding Mode ◽  
Impedance Control ◽  
Flexible Link ◽  
Singular Perturbation Method ◽  
Flexible Links ◽  
Assumed Mode Method ◽  
Mode Control ◽  
Mode Method

In this article, impedance control of a two link flexible link manipulators is addressed. The concept of impedance control of flexible link robots is rather new and is being addressed for the first time. Impedance Control provides a universal approach to the control of flexible robots — in both constrained and unconstrained maneuvers. The initial part of the paper concerns the use Hamilton’s principle to derive the mathematical equations governing the dynamics of joint angles, vibration of the flexible links and the constraining forces. The approximate elastic deformations are then derived by means of the Assumed-Mode-Method (AMM). Using the singular perturbation method, the dynamic of the manipulator is decomposed to the fast and the slow subsystems. The slow dynamic corresponds to the rigid manipulator and fast dynamic is due to vibrations of flexible links. The sliding mode control (SMC) theory has been used as the means to achieve the 2nd order target impedance for the slow dynamics. A controller based on state feedback is also designed to stabilize the fast dynamics. The composite controller is constructed by using the slow and fast controllers. Simulation results for a 2 DOF robot in which only the 2nd link is flexible confirm that the controller performs remarkably well under various simulation conditions.

A composite controller for manipulator with flexible joint and link under uncertainties and disturbances

2021 ◽  
pp. 107754632098819
Author(s):  
Jiahao Zhu ◽  
Jian Zhang ◽  
Jiangling Zhu ◽  
Lingbin Zeng ◽  
Yangjun Pi
Keyword(s):  
Sliding Mode ◽  
Adaptive Dynamic Programming ◽  
Singular Perturbation Theory ◽  
Fast Subsystem ◽  
Slow Dynamic ◽  
Flexible Joint ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Joint Tracking ◽  
Assumed Mode

In this article, a composite controller is proposed for the manipulator with the flexible joint and link under uncertainties and time-varying disturbances. The dynamic of the system is developed by the Euler–Lagrange and assumed mode method, which is a nonlinear, strong coupling, and underacted system. Therefore, based on the singular perturbation theory, the dynamic is decomposed into a slow and fast subsystem. For the slow dynamic, a novel adaptive-gain super-twisting sliding mode controller is designed to guarantee joint tracking under the uncertainties and disturbances. For the fast dynamics, adaptive dynamic programming is used to deal with the uncertainty. The simulation result shows that the proposed composite controller can effectively track the trajectory and suppress the vibration simultaneously.

Flexible Manipulator Control Based on Singular Perturbation Theory Study

2013 ◽  
Vol 346 ◽  
pp. 69-73 ◽  
Author(s):  
Ping Lin Zeng ◽  
San Xiu Wang ◽  
Ji Jian Qiu ◽  
Shou Ren Ma ◽  
Xiao Fei Wan
Keyword(s):  
Perturbation Theory ◽  
Singular Perturbation ◽  
Sliding Mode ◽  
Flexible Manipulator ◽  
Singular Perturbation Theory ◽  
Reference Trajectory ◽  
Flexible Link ◽  
Fast Subsystem ◽  
Slow Subsystem ◽  
Manipulator Control

Aiming at the problem of tracking the reference trajectory and suppressing the beam vibration for flexible manipulator, this paper separated the system of flexible-link manipulator into slow subsystem and fast subsystem two different time scale subsystems based on singular perturbation theory and proposes a simple composite control algorithm. For the slow subsystem, a sliding mode controller is employed to track the desired trajectory, while optimal controller is used to stabilize the fast subsystem to suppress the vibration. Finally, the simulation results demonstrate the good performance of the proposed control strategy.

Oblique Impact of Multi-Flexible-Link Systems

2016 ◽  
Vol 24 (5) ◽  
pp. 904-923 ◽  
Author(s):  
AM Shafei ◽  
HR Shafei
Keyword(s):  
Beam Theory ◽  
Oblique Impact ◽  
Algebraic Equations ◽  
Flexible Link ◽  
Governing Equations ◽  
Assumed Mode Method ◽  
Virtual Links ◽  
Mode Method ◽  
Impact Phase ◽  
Curved Walls

The main goal of this paper is to present an automatic approach for the dynamic modeling of the oblique impact of a multi-flexible-link robotic manipulator. The behavior of a multi-flexible-link system confined inside a closed environment with curved walls can be completely expressed by two distinct mathematical models. A set of differential equations is employed to model the system when it has no contact with the curved walls (Flight phase); and a set of algebraic equations is used whenever it collides with the confining surfaces (Impact phase). In this article, in addition to the Assumed Mode Method (AMM), the Euler-Bernoulli Beam Theory (EBBT), and the Newton’s kinematic impact law, the Gibbs-Appell (G-A) formulation has been employed to derive the governing equations in both phases. Also, instead of using 3 × 3 rotational matrices, which involves lengthy kinematic and dynamic formulations for deriving the governing equations, 4 × 4 transformation matrices have been used. Moreover, for the systematic modeling of flexible multiple links through the space, two virtual links have been added to the n real links of a manipulator. Finally, two case studies have been simulated to demonstrate the validity of the proposed approach.

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