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Journal articles on the topic 'Flexible link control'

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Published: 4 June 2021

Last updated: 6 February 2022

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1

Khan, Barlas Raheel, Shingo Okamoto, and Jae Hoon Lee. "617 Vibration Control of a Flexible Link Manipulator Using Piezoelectric Actuators." Proceedings of Conference of Chugoku-Shikoku Branch 2014.52 (2014): _617–1_—_617–3_. http://dx.doi.org/10.1299/jsmecs.2014.52._617-1_.

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2

Fareh, Raouf, Mohamad Saad, and Maarouf Saad. "Distributed control strategy for flexible link manipulators." Robotica 33, no. 4 (2014): 768–86. http://dx.doi.org/10.1017/s0263574714000459.

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SUMMARYThis paper presents a nonlinear distributed control strategy for flexible-link manipulators to solve the tracking control problem in the joint space and cancel vibrations of the links. First, the dynamic of an n-flexible-link manipulator is decomposed into n subsystems. Each subsystem has a pair of one joint and one link. The distributed control strategy is applied to each subsystem starting from the last subsystem. The strategy of control consists in controlling the nth joint and stabilizing the nth link by assuming that the remaining subsystems are stable. Then, going backward to the (n − 1)th subsystem, the same control strategy is applied to each corresponding joint-link subsystem until the first. Sliding mode technique is used to develop the control law of each subsystem and the global stability of the resulting tracking errors is proved using the Lyapunov technique. This algorithm was tested on a two-flexible-link manipulator and gave effective results, a good tracking performance, and capability to eliminate the links' vibrations.

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3

Kilicaslan, S., S. K. Ider, and M. K. Özgören. "Motion control of flexible-link manipulators." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222, no. 12 (2008): 2441–53. http://dx.doi.org/10.1243/09544062jmes1015.

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A new method is proposed for the end-effector trajectory tracking control of flexible robot manipulators. The equations of motion are separated into two parts that represent the pseudostatic equilibrium and the deviations from it. The part of the control input for the pseudostatic equilibrium is determined algebraically, and the other part of the control input for the stabilization of the deviations is obtained by a state variable feedback law, by using strain, joint variable, and end-effector position measurements. The feedback gain matrix is determined online by continuously updated pole placement. The pseudostatic equilibrium is defined here as a hypothetical state, in which the velocity and acceleration of the end-effector have their desired values whereas the elastic deformations are instantaneously constant. In order to demonstrate the method, a planar two-link robot with a flexible forearm is taken into consideration. The elasticity of the forearm is approximately described by the first two modes, and a controller is designed by using this two-mode model. Furthermore, in order to investigate the effects of modelling discrepancies, a ‘submodel controller’ is designed by using a model with only the first mode and it is applied to the same system with the two-mode model. The performances of these two controllers are compared by means of simulations. The behaviour of the flexible robot is also simulated by using the computed torque method as if the robot is rigid in order to illustrate the importance of including the flexibility effects in the formation of an appropriate control law. The spillover effect that causes the dominant poles to approach towards the imaginary axis is inspected by monitoring the real parts of the dominant poles of the closed-loop system under the effect of the ‘submodel’ and ‘computed torque’ controllers.

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4

Sun, Qiao. "Control of Flexible-Link Multiple Manipulators." Journal of Dynamic Systems, Measurement, and Control 124, no. 1 (2001): 67–75. http://dx.doi.org/10.1115/1.1435362.

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In this paper, we consider the object trajectory tracking control for flexible-link cooperating manipulators. In particular, we develop a stable inversion control law which is commonly known as the inverse dynamics control or the computed torque method for rigid manipulators. Difficulties in applying this method to the control of flexible link manipulators are due to the fact that the inverse dynamics system is generally unstable because of the inherently unstable zero dynamics. As such, bounded actuator torques cannot be guaranteed. For multiple manipulators handling a common object, there are more actuators than the degrees of freedom of the system. Through decomposing the manipulator end-effector wrenches into resultant and internal force components, control laws are derived such that the internal forces are used to stabilize the system zero dynamics. Consequently, nonlinear inversion control can be applied for the object trajectory tracking control. Numerical simulations are performed to illustrate the performance of the control strategy developed in the paper.

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5

Zhang, Qinghua, Xianmin Zhang, and Junyang Wei. "Experimental Study of Active Vibration Control of Planar 3-RRR Flexible Parallel Robots Mechanism." Shock and Vibration 2016 (2016): 1–17. http://dx.doi.org/10.1155/2016/4780181.

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An active vibration control experiment of planar 3-RRR flexible parallel robots is implemented in this paper. Considering the direct and inverse piezoelectric effect of PZT material, a general motion equation is established. A strain rate feedback controller is designed based on the established general motion equation. Four control schemes are designed in this experiment: three passive flexible links are controlled at the same time, only passive flexible link 1 is controlled, only passive flexible link 2 is controlled, and only passive flexible link 3 is controlled. The experimental results show that only one flexible link controlled scheme suppresses elastic vibration and cannot suppress the elastic vibration of the other flexible links, whereas when three passive flexible links are controlled at the same time, they are able to effectively suppress the elastic vibration of all of the flexible links. In general, the experiment verifies that a strain rate feedback controller is able to effectively suppress the elastic vibration of the flexible links of plane 3-RRR flexible parallel robots.

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6

Raouf, Fareh, Saad Mohamad, Saad Maarouf, and Bettayeb Maamar. "Distributed adaptive control strategy for flexible link manipulators." Robotica 35, no. 7 (2016): 1562–84. http://dx.doi.org/10.1017/s0263574716000448.

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SUMMARYThis paper presents an adaptive distributed control strategy for n-serial-flexible-link manipulators. The proposed adaptive controller is used for flexible-link-manipulators: (1) to solve the tracking control problem in the joint space, and (2) to reduce vibrations of the links. The dynamical model of flexible link manipulators is reorganized to take the form of n interconnected subsystems. Each subsystem has a one-joint and one-link pair. The system parameters are deemed to be unknown. The adaptive distributed strategy controls one subsystem in each step, starting from the last one. The nth subsystem is controlled by assuming that the remaining subsystems are stable. Then, proceeding backward to the (n-1)th system, the same strategy is applied, and so on, until the first subsystem is reached. The gradient-based estimator is used to estimate the parameters of each subsystem. The control law of the ith subsystem uses its own estimated parameters and the estimated parameters of all upper level subsystems. The global stability of the error dynamics is proved using Lyapunov approach. This algorithm was implemented in real time on a two-flexible-link manipulator, and a comparison with the non-adaptive version shows the effectiveness of this approach.

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7

SENDA, Kei, Yoshisada MUROTSU, Akira MITSUYA, Tatsuya NUNOHARA, and Keisuke YAMANE. "Control Experiments of One-Link Flexible Manipulator." Journal of the Robotics Society of Japan 11, no. 4 (1993): 593–96. http://dx.doi.org/10.7210/jrsj.11.593.

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8

SENDA, Kei, Yoshisada MUROTSU, Akira MITSUYA, Tatsuya NUNOHARA, and Keisuke YAMANE. "Control Experiments of Two-Link Flexible Manipulator." Journal of the Robotics Society of Japan 11, no. 4 (1993): 597–600. http://dx.doi.org/10.7210/jrsj.11.597.

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9

Akbarzadeh-T., M. R., and M. Jamshidi. "Evolutionary Fuzzy Control of a Flexible-Link." Intelligent Automation & Soft Computing 3, no. 1 (1997): 77–88. http://dx.doi.org/10.1080/10798587.1997.10750694.

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10

Davis, J. H., and R. M. Hirschorn. "Tracking control of a flexible robot link." IEEE Transactions on Automatic Control 33, no. 3 (1988): 238–48. http://dx.doi.org/10.1109/9.401.

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11

Wang, David, and M. Vidyasagar. "Passive Control of a Stiff Flexible Link." International Journal of Robotics Research 11, no. 6 (1992): 572–78. http://dx.doi.org/10.1177/027836499201100606.

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12

KOMATSU, Tadashi, Michihiro UENOHARA, Shouichi IIKURA, Hirofumi MIURA, and Isao SHIMOYAMA. "Dynamic control for two-link flexible manipulator." Transactions of the Japan Society of Mechanical Engineers Series C 55, no. 516 (1989): 2022–28. http://dx.doi.org/10.1299/kikaic.55.2022.

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13

Jung Hua Yang, Feng Li Lian, and Li Chen Fu. "Nonlinear adaptive control for flexible-link manipulators." IEEE Transactions on Robotics and Automation 13, no. 1 (1997): 140–48. http://dx.doi.org/10.1109/70.554355.

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14

Stavenuiter, ACJ, G. Ter Reehorst, and AWP Bakkers. "Transputer control of a flexible robot link." Microprocessors and Microsystems 13, no. 3 (1989): 227–32. http://dx.doi.org/10.1016/0141-9331(89)90130-0.

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15

Feng, Dexing, and Weitao Zhang. "Feedback control of single-link flexible arms." Acta Mathematicae Applicatae Sinica 11, no. 1 (1995): 1–10. http://dx.doi.org/10.1007/bf02012617.

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16

Yu, Xiao Yan, and Li Chen. "Singular perturbation adaptive control and vibration suppression of free-flying flexible space manipulators." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 11 (2014): 1989–97. http://dx.doi.org/10.1177/0954406214551777.

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Singular perturbation adaptive control is designed for free-flying space manipulators with multiple flexible links and unknown physical parameters. The dynamical Lagrange equation was established based on assumed mode technique and linear momentum conservation theory. A singular perturbation model has been formulated and used for designing a reduced-order controller. This controller consisted of a slow control component and a fast control component. An adaptive control law was constructed for the slow counterpart of the flexible manipulator. The flexible-link fast subsystem controller would damp out the vibrations of flexible links by optimal linear quadratic regulator method. Numerical simulations by undertaking a computer simulation of a two-flexible-link space manipulator using the fourth-order Runge–Kutta integration method showed that the link vibrations had been stabilized effectively with good tracking performance.

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17

Uchiyama, Masaru, Zhao Hui Jiang, and Kyojiro Hakomori. "Compensating Control of a Flexible Robot Arm." Journal of Robotics and Mechatronics 2, no. 2 (1990): 97–106. http://dx.doi.org/10.20965/jrm.1990.p0097.

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Since the characteristics of flexible robot arm motion is far more complex than that of rigid arm motion due to its link elastic deflections, the flexible arm end-effector positioning problem also becomes more complex. The problem is finally resolved into the following three subproblems: (1) how to suppress the link elastic vibration, (2) how to achieve accurate joint positioning, and (3) how to compensate the end-effector positioning errors due to the link deflections. The problem (1) is being solved by many pieces of work. The problem (2) arises also in the case of rigid arms but, since the joint positioning and link vibration suppressing are coupled, it becomes more complex for the case of flexible arms. The problem (3) is important in order for the arms to perform tasks but no effective method has been presented so far to solve it. This paper presents a hierarchical control system which incorporates organically three control functions: joint positioning, link vibration suppression, and end-effector positioning error compensation. The convergence condition for the compensating control is derived theoretically for the condition of static gravitational loads. The effectiveness of the proposed control system is proved by experiments using a two-link flexible arm. The link deflections are measured by a newly devised and developed sensor consisting of a semiconductor laser and a position sensitive detector (PSD).

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18

Gawronski, W., C. H. C. Ih, and S. J. Wang. "On Dynamics and Control of Multi-Link Flexible Manipulators." Journal of Dynamic Systems, Measurement, and Control 117, no. 2 (1995): 134–42. http://dx.doi.org/10.1115/1.2835173.

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This paper presents solutions of dynamics, inverse dynamics, and control problems of multi-link flexible manipulators. In deriving the manipulator dynamics, flexible deformations are assumed to be small in relation to the link length, angular rates of the links are assumed to be much smaller than their fundamental frequencies, and nonlinear terms (centrifugal and Coriolis forces) in the flexible manipulator model are assumed to be the same as those in the rigid body model. Flexible displacements are measured with respect to the rigid body configuration, obtained from its rigid body inverse kinematics. As a result, a linear time-varying system is obtained. The inverse dynamics problem consists of determination of joint torques for a given tip trajectory such that joint angles in the flexible configuration are equal to the angles in the rigid body configuration. The manipulator control system consists of the feedforward compensation and feedback control loops. Simulation results of a two-link space crane with a large payload show that the performance of this linearized dynamics and control approach is accurate, and at the same time is robust when subjected to parameter variations during slew operations.

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19

Lin, Yueh-Jaw, and Aiping Yu. "Linear robust trajectory control of flexible joint manipulators." Robotica 14, no. 4 (1996): 375–80. http://dx.doi.org/10.1017/s0263574700019767.

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SUMMARYThis paper presents a practical approach for the point-to-point control of elastic-jointed robot manipulators. With the proposed approach only position and velocity feedback are referenced, as opposed to most of the existing control schemes of elastic-jointed manipulators which require additional acceleration and/or jerk feedback. To guarantee the robustness of the controller, it is designed on extreme parameter uncertainties due to highly elastic joints of manipulators and energy motivated Lyapunov functions are used to derive the control law. Four pertinent controller gains are chosen in light of the on-line position and velocity feedback of the links and joint sensors. Through a simulated experimental verification, it is demonstrated that the designed simple position and velocity feedback controller, similar to that used for rigid-jointed robots, can globally stabilize the elastic-jointed robot for a bounded reference position. In addition, the tracking performance of the controller reveals that this simple control algorithm is robust in terms of joint flexibility. And the simplicity of the presented control algorithm, as compared to other model-based techniques for flexiblejoint robots, is particularly advantageous. Even though the simulated experiments are conducted on a single-link flexible joint robot, control law derived in this paper has general meaning for multi-link flexible joint robots.

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20

Lee, Ho-Hoon. "New Dynamic Modeling of Flexible-Link Robots." Journal of Dynamic Systems, Measurement, and Control 127, no. 2 (2003): 307–9. http://dx.doi.org/10.1115/1.1902843.

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This paper shows that the conventional Lagrangian modeling of flexible-link robots does not fully incorporate the bending mechanism of flexible links. The conventional link deflection model allows free link elongation in addition to link deflection; the link elongation increases as link deflection increases. The link elongation, however, causes certain degrees of modeling inaccuracy in association with the rotational motion of the links. Therefore, this paper proposes a new link deflection model, compatible with the bending mechanism of flexible links. Then a new nonlinear dynamic model is derived based on the new link deflection model, fixing the modeling inaccuracy of the conventional dynamic model.

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21

Morris, A. S., and A. Madani. "Quadratic optimal control of a two-flexible-link robot manipulator." Robotica 16, no. 1 (1998): 97–108. http://dx.doi.org/10.1017/s0263574798000186.

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Manipulators with some flexible links are attractive because they avoid the severe control problems associated with the large inertia forces generated when the large-mass, rigid links in conventional robot manipulators move at high speed. In fact only two of the links within a typical six degrees of freedom revolute-geometry industrial robot cause significant inertia forces, and so only these two links need to be flexible. The development of a two-flexible-link system controller is therefore very relevant to larger manipulators, because it can be readily expanded by adding simple controllers for the other rigid links. Two alternative controllers are developed in this paper, a computed-torque controller and a quadratic optimal controller. Simulations confirm the superior performance of the latter.

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22

LEE, Ho Gil, Fumio MIYAZAKI, and Suguru ARIMOTO. "PDS Feedback Control for Flexible Multi-Link Manipulators." Transactions of the Society of Instrument and Control Engineers 25, no. 6 (1989): 675–81. http://dx.doi.org/10.9746/sicetr1965.25.675.

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23

Akbarzadeh, M. R. T., and M. Jaṁshidi. "Hierarchical Fuzzy Control of flexible link robotic systems." IFAC Proceedings Volumes 31, no. 20 (1998): 105–10. http://dx.doi.org/10.1016/s1474-6670(17)41780-0.

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24

Lucibello, Pasquale, and Stefano Panzieri. "Cyclic Control of a Two-Link Flexible Arm *." IFAC Proceedings Volumes 29, no. 1 (1996): 79–84. http://dx.doi.org/10.1016/s1474-6670(17)57642-9.

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25

Matsuno, Fumitoshi, Shozaburo Kasai, Miwako Tanaka, and Kuniko Wakashiro. "Robust Force Control of One-Link Flexible Arms." IFAC Proceedings Volumes 29, no. 1 (1996): 115–20. http://dx.doi.org/10.1016/s1474-6670(17)57648-x.

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26

Ouyang, H., D. Richiedei, and A. Trevisani. "Pole assignment for control of flexible link mechanisms." Journal of Sound and Vibration 332, no. 12 (2013): 2884–99. http://dx.doi.org/10.1016/j.jsv.2013.01.004.

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27

Tinkir, M., Ü. Önen, and M. Kalyoncu. "Modelling of neurofuzzy control of a flexible link." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 224, no. 5 (2010): 529–43. http://dx.doi.org/10.1243/09596518jsce785.

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28

Tchernychev, A., A. Sideris, and Jie Yu. "Constrained H∞ Control of an Experimental Flexible Link." Journal of Dynamic Systems, Measurement, and Control 119, no. 2 (1997): 206–11. http://dx.doi.org/10.1115/1.2801234.

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A new approach is presented to design robust controllers for an experimental flexible beam with noncolocated sensors-actuator. The objective is to position the free end of the beam in the specified time under tight bounds on the trajectory of the tip and control action. We derive a transfer function nominal model for the beam and a quantitative description of model uncertainties based on experimentally obtained frequency response data. Robust controllers are designed by applying the recently developed Constrained H∞ control approach (Sideris and Rotstein, 1993, 1994), in which time-domain constraints are treated directly without translation to the frequency-domain. Constrained H∞ controllers are compared with standard H∞ and μ-synthesis designs in terms of both simulation and experimental results and are found to be superior in the considered case of stringent time-domain specifications.

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29

Moudgal, V. G., W. A. Kwong, K. M. Passino, and S. Yurkovich. "Fuzzy learning control for a flexible-link robot." IEEE Transactions on Fuzzy Systems 3, no. 2 (1995): 199–210. http://dx.doi.org/10.1109/91.388164.

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30

Karagülle, H., L. Malgaca, M. Dirilmiş, M. Akdağ, and Ş. Yavuz. "Vibration control of a two-link flexible manipulator." Journal of Vibration and Control 23, no. 12 (2015): 2023–34. http://dx.doi.org/10.1177/1077546315607694.

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In this study, a two-link manipulator with flexible members is considered. The end point vibration signals are simulated by developing a MatLAB code based on the finite element theory and Newmark solution. Experimental results are also presented and compared with simulation results. The mass and stiffness matrices are time dependent because the angular positions of the links change during the motion. Trapezoidal velocity profiles for the actuating motors are used. The time dependent inertia forces are calculated by using the rigid body dynamics. The inertia forces are due to the motors, end point payload mass and distributed masses of the links. The acceleration, constant velocity and deceleration time intervals of the trapezoidal velocity profile are selected by considering the lowest natural frequency of the manipulator structure at the stopping position. Various starting and stopping positions are considered. The root mean square (RMS) acceleration values of the vibration signals after stopping are calculated. It is observed that the residual vibration is sensitive to the deceleration time. The RMS values are lowest if the inverse of the deceleration time equals to the first natural frequency. It is highest if the inverse of the deceleration time equals to the half of the first natural frequency. It is observed that simulation and experimental results are in good agreement.

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31

Moudgal, V. G., K. M. Passino, and S. Yurkovich. "Rule-based control for a flexible-link robot." IEEE Transactions on Control Systems Technology 2, no. 4 (1994): 392–405. http://dx.doi.org/10.1109/87.338648.

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32

Skaar, S. B., and D. Tucker. "Point Control of a One-Link Flexible Manipulator." Journal of Applied Mechanics 53, no. 1 (1986): 23–27. http://dx.doi.org/10.1115/1.3171731.

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An alternative approach to the control of nonrigid, distributed parameter systems is presented. Transfer functions that relate the response of points on the system to a controlling force or torque are used in place of ordinary differential equations, which represent an approximation to the system dynamics. The implications of this “point control” approach are discussed with regard to plant modeling accuracy, uncontrolled regions, open-loop and closed-loop control strategies, system identification, and feedback estimation. Sample optimal control histories are illustrated for a single-link manipulator member with end load.

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33

Jnifene, A., and A. Fahim. "Endpoint Control of a Two-Link Flexible Manipulator." Journal of Vibration and Control 4, no. 6 (1998): 747–66. http://dx.doi.org/10.1177/107754639800400606.

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34

Siddique, M. N. H., and M. O. Tokhi. "GA-NEURO-FUZZY CONTROL OF FLEXIBLE-LINK MANIPULATORS." IFAC Proceedings Volumes 35, no. 1 (2002): 379–84. http://dx.doi.org/10.3182/20020721-6-es-1901.00969.

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35

Goldenberg, A. A., and F. Rakhsha. "Feedforward control of a single-link flexible robot." Mechanism and Machine Theory 21, no. 4 (1986): 325–35. http://dx.doi.org/10.1016/0094-114x(86)90054-6.

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36

CHEN, Y. P., and K. S. YEUNG. "Sliding-mode control of multi-link flexible manipulators." International Journal of Control 54, no. 2 (1991): 257–78. http://dx.doi.org/10.1080/00207179108934159.

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37

KOMATSU, Tadashi, Michihiro UENOHARA, Shoichi IIKURA, Hirofumi MIURA, and Isao SHIMOYAMA. "Compliance control for a two-link flexible manipulator." Transactions of the Japan Society of Mechanical Engineers Series C 56, no. 530 (1990): 2642–48. http://dx.doi.org/10.1299/kikaic.56.2642.

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38

Feliu, V., K. S. Rattan, and H. B. Brown. "Adaptive control of a single-link flexible manipulator." IEEE Control Systems Magazine 10, no. 2 (1990): 29–33. http://dx.doi.org/10.1109/37.45791.

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39

Parker, Gordon G., Daniel J. Segalman, Rush D. Robinett, and Daniel J. Inman. "Decentralized sliding mode control for flexible link robots." Journal of Intelligent and Robotic Systems 17, no. 1 (1996): 61–79. http://dx.doi.org/10.1007/bf00435716.

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40

Kumar, Amit, Pushparaj Mani Pathak, and N. Sukavanam. "Bond Graph Modeling and Computational Control Analysis of a Rigid-Flexible Space Robot in Work Space." International Journal of Intelligent Mechatronics and Robotics 1, no. 3 (2011): 18–30. http://dx.doi.org/10.4018/ijimr.2011070102.

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The combination of a rigid and a flexible link in a space robot is an interesting field of study from modeling and control point of view. This paper presents the bond graph modeling and overwhelming trajectory control of a rigid-flexible space robot in its work space using the Jacobian based controller. The flexible link is modeled as Euler Bernoulli beam. Bond graph modeling is used to model the dynamics of the system and to devise the control strategy, by representing the dynamics of both rigid and flexible links in a unified manner. The scheme has been verified using simulation for a rigid-flexible space manipulator with two links.

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41

Thomas, S., and B. Bandyopadhyay. "Position Control of Single Link Flexible Manipulator by Variable Structure Model Following Control." Journal of Dynamic Systems, Measurement, and Control 119, no. 2 (1997): 330–35. http://dx.doi.org/10.1115/1.2801259.

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A variable structure model following controller (VSMFC) is designed for the tip position control of a single flexible link. The design is done for the system model in which only the first two flexible modes are included. Due to the simplicity in choosing second order models for the subsystems representing the dynamics of the various flexible modes, the design can be easily extended to include any desired number of flexible modes. The tip position response is made to assume a second order step response by suppressing the flexible modes very quickly. Hence the tip position response can be easily controlled by a suitable choice of the damping factor and natural frequency of the second order model which the rigid body mode of the link is made to follow. The controller is robust to parameter variations and disturbances.

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42

de Queiroz, M. S., S. Donepudi, T. Burg, and D. M. Dawson. "Model-based control of rigid-link flexible-joint robots: an experimental evaluation." Robotica 16, no. 1 (1998): 11–21. http://dx.doi.org/10.1017/s0263574798000113.

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In this paper, we present an experimental evaluation of several link position tracking control algorithms for rigid-link flexible-joint robot manipulators. To study the performance of the controllers, an IMI 2-link direct-drive planar robot manipulator was modified to approximate linear torsional spring couplings from the actuators to the links. Preliminary experimental results seem to indicate that reduced-order, model-based controllers with an actuator feedback loop provide relatively good link position tracking while a full-order, model-based controller offers some further improvement in link position tracking at the expense of increased computation.

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43

Vossoughi, G. R., and A. Karimzadeh. "Impedance control of a two degree-of-freedom planar flexible link manipulator using singular perturbation theory." Robotica 24, no. 2 (2005): 221–28. http://dx.doi.org/10.1017/s0263574705002055.

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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.

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Lin, Lih-Chang, and Sy-Lin Yeh. "A composite adaptive control with flexible quantity feedback for flexible-link manipulators." Journal of Robotic Systems 13, no. 5 (1996): 289–302. http://dx.doi.org/10.1002/(sici)1097-4563(199605)13:5<289::aid-rob3>3.0.co;2-m.

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Liao, C. Y., and C. K. Sung. "An Elastodynamic Analysis and Control of Flexible Linkages Using Piezoceramic Sensors and Actuators." Journal of Mechanical Design 115, no. 3 (1993): 658–65. http://dx.doi.org/10.1115/1.2919241.

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This paper presents an analytical and experimental study on the elastodynamic analysis and control of flexible linkages mechanisms using piezoceramic sensors and actuators. A mixed variational principle is developed to provide the basis for deriving the finite element equations which govern the dynamic responses of the flexible links, behavior of the piezoelectric materials and their coupling relationships, while being subjected to both mechanical and electric boundary conditions. The piezoceramic devices featuring the characteristics of smart materials capable of sensing and controlling elastodynamic responses of the flexible links are employed in an LQG/LTR (Linear Quadratic Gaussian with Loop Transfer Recovery) control scheme to ensure a stable performance. Finally, a four-bar linkage mechanism with one flexible link is utilized as an illustrative example. The results show that the midspan vibration of the flexible link has been greatly suppressed and the control/observer spillover-induced instability has been avoided.

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Benosman, M., and G. Le Vey. "Control of flexible manipulators: A survey." Robotica 22, no. 5 (2004): 533–45. http://dx.doi.org/10.1017/s0263574703005642.

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A survey of the field of control for flexible multi-link robots is presented. This research area has drawn great attention during the last two decades, and seems to be somewhat less “attractive” now, due to the many satisfactory results already obtained, but also because of the complex nature of the remaining open problems. Thus it seems that the time has come to try to deliver a sort of “state of the art” on this subject, although an exhaustive one is out of scope here, because of the great amount of publications. Instead, we survey the most salient progresses – in our opinion – approximately during the last decade, that are representative of the essential different ideas in the field. We proceed along with the exposition of material coming from about 119 included references. We do not pretend to deeply present each of the methods quoted hereafter; however, our goal is to briefly introduce most of the existing methods and to refer the interested reader to more detailed presentations for each scheme. To begin with, a now well-established classification of the flexible arms control goals is given. It is followed by a presentation of different control strategies, indicating in each case whether the approach deals with the one-link case, which can be successfully treated via linear models, or with the multi-link case which necessitates nonlinear, more complex, models. Some possible issues for future research are given in conclusion.

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Pham, CM, W. Khalil, and C. Chevallereau. "A nonlinear model-based control of flexible robots." Robotica 11, no. 1 (1993): 73–82. http://dx.doi.org/10.1017/s0263574700015459.

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SUMMARYThis paper present a nonlinear, model-based control of flexible link robots. The control task is formulated requiring rigid joints variables to track reference time-varying trajectory and elastic deflection to be damped. The stability and robustness properties of the control scheme are analyzed from a passive energy consideration. A direct adaptive version is also proposed. Extensive evaluation of this approach is performed using experimental validations involving a single-flexible-link and a two-flexible-link horizontal robot. Experimental results show significant performances of the controller under relatively severe working conditions: 700% payload to arm ratio and 20% elastic deflection ratio at highest acceleration stages.

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Zhang, Xuping, James K. Mills, and William L. Cleghorn. "MULTI-MODE VIBRATION CONTROL AND POSITION ERROR ANALYSIS OF PARALLEL MANIPULATOR WITH MULTIPLE FLEXIBLE LINKS." Transactions of the Canadian Society for Mechanical Engineering 34, no. 2 (2010): 197–213. http://dx.doi.org/10.1139/tcsme-2010-0012.

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This paper presents multi-mode vibration control and analysis of moving platform position errors of a planar 3-PRR parallel manipulator with three flexible intermediate links using PZT transducers. The active vibration controller is designed in modal space with modal filters and modal synthesizers determined from the flexible link vibration characteristics. Estimation of the moving platform position error is conducted using measurements of the flexible link deflection from PZT sensors mounted on the flexible intermediate links. An effective strategy for determining the control gains to reduce the vibrations of higher order modes is proposed through modification of the independent modal space control (IMSC) method. The proposed independent modal control strategy is experimentally implemented with first two modes targeted for control on a parallel manipulator with multiple flexible links. The experimental results show that the vibrations of the first two modes are effectively suppressed, and the position error of the moving platform is substantially reduced.

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Williams, Darren, Hamed Haddad Khodoparast, and Chenyuang Yang. "Active vibration control of a flexible link robot with the use of piezoelectric actuators." MATEC Web of Conferences 148 (2018): 11005. http://dx.doi.org/10.1051/matecconf/201814811005.

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Within robot systems the use of flexible links could solve many issues raised by their rigid counterparts. However, when these flexible links are integrated within systems which include moving parts their main issue lies in the vibrations experienced along their length due to disturbances. Much research effort has been made to solve this issue, with particular attention being paid to the application of piezoelectric patches as actuators within active vibration control (AVC). The study will consist of accurate models of a flexible link and two surface bonded piezoelectric patches, where the link and the piezoelectric patches will be modelled through the use of Euler-Bernoulli beam theory (EBT). The link will be subject to an initial displacement at its free end, and the resulting displacement of this end of the beam is to be controlled using a classic proportional-differential (PD) controller. The voltages to be applied across each of the actuators is to be controlled in accordance with the displacement of the free end of the beam, the actuators will then induce a strain upon the link opposing the movement of the tip. This research outlines this general method, obtains the best location of the piezoelectric patches and the control gains to be used, and proves that the method can be used to attenuate the vibrations experienced by a flexible link.

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Choi, B. O., and K. Krishnamurthy. "Force control of a two-linke planar manipulator with one flexible link." Robotics and Autonomous Systems 8, no. 4 (1991): 281–89. http://dx.doi.org/10.1016/0921-8890(91)90050-u.

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