Flexible Link Manipulator Research Articles

Design of Dynamic Nonlinear Control Techniques for Flexible-Link Manipulators

In this paper, we develop robust dynamical controllers for addressing the problems of tracking and regulation of flexible-link manipulators. The design of dynamical controllers is based on construction of a two-time scale dynamical motion of the closed-loop system. The main control objective is to achieve stability of the closed-loop system while ensuring boundedness of all the control signals as well as sufficiently small tip-position tracking requirement. In order to achieve a minimum phase behaviour for utilizing output feedback control strategy, a new redefined output is proposed. Instead of using the joint angles as outputs in the rigid-link case, a new output is chosen for the flexible-link case which will provide and guarantee stability of the closed-loop flexible system. Simulations results are provided for flexible-link manipulators using the proposed control strategies. A comparative analysis is also included to demonstrate and illustrate the advantages and disadvantages of the considered control methodologies.

A Constrained Lagrange Formulation of Multilink Planar Flexible Manipulator

In this article, the closed-form dynamic equations of planar flexible link manipulators (FLMs), with revolute joints and constant cross sections, are derived combining Lagrange’s equations and the assumed mode shape method. To overcome the lengthy and complicated derivative calculation of the Lagrangian function of a FLM, these computations are done only once for a single flexible link manipulator with a moving base (SFLMB). Employing the Lagrange multipliers and the dynamic equations of the SFLMB, the equations of motion of the FLM are derived in terms of the dependent generalized coordinates. To obtain the closed-form dynamic equations of the FLM in terms of the independent generalized coordinates, the natural orthogonal complement of the Jacobian constraint matrix, which is associated with the velocity constraints in the linear homogeneous form, is used. To verify the proposed closed-form dynamic model, the simulation results obtained from the model were compared with the results of the full nonlinear finite element analysis. These comparisons showed sound agreement. One of the main advantages of this approach is that the derived dynamic model can be used for the model based end-effector control and the vibration suppression of planar FLMs.

Vibration Control of a Flexible Link Manipulator Using Smart Structures

The active vibration suppression of a flexible link manipulator using a smart structure (piezoelectric actuator) is investigated. For this purpose, a Finite Element (FE) model is developed for the modal and transient analysis of a cantilever beam and a flexible link manipulator. The novelty of this work is in the development of an accurate finite element model of a piezoelectric and beam/manipulator. Also, the effect of the placement of the piezoelectric actuator along the beam, based on the controllability of the system states and using FE analysis, is investigated. To avoid system instability, a collocated sensor-actuator pair is used and a proportional control strategy is employed to adjust the voltage applied to the piezoelectric actuator so as to control vibrations. For the flexible link manipulator, it is shown that the vibration is well suppressed during and at the end of a maneuver by locating the piezoelectric actuator at the optimum location. The effect of the controller gain on the vibration behavior of the system is investigated and the optimum controller gain is found using two main evaluation criteria; these are the contribution of the dominant frequencies in the response and the error norms of the vibration amplitudes.

Modified PID Control of a Single-Link Flexible Robot

The use of flexible links in robots has become very common in different engineering fields. The issue of position control for flexible link manipulators has gained a lot of attention. Using the vibration signal originating from the motion of the flexible-link robot is one of the important methods used in controlling the tip position of the single-link arms. Compared with the common methods for controlling the base of the flexible arm, vibration feedback can improve the use of the flexible-link robot systems. In this paper a modified PID control (MPID) is proposed which depends only on vibration feedback to improve the response of the flexible arm without the massive need for measurements. The arm moves horizontally by a DC motor on its base while a tip payload is attached to the other end. A simulation for the system with both PD controller and the proposed MPID controller is performed. An experimental validation for the control of the single-link flexible arm is shown. The robustness of the proposed controller is examined by changing the loading condition at the tip of the flexible arm. The response results for the single-link flexible arm are presented with both the PI and MPID controller used. A study of the stability of the proposed MPID is carried out.

ダイナミクスの拡張にもとづいた2自由度平面フレキシブルマニピュレータの手先位置制御

ダイナミクスの拡張にもとづいた2自由度平面フレキシブルマニピュレータの手先位置制御

2A1-G06 視覚センサ情報の欠落を考慮したビジョンペースト振動抑制制御(フレキシブルロボット・メカニズム)

A vision-based vibration control approach had been proposed for flexible-link manipulators. It utilizes the information from end-effector camera to estimate vibration. Particularly, the image features necessary for this approach are not specified to the ones from any assumed objects like artificial markers. Thus this control method has to be capable of dealing with the random variation of the detected features. In this paper, a strategy is proposed to treat the case of feature disappearance.

A fast on-line frequency estimator of lightly damped vibrations in flexible structures

A significant research effort has been conducted in the past to achieve a reliable on-line vibration mode estimator. Frequently, pure sinusoidal models of the underlying mechanical system have been used to accomplish the estimation task. In this paper, an algebraic approach is proposed for the fast and reliable, on-line identification of the natural frequency of a flexible-link manipulator. The proposed method uses the pure sinusoidal model in combination with the algebraic derivative method for parameter identification. The method leads, in the time domain, to an exact computation formulae for the unknown frequency parameter. This formula is synthesized in terms of time-varying linear unstable filters in combination with classical low-pass filters of the Butterworth type. The computations are performed in a quite small-time interval which is only a small fraction of the first full cycle of the measured sinusoidal signal. The proposed method is verified to be robust with respect to un-modeled small attenuations, present in the flexible structure, and to measurement noise. An experimental setup has been developed as a benchmark to test and compare the proposed method with other recently developed parameter estimation techniques.

Dynamic model of a flying manipulator with two highly flexible links

Nonlinear dynamic model of a flying manipulator with two revolute joints and two highly flexible links is obtained using Hamilton’s principle. Flying base of the manipulator is a rigid body. Stress is treated three dimensionally in the isotropic linearly-elastic links, but the in-plane and out-of-plane warpings of the links’ cross-sections are neglected. Although the links’ cross-sections undergo negligible elastic orientation, their models are more accurate than a nonlinear 3D Euler–Bernoulli beam. Tension, compression, twisting and spatial deflections of each link are coupled to each other by some nonlinear terms including two new ones. In the issue of flying flexible-link manipulators new terminologies, namely forward/inverse kinetics instead of forward/inverse kinematics are suggested, since determination of position and orientation of the end-effector is coupled to the partial differential motion equations.

Active Vibration Control Strategy for a Single-Link Flexible Manipulator Using Ionic Polymer Metal Composite

Ionic polymer metal composites (IPMC) are a class of electro-active polymers (EAP) that produce mechanical strain in response to electrical stimulation and vice versa. The property of generating high strains with low actuation voltage makes IPMC suitable for mechanical actuators in applications involving control of high-amplitude vibration. This article describes results on an application of IPMC as an active damper for large deflection vibration control of a single link rotating flexible manipulator. Modeling of the flexible rotating link has been done using modal approach and it was found that the first two modes of vibration take the maximum amount of energy. Based on this, two IPMC actuators were fixed at suitable positions on the link to suppress vibrations. A dynamic model of the link with IPMC was derived and a distributed PD controller designed to actuate the IPMC to control the vibration of the flexible link. Simulations were first done to demonstrate the effectiveness of IPMC and then experiments are conducted to validate the results. The results prove that IPMC can be used as an active damper for suppressing vibration in a flexible link manipulator.

Comprehensive mathematical modelling of a lightweight flexible link robot manipulator

This paper deals with a comprehensive study of the application of the Timoshenko Beam Theory (TBT) concepts to the mathematical modelling of a planar lightweight single link flexible robot manipulator arm pinned at its actuated base and carrying a payload at its free end-point. The emphasis being essentially set on obtaining accurate and complete equations of the transversely vibrating motion that display the most relevant aspects of structural properties inherent to the modelled lightweight flexible link, two important damping mechanisms, internal structural viscoelasticity (Kelvin-Voigt damping) and external viscous air damping, have been included in addition to the TBT classical effects of cross section shear deformation and rotational inertia. Torsional, gravitational and longitudinal elongation effects have been neglected. Digital simulations are performed to show the free vibrational behaviour of the modelled robotic system.

Modeling of impact dynamics of flexible robots

The dynamic modeling of flexible robots colliding with its working environments is discussed. The system considered is an n-axis serial flexible-link manipulator connected by n joints. The flexibility of each flexible link is described by using the approach of assumed modes. The concept of impulse potential energy is introduced, and the generalized impulse-momentum equations which describe the dynamic responses of the flexible robots with external impacts are developed by employing Lagrange equations. The dynamic responses of the two flexible robots colliding with each other are obtained by combining the generalized impulse-momentum equations and the equations involving coefficient of restitution. The resulting equations are not coupled between the increment of generalized velocities and the impulses, and they are ready for computer programming. The jump discontinuities in system generalized velocities and the impulses at the impact points can be explicitly obtained by solving this mathematic model. In order to validate the method presented, the dynamic simulation of a robot involving impact with its environments is given as an example, which demonstrates the availability of the method.

Position control of a single-link flexible manipulator using H∞-based PID control

The application of the H∞ proportional-integral-derivative (PID) control synthesis method to tip position control of a flexible-link manipulator is investigated. For this system, it is first shown that the classical PID tuning formula may yield poor closed-loop performance. This underlines the need for a rigorous PID control synthesis methodology for this infinite-dimensional and non-minimum-phase system. To achieve high performance in PID control, this particular control design problem is cast into the H∞ framework. On the basis of a recently proposed H∞ PID control synthesis method, a set of admissible controllers is then obtained to be robust against uncertainty introduced by neglecting the higher-order modes of the link and to achieve the desired time-response specifications. The most important feature of the H∞ PID control synthesis method is its ability to provide the knowledge of the entire admissible PID controller gain space, which can facilitate controller fine tuning. Finally, experimental results are given to demonstrate the effectiveness of the H∞ PID control.

Neural network control of flexible-link manipulators using sliding mode

This paper focuses on tracking control problem of flexible-link manipulators. In order to alleviate the effects of nonlinearities and uncertainties, a combined control strategy based on neural network (NN) and the concept of sliding mode control (SMC) is proposed systematically. The chattering phenomenon in conventional SMC is eliminated by incorporated a saturation function in the proposed controller, and the computation burden caused by model dynamics is reduced by applying a two-layer NN with an analytical approximated upper bound, which is used to implement a certain functional estimate. In addition, the Lyapunov analysis can guarantee the signals of closed-loop system bounded and the online NN adaptive laws can make the system states converge to the sliding surface. Furthermore, the boundary layer thickness as well as the gain of corrective control term is also discussed in detail. At last, the theoretic results are validated on the flexible-link manipulator experimental system in Tsinghua University.

End-effector Trajectory Control in a Two-Link Flexible Manipulator Through Reference Joint Angle Values Modification by Neural Networks

The basic difficulty in the control of flexible link manipulators stems from the fact that the link deflections cannot be controlled directly. Since the number of control inputs, applied by the actuators, is less than the total number of variables to be controlled, control approaches aiming at the suppression of deflections and vibrations are generally insufficient. Another possible approach is to determine new joint trajectories to minimize the error of the end-effector in the operational space. In this paper, a neural network is designed to compute incremental changes for the reference values of the joint angles to achieve successful tip tracking in the operational space. Tip position errors in the x-and y-directions are utilized as inputs to the neural network. The cost function, which is minimized in training the neural network, is also chosen as the sum of squares of the tip position error in both directions. Joint angle control is provided by a PD controller. Simulations are carried out to evaluate the performance of the neural-network-based trajectory tracking method, and the results are depicted in both joint and operational spaces.

EXPERIMENTS WITH POSITION AND INTERACTION CONTROL FOR A ROBOT WITH ONE FLEXIBLE LINK

One of the major drawbacks of flexible-link robot applications is its low tip precision, which is an essential characteristic for applications with position and interaction control with a contact surface. In this paper, position and interaction control strategies considering a rigid contact surface are applied to a flexible-link manipulator. The applied strategies are based on the closed-loop inverse kinematics algorithm (CLIK) to obtain the desired angular references to the joint position controller. The control schemes were previously tested by simulation and further implemented on a two degrees of mobility flexible-link planar robot. The obtained experimental results exhibit a good position and force tracking performance. The overall results reveal the successful implementation of the control architectures for a robot with one flexible link.

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

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.

Application of orthonormal basis functions for identification of flexible-link manipulators

The advantage of generalized orthonormal bases, as compared to other orthonormal basis functions such as the Laguerre and Kautz functions, is the ability to include a priori knowledge of the real and complex pole locations of the model. In this paper, the implementation of generalized orthonormal basis functions (GOBF) for system identification is discussed and applied to identification of the dynamics of a single flexible-link manipulator. The plant is non-minimum phase with real and complex poles. A global optimization strategy for selecting the location of the poles of the basis functions is proposed. This method is evaluated through simulation and experimental studies and shows superior performance as compared to ARMAX and FIR identification.

Nonlinear Dynamic Analysis of Planar Flexible Underactuated Manipulators

The influence of passive joint on the dynamics of planar flexible underactuated manipulators is studied. A vibration reduction method based on the internal resonance phenomenon of multi-degree nonlinear dynamic system is proposed. The dynamic simulation results reveal that the harmonic input for the actuated joint will induce the passive joint deviating from its equilibrium position, the excursion speed and direction depend on t he amplitude of the input. A passive joint position control scheme making use of the vibration of the flexible structure is suggested, and the numerical simulation results of a model of planar two- link flexible underactuated manipulator is shown.

Stability Guaranteed Control: Time Domain Passivity Approach

A general framework for expanding the time-domain passivity control approach, to large classes of control systems is proposed. We show that large classes of control systems can be described from a network point of view. Based on the network presentation, the large classes of control systems are analyzed in a unified framework. In this unified network model, we define input energy, which is a virtual source of for control, and real output energy that is physically transferred to a plant to allow the concept of passivity to be used to study the stability of large classes of control systems. For guaranteeing the stability condition, the time-domain passivity controller for two-port is applied. Design procedure is demonstrated for a motion control system. The developed method is tested with numerical simulation in the regulation of a single link flexible manipulator. Totally stable control is achieved under wide variety of operating condition and uncertainties without any model information.

A Neural Network Controller for a Class of Nonlinear Non-Minimum Phase Systems with Application to a Flexible-Link Manipulator

This paper investigates the problem of controlling a nonlinear nonminimum phase system. An output re-definition strategy is first introduced to guarantee stable zero dynamics. This output re-definition scheme is applicable to a class of open-loop stable nonlinear systems whose input–output maps contain nonlinear terms in the output and linear terms in the input. No explicit knowledge about the nonlinearities of the system is required. The nonlinearities of the system are identified by a neural network. The identified neural network model is then used in modifying the zero dynamics of the system. A stable∕anti-stable factorization is performed on the zero dynamics of the system. The new output is re-defined using the neural identifier and the stable part of the zero dynamics. A controller is then designed based on the new output whose zero dynamics are stable and can be inverted. An experimental setup of a single-link flexible manipulator is considered as a practical case study of a nonlinear nonminimum phase system. Experimental results are presented to illustrate the advantages and improved performance of the proposed tracking controller over both linear and nonlinear conventional controllers in the presence of unmodeled dynamics and parameter variations.