Single-link Flexible Manipulator Research Articles

An intelligent control method for a flexible-link manipulator with uncertain backlash and model uncertainty

This study examines a new intelligent control method for a single-link flexible manipulator that addresses backlash and model uncertainty. First, a smooth backlash inverse model is constructed to mitigate backlash nonlinearity. Subsequently, a ‘disturbance-like’ term is formulated to recharacterize the coupled term composed of external disturbances and model uncertainty. A new adaptive controller is proposed to compensate for the unknown ‘disturbance-like’ term. Using the proposed control method, the stability of the system is evaluated using the direct Lyapunov theory, ensuring uniform ultimate boundedness. Finally, numerical simulations and experiments are conducted using the Quanser platform. The numerical simulation and experimental results show that the proposed control can ensure a faster convergence rate and effectively reduce actuator input chattering.

Effect of nonlinear stiffness on single link flexible joint robotic manipulator and its control

This study aims to investigate the significant dynamics of a Single Link Flexible Joint (SLFJ) Robotic Manipulator and implement chaotic control using the Adaptive Sliding Mode Control (ASMC) algorithm. The mathematical model of the system incorporates stiffness nonlinearity by introducing the function (x-x3) Various dynamical tools such as stability analysis of equilibrium points, sensitivity to initial conditions, orbit diagrams for parameter variations, Lyapunov spectrum, and frequency spectrum analysis are employed. The ASMC algorithm is utilized to suppress the chaotic behavior of the system. The equilibrium points are determined for critical parameter values, with the Jacobian matrix and corresponding eigenvalues exhibiting conjugate complex with negative real parts, indicating stability resembling a spiral saddle. Phase portraits illustrate the location and range of the chaotic attractor. Investigation of parameter ′a′ using orbit diagrams and Lyapunov spectrum reveals the transition from periodic to chaotic oscillations. The frequency spectrum confirms the chaotic nature of the system. Parameter estimation, state trajectories, and sliding surface analysis demonstrate that the ASMC scheme can effectively control the system in less than 0.3 s. Nonlinear stiffness has not been previously considered in SLFJ Robotic Manipulators, highlighting a novel aspect of this study. The results unveil new chaotic ranges for parameter variation previously undocumented. Frequency spectrum analysis is employed to distinguish between noise and chaotic oscillations, addressing a significant challenge in real-time systems. The ASMC algorithm is specifically designed to control chaotic oscillations, demonstrating its effectiveness in this context.

Nonlinear Observer-Based Visual Servoing and Vibration Control of Flexible Robotic Manipulators With a Fixed Camera.

This article studies the visual servoing and vibration suppression control for flexible manipulators when the system states are unmeasurable and only the image feedback is available. The dynamic equations of flexible manipulators are decomposed into the slow and fast subsystems based on the singular perturbation theory. The nonlinear observers based on the state transformation using the Lie derivatives are proposed to estimate the unmeasurable system states and unknown camera intrinsic parameters at the same time. Then, the image-based controllers utilizing the estimated states are, respectively, designed in the slow and fast subsystems to regulate the image positions of feature points and suppress the vibration of flexible manipulators simultaneously. In the proposed approach, only the visual feedback is required to generate the control input for flexible manipulators, which simplifies the controller implementation. The stability of the proposed control scheme is proved based on the Lyapunov theory. Finally, experimental results on a flexible single-link manipulator are provided to demonstrate the effectiveness of the proposed control approach.

Adaptive Inverse Compensation Fault-Tolerant Control for a Flexible Manipulator With Unknown Dead-Zone and Actuator Faults

This study presents an adaptive inverse compensation control of a flexible single-link manipulator with an unknown dead-zone and actuator faults. First, a dead-zone inverse model and a smooth inverse operator are constructed to address dead-zone nonlinearity. Second, an adaptive fault-tolerant control is utilized to compensate for the partial loss of the effectiveness of the actuator. Third, the coupling errors of the dead-zone and faults are effectively removed and resolved by introducing an estimate for unknown bounds. Then, the direct Lyapunov theory is used to guarantee uniformly ultimately bounded stability in the controlled system. Finally, the simulations and experiments demonstrate the efficiency of the presented method.

Performance analysis of input shaped model reference adaptive control for a single-link flexible manipulator

Motion control for flexible link manipulators will have a great influence on their overall performance. Conventional control systems have the problem that they cannot compensate for the presence of uncertainty due to a variety of factors such as a change in the system itself-payload variations, degradation and modelling uncertainty. In addition, the underdamped structure of these systems entails motion-induced transient deflection and residual vibration. On the contrary, adaptive control, in particular Model Reference Adaptive Control (MRAC), has therefore been proposed to handle problems of this type dealing with other systems such as cranes, steering stability control for ground vehicles, airplanes and so on. This study presents a review and discussion on the MRAC and some individual issues of MRAC for these flexible link manipulators are addressed to specify: the state tracking error, the limitation of the adaptation values corresponding to the control gains and the control effort. Dealing with the last one, this work proves that shaping the command input to a Model Reference Adaptive Control (IS-MRAC) reduces the control effort necessary for the plant to follow the reference model and also mitigates the detrimental effects of flexibility. The IS-MRAC is implemented in a Single-Link Flexible Manipulator whose natural frequencies, experimentally and analytically estimated using the Transfer Matrix Method plus symbolic computation, vary significantly depending on payload mass and position. To this structured or parametric uncertainty, the proposed Lyapunov control law using the states associated with the low mode is designed for asymptotic stability and accommodates correctly. The state tracking, vibration suppression and control effort reduction performances of the proposed IS-MRAC combined controller are analysed via numerical simulations and experiments.

Consensus tracking and vibration control for multiple single-link flexible manipulators with input signal quantization

This study examines consensus tracking and vibration control of a multiagent system consisting of multiple single-link flexible manipulators with input signal quantization. The dynamics of each flexible manipulator are described by fourth-order partial differential equations (PDEs). A logarithmic quantizer with changeable parameters is adopted to quantize control inputs, and adaptive laws are designed to compensate for the effect caused by quantization. A distributed adaptive boundary control protocol is proposed based on the PDE model to ensure all manipulators track the desired angular position and eliminate vibrations without knowledge of quantizer parameters. The proposed control protocol is proven to ensure the uniformly bounded stability of the closed-loop system. Simulations are carried out under three cases to illustrate the effectiveness of the designed strategy.

Experimental modal analysis of a single-link flexible robotic manipulator with curved geometry using applied system identification methods

In this paper, the principal time-domain system identification methods are studied and used to carry out the experimental modal analysis of a single-link flexible manipulator with curved geometry in a comparative fashion. The identification process carried out in this study is aimed at deriving first-order state-space dynamical models and second-order configuration-space dynamical models of the single-link flexible manipulator by using an array of fundamental system identification procedures, which includes the ARX (AutoRegressive eXogenous method), SSEST (State-Space ESTimation method), N4SID (Numerical Algorithm for Subspace State-Space System Identification), ERA/OKID (Eigensystem Realization Algorithm combined with the Observer/Kalman Filter Identification method), and TFEST (Transfer Function ESTimation method) methods. The main goal of this paper is, therefore, to perform a comparative study between the most fundamental system identification procedures applied to the numerical and experimental analysis of the structural vibrations of a flexible manipulator having a curved geometric shape. First, this paper poses the theoretical foundations for the development of the numerical study and the experimental testing to be performed for the case study. Subsequently, the flexible manipulator analyzed in this work is modeled with various levels of complexity, which range from a simple lumped parameter model to a linear finite element model developed by integrating the interconnections between the SOLIDWORKS and ANSYS software. By doing so, the computational procedures applied to the time-domain experimental measurements of the dynamic behavior of the flexible manipulator allow for reconstructing first-order and second-order mechanical models of the structural system of interest in the MATLAB simulation environment. The numerical results and the experimental tests reported in this investigation demonstrate the effectiveness of all the time-domain system identification approaches considered in the paper.

Hybrid Controller for a Single Flexible Link Manipulator

In this study, the dynamic modeling and step input tracking control of single flexible link is studied. The Lagrange-assumed modes approach is applied to get the dynamic model of a planner single link manipulator. A Step input tracking controller is suggested by utilizing the hybrid controller approach to overcome the problem of vibration of tip position through motion which is a characteristic of the flexible link system. The first controller is a modified version of the proportional-derivative (PD) rigid controller to track the hub position while sliding mode (SM) control is used for vibration damping. Also, a second controller (a fuzzy logic based proportional-integral plus derivative (PI+D) control scheme) is developed for both vibration damping and hub position tracking. A comparison is made between the performances of these two controllers. The Hybrid controller with PD and SM shows better tracking behavior than obtained from the suggested fuzzy (PI+D)2 controller for a single link flexible manipulator.

Trajectory Tracking and Adaptive Fuzzy Vibration Control of Multilink Space Manipulators with Experimental Validation

This paper investigates the problem of modeling and controlling a space manipulator system with flexible joints and links. The dynamic model of the flexible manipulator system is derived by using the Lagrange equation and the floating frame of reference formulation, where the assumed mode method is adopted to discretize flexible links, while the flexible joints are regarded as linear torsion springs. The natural characteristics of a single flexible link manipulator, under three different boundary conditions, are compared to reveal the effect of the flexibility of joints on the manipulator system and to choose suitable assumed modes. Furthermore, singular perturbation theory is introduced to decompose the system into a slow subsystem that describes the rigid-body motion, and a fast subsystem that describes the elastic vibration. Since the system is underactuated, a compound control strategy, which consists of the underactuated computed torque controller and the adaptive fuzzy controller, is presented to improve the accuracy of the trajectory tracking of the flexible joints and to suppress the elastic vibration of the flexible links, in the meantime. Both numerical simulation and experimentation are performed to verify the effectiveness of the proposed compound controller, and a comparison with the proportional-derivative (PD) controller is provided to highlight its superiority in suppressing the residual vibration of the tip.

Implementation of Crow Search Algorithm for Achieving Optimal Control of a Single-Link Flexible Manipulator

A metaheuristic optimizer based on the cognitive behavior of crows, called the Crow Search Algorithm (CSA), is suggested in this paper for the optimization of the performance of the single link flexible manipulator as a constrained optimal control problem, which comprises objective functions, constraints, and decision variables. The CSA outperformed other algorithms, such as Differential Evolution, Grey Wolf Optimization, and Particle Swarm Optimization. Parameter setting is another highlight of the current paper. In conclusion, CSA yields more promising results than other approaches.

Discrete Geometric Control of Planar Flexible Link Manipulators

Discrete control laws for flexible beam models obtained using structure-preserving discretization procedures are few in the existing literature so far and many control laws, including distributed ones, exist for continuous time models. Much of the effort has focussed on the discretization of the flexible structure and the fidelity of such models. The work in this paper examines the feasibility of a discretized version of a continuous time distributed control strategy, with a few approximations, to the discrete variational integrator of a flexible beam, in our case, a flexible single-link manipulator (FLM). The nonlinear control strategy is inspired by a potential shaping method in the literature based on the Cosserat continuum framework. We provide stability proof for this continuous-time control and approximate it to a discrete-time geometric framework. We use a geometrically exact beam model in which the manipulator's configuration space lies on an infinite-dimensional Lie group. The model-based discrete-time control uses a Lie Group Variational Integrator obtained by applying the variational principle on the Lagrangian of the FLM. Results show that the discrete closed-loop system stabilizes the FLM at setpoints during point-to-point rotational maneuvers. The controller demands fine time-sampling and we acknowledge the associated challenges for real-time implementation of the control scheme and intend to pursue it as our future work.

Q-learning based model-free input-output feedback linearization control method⋆

Input-output feedback linearization is a nonlinear control method that relies on a precise dynamical model. Combining Q-learning techniques, an input-output feedback linearization correction framework is presented to accomplish model-free feedback linearization of affine nonlinear systems in order to tackle the problem caused by the unknown dynamics model. This framework formulates a model reference tracking control problem that guides the input-output relationship of the nonlinear system into a linear relationship. Due to the two Lie derivative terms present in the feedback linearized controller, the controller is designed as a dual network structure. To overcome the issue of coupling in the dual-network controller, a model-free Q-learning method is presented to solve the unknown controller network weights. The proposed method is experimentally validated on a single-link flexible joint manipulator system, and the resultant linearized system exhibits dynamics similar to the desired linear system in a new tracking task, proving the effectiveness of the proposed method.

Dynamic Stability Control and Calculating Inverse Dynamics of a Single-link Flexible Manipulator

Dynamic Stability Control and Calculating Inverse Dynamics of a Single-link Flexible Manipulator

Study on dynamic modelling and vibration analysis of single-link flexible manipulator

In this study, SimMechanics-based dynamic modeling and vibration analysis of a single-link flexible manipulator are studied. A flexible beam model is set up for modeling the manipulator. Transient analysis is performed to obtain the endpoint acceleration vibration responses of the manipulator moved with different motion profiles. Both the experimental and simulation acceleration results are presented for different cases. The root means square (RMS) values of the acceleration responses are calculated to evaluate the compatibility performance in verifying the simulation results with the experimental results. It has been observed that the results match each other successfully for different cases. The reliability of the SimMechanics-based dynamic modeling method of manipulators is discussed with the experimental results.

Adaptive Event-Triggered Boundary Control for a Flexible Manipulator With Input Quantization

In this article, an adaptive event-triggered boundary control scheme is proposed for a flexible single-link manipulator (FSLM) system with communication constraints. The hysteresis quantizer with unknown parameters is applied to the control input, which brings a negative effect on the control performance. To reduce the communication burden, we take into account a relative threshold event-triggered mechanism. An adaptive strategy is adopted to compensate for the quantization error and evaluate the unknown parameters. In terms of the Lyapunov direct method, the angle tracking error and the vibration displacement of the FSLM are proved to exponentially converge to the neighborhood of zero. Furthermore, the performance of the developed control algorithm is presented by numerical simulations and experiments.

CONTROL OF A SINGLE LINK FLEXIBLE MANIPULATOR USING SEQUENCED CONTROL

Mekanik sistemler çalışmaları esnasında titreşimlere ve bozucu etkilere maruz kalırlar. Bu etkilerden kurtulmak için çeşitli kontrol yöntemleri geliştirilmiştir. Sıralı kontrol, PID kontrol ve giriş şekillendirmeyi bir araya getiren bir kontrol yöntemidir. Temelinde giriş şekillendirme kullanarak sistemin hızlı ve titreşimsiz bir şekilde istenen referans değerine ulaşması sağlandıktan sonra, anahtarlama yardımıyla PID kontrole geçilerek sistemin bozucu etkilere karşı dayanıklı olmasını sağlamak yatar. Sıralı kontrol, PID kontrol ve giriş şekillendirmeyi optimum zamanlarda kullandığı için, her iki kontrol yönteminin avantajlarından faydalanırken, dezavantajlarından kurtulmayı amaçlar. Sıralı kontrolün, doğru uygulandığında, her iki kontrol yönteminin birlikte kullanıldığı hibrit kontrol yöntemlerinden avantajlı olduğu görülmüştür. Bu çalışmada tek eklemli esnek robotun transfer fonksiyonu MATLAB-Simulink ortamında modellenmiştir. Modellenen sisteme sırasıyla basamak giriş, giriş şekillendirme, PID kontrol ve sıralı kontrol uygulanarak sistem yanıtları elde edilmiş, çıkışlar performans açısından karşılaştırılarak sistem performansının iyileştirilmesi için öneriler sunulmuştur.

An active control method for vibration reduction of a single-link flexible manipulator

There are three motion stages for an industrial robot manipulator, including the acceleration stage, the constant velocity stage, and the deceleration stage. Aiming at reducing the residual vibration of the manipulator after the movement of the deceleration, a new method is proposed by configuring the movement parameters of the flexible manipulator. Firstly, we conduct experiments to verify a numerical vibration model of the manipulator, and then, we analyze the vibration suppression effect under different conditions based on the numerical model. The results show that in the range of one movement, the residual vibration can be well suppressed when the acceleration and deceleration time are set as a positive integer to the natural period of the manipulator operation; otherwise, the vibration suppression effect is not obvious and proportional to the difference between the acceleration/deceleration time and the manipulator natural period.

Sliding Mode Controller with Generalized Extended State Observer for Single Link Flexible Manipulator

This paper presents an enhanced generalized extended state observer (EGESO) based sliding mode control (SMC) technique for dealing with the disturbance attenuation problem for a class of non-integral chain systems with mismatched uncertainty. In the proposed control law, the robust SMC with reaching phase elimination is applied in the proposed control law, which uses the estimated states of a system. The stability analysis is thoroughly examined for both EGESO and SMC. The efficacy of the proposed controller is verified using specific examples, and later it is applied on a single-link flexible manipulator. Through simulation and experimentation analysis, it is observed that the proposed controller is giving a robust transient response as compared to existing GESO based controllers.

Robust event-triggered finite-time control of faulty networked flexible manipulator under external disturbance

In this paper, finite-time contractive stability analysis and observer-based H ∞ fault tolerant control problem is discussed for a networked single-link flexible manipulator subject to external disturbance, actuator, and sensor faults. The variable delay is considered in both sensor-to-controller and controller-to-actuator channels. In order to conserve the network resources and avoid Zeno phenomenon, the sampled-data-based event-triggered scheme is employed, which only requires the system states in discrete instants. The nonlinear unknown input observer is first designed to achieve the estimation of the system states and faults simultaneously. To reduce the conservatism of designing procedure, the Lyapunov–Krasovskii functional approach is used, which includes the information of the lower and upper bounds of variable data transmission delay. Then, sufficient delay dependent conditions are derived and an observer-based feedback control law and observer gains are computed by a set of linear matrix inequalities to realize that the augmented system is finite-time contractive stable and the states of the system remain within a specified threshold during a fixed time interval, which is smaller than the initial state bound. Furthermore, the prescribed H ∞ performance is satisfied in the presence of external disturbance. At last, simulation results are given to confirm the validity of the presented approach.

Dynamic analysis and control of a string-stiffened single-link flexible manipulator with flexible joint

In this paper, an innovative method of controlling the endpoint precision of a single-link flexible manipulator has been presented. The flexibility of the link has been stiffened by using a pair of strings while retaining its advantage of being lightweight. The flexible link is modeled as an Euler-Bernoulli beam. Dynamic analyses of the string-stiffened single-link flexible manipulator (SSSLFM) with flexible joint have been carried out using Euler-Lagrange’s formulation with the assumed mode method. The effects of string-stiffening on tip deflection of the link have been found. Coupling effects of string vibration on tip deflection of the link as well as on the joint of the manipulator have also been investigated. It has been observed that by the stiffening of the flexible link with a pair of strings, tip deflection of the link has been reduced significantly. Residual vibrations have been controlled by applying robust proportional-integral and derivative (PID) control.