Adaptive Leader-Follower Consensus Control of Multiple Flexible Manipulators With Actuator Failures and Parameter Uncertainties

In this paper,the leader-follower consensus problem for a multiple flexible manipulator network with actuator failures,parameter uncertainties,and unknown time-varying boundary disturbances is addressed.The purpose of this study is to develop distributed controllers utilizing local interactive protocols that not only suppress the vibration of each flexible manipulator but also achieve consensus on joint angle position between actual followers and the virtual leader.Following the accomplishment of the reconstruction of the fault terms and parameter uncertainties,the adaptive neural network method and parameter estimation technique are employed to compensate for unknown items and bounded disturbances.Furthermore,the Lyapunov stability theory is used to demonstrate that followers’angle consensus errors and vibration deflections in closed-loop systems are uniformly ultimately bounded.Finally,the numerical simulation results confirm the efficacy of the proposed controllers.

Vibration Reduction of Open-chain Flexible Manipulators by Optimizing Independent Motions of Branch Links

In order to suppress vibration in flexible manipulators, a new type of manipulator mechanism with controllable local degrees of freedom is proposed. This mechanism consists of a main chain and some branch links. The main chain is of a flexible open-chain configuration with an end-effector installed at its tip, and the rigid branch links are able to perform active movements. It is proved by kinematics and dynamic analysis that, the branch links bear no direct kinematic relation to the main chain, but their independent motions can strongly affect the dynamic behavior and performance of the flexible manipulator. Then comes a new idea of suppressing vibration, in which independent motions of the branch links are used to suppress the undesired vibration of the flexible main chain through dynamic coupling. On this basis, an optimal method for reducing vibration of flexible manipulators is proposed. Finally, the effectiveness of this method is verified by numerical simulations.

FUZZY ADAPTIVE CONTROL OF FLEXIBLE-LINK ROBOT MANIPULATOR

A fuzzy adaptive control method is proposed for a flexible robot manipulator. Due to the structure characteristics of the flexible manipulator, the vibration modes must be controlled to realize the high-precision tip position. The Lagrangian principle is utilized to model the dynamic function of the single-degree flexible manipulator incorporating the assumed modes method. Simulation results of the fuzzy adaptive control method in the location control and the trajectory tracking with different tip disturbances are presented and compared with the results of the classic PD control. It shows that the controller can obtain the stable and robust performance.

Optimal Joint Space Control of a Cable-Driven Aerial Manipulator

This article proposes a novel method for maintaining the trajectory of an aerial manipulator by utilizing a fast nonsingular terminal sliding mode(FNTSM)manifold and a linear extended state observer(LESO).The developed controlmethod applies an FNTSMto ensure the tracking performance’s control accuracy,and an LESO to estimate the system’s unmodeled dynamics and external disturbances.Additionally,an improved salp swarm algorithm(ISSA)is employed to parameter tune the suggested controller by integrating the salp swarmtechnique with a cloud model.This approach also uses a model-free scheme to reduce the complexity of controller design without relying on complex and precise dynamics models.The simulation results show that the proposed controller outperforms linear active rejection disturbance control and PID controllers in terms of transient performance and resilience against lumped disturbances,and the ISSA can help the proposed controller find optimal control parameters.

Observer-Based Control for a Cable-Driven Aerial Manipulator under Lumped Disturbances

With the increasing demand for interactive aerial operations,the application of aerial manipulators is becoming more promising.However,there are a few critical problems on how to improve the energetic efficiency and pose control of the aerialmanipulator forpractical application.In this paper,a novel cable-drivenaerialmanipulatorused for remote water sampling is proposed and then its rigid-flexible coupling dynamics model is constructed which takes joint flexibility into account.To achieve high precision joint position tracking under lumped disturbances,a newly controller,which consists of three parts:linear extended state observer,adaptive super-twisting strategy,and fractional-order nonsingular terminal sliding mode control,is proposed.The linear extended state observer is adopted to approximate unmeasured states and unknown lumped disturbances and achieve model-free control structure.The adaptive super-twisting strategy and fractional-order nonsingular terminal sliding mode control are combined together to achieve good control performance and counteract chattering problem.The Lyapunovmethod is utilized to prove the overall stability and convergence of the system.Lastly,various visualization simulations and ground experiments are conducted,verifying the effectiveness of our strategy,and all outcomes demonstrate its superiorities over the existing control strategies.

Flexible Bio-tensegrity Manipulator with Multi-degree of Freedom and Variable Structure

Conventional manipulators with rigid structures and sti ness actuators have poor flexibility,limited obstacle avoidance capability,and constrained workspace.Some developed flexible or soft manipulators in recent years have the characteristics of infinite degrees of freedom,high flexibility,environmental adaptability,and extended manipulation capability.However,these existing manipulators still cannot achieve the shrinking motion and independent control of specified segments like the animals,which hinders their applications.In this paper,a flexible bio-tensegrity manipulator,inspired by the longitudinal and transversal muscles of octopus tentacles,was proposed to mimic the shrinking behavior and achieve the variable motion patterns of each segment.Such proposed manipulator uses the elastic spring as the backbone,which is driven by four cables and has one variable structure mechanism in each segment to achieve the independent control of each segment.The variable structure mechanism innovatively contains seven lock-release states to independently control the bending and shrinking motion of each segment.After the kinematic modeling and analysis,one prototype of such bionic flexible manipulator was built and the open-loop control method was proposed.Some proof-of-concept experiments,including the shrinking motion,bending motion,and variable structure motion,were carried out by controlling the length of four cables and changing the lock-release states of the variable structure mechanism,which validate the feasibility and validity of our proposed prototype.Meanwhile,the experimental results show the flexible manipulator can accomplish the bending and shrinking motion with the relative error less than 6.8%through the simple independent control of each segment using the variable structure mechanism.This proposed manipulator has the features of controllable degree-of-freedom in each segment,which extend their environmental adaptability,and manipulation capability.

Effects of Joint Controller on Analytical Modal Analysis of Rotational Flexible Manipulator

Modal analysis is a fundamental and important task for modeling and control of the flexible manipulator. However, almost all of the traditional modal analysis methods view the flexible manipulator as a pure mechanical structure and neglect feedback action of joint controller. In order to study the effects of joint controller on the modal analysis of rotational flexible manipulator, a closed-loop analytical modal analysis method is proposed. Firstly, two exact boundary constraints, namely servo feedback constraint and bending moment constraint, are derived to solve the vibration partial differential equation. It is found that the stiffness and damping gains of joint controller are both included in the boundary conditions, which lead to an unconventional secular term. Secondly, analytical algorithm based on Ritz approach is developed by using Laplace transform and complex modal approach to obtain the natural frequencies and mode shapes. And then, the numerical simulations are performed and the computational results show that joint controller has pronounced influence on the modal parameters： joint controller stiffness reduces the natural frequency, while joint controller damping makes the shape phase non-zero. Furthermore, the validity of the presented conclusion is confirmed through experimental studies. These findings are expected to improve the performance of dynamics simulation systems and model-based controllers.

COUPLING EFFECT OF FLEXIBLE JOINT AND FLEXIBLE LINK ON DYNAMIC SINGULARITY OF FLEXIBLE MANIPULATOR

The coupling effect of the flexible joint and the flexible link on the dynamic singularity of the flexible manipulator is addressed. Firstly, the dynamic equations of a flexible manipulator with a flexible joint and a flexible link are derived. Secondly, the relationship and property between the flexible joint and the flexible link are analyzed. It shows that the flexible joint＇s amplitude will increase abruptly, thereby the dynamic singularity occurs if the frequency of a flexible joint is near or equal to some natural frequency of a flexible link. Finally, some numerical simulations which will verify the correctness of the theoretical analysis, are carded out. The results are fundamental for the design of a flexible manipulator and for the avoidance of the dynamic singularity.

Fuzzy Torque Control of the Bionic Flexible Manipulator Actuated by Pneumatic Muscle Actuators

A bionic flexible manipulator driven by pneumatic muscle actuator(PMA)can better reflect the flexibility of the mechanism.Current research on PMA mainly focuses on the modeling and control strategy of the pneumatic manipulator system.Compared with traditional electro-hydraulic actuators,the structure of PMA is simple but possesses strong nonlinearity and flexibility,which leads to the difficulty in improving the control accuracy.In this paper,the configuration design of a bionic flexible manipulator is performed by human physiological map,the kinematic model of the mechanism is established,and the dynamics is analyzed by Lagrange method.A fuzzy torque control algorithm is designed based on the computed torque method,where the fuzzy control theory is applied.The hardware experimental system is established.Through the co-simulation contrast test on MATLAB and ADAMS,it is found that the fuzzy torque control algorithm has better tracking performance and higher tracking accuracy than the computed torque method,and is applied to the entity control test.The experimental results show that the fuzzy torque algorithm can better control the trajectory tracking movement of the bionic flexible manipulator.This research proposes a fuzzy torque control algorithm which can compensate the error more effectively,and possesses the preferred trajectory tracking performance.

Extremum response surface method of reliability analysis on two-link flexible robot manipulator

In order to present a new method for analyzing the reliability of a two-link flexible robot manipulator,Lagrange dynamics differential equations of the two-link flexible robot manipulator were established by using the integrated modal method and the multi-body system dynamics method.By using the Monte Carlo method,the random sample values of the dynamic parameters were obtained and Lagrange dynamics differential equations were solved for each random sample value which revealed their displacement,speed and acceleration.On this basis,dynamic stresses and deformations were obtained.By taking the maximum values of the stresses and the deformations as output responses and the random sample values of dynamic parameters as input quantities,extremum response surface functions were established.A number of random samples were then obtained by using the Monte Carlo method and then the reliability was analyzed by using the extremum response surface method.The results show that the extremum response surface method is an efficient and fast reliability analysis method with high-accuracy for the two-link flexible robot manipulator.

On Frequency Sensitivity and Mode Orthogonality of Flexible Robotic Manipulators

This paper presents sensitivity analysis of vibration frequencies of flexible manipulators with respect to variations of systems parameters such as rotational inertia of hub, and mass, moment, and side of tip load. Both Euler-Bernoulli and Timoshenko dynamical models of flexible manipulators are discussed. By using variational method, sensitivity indices are obtained with explicit expressions for measuring the sensitivity of frequencies. Based on variational formulations, a novel method for deriving the orthogonal relations among vibration modal shape functions of flexible manipulators is introduced. With this method, the orthogonal relations can be derived easily without invoking the tedious process of differentiation and integration by part, as commonly used in their derivation. © 2014 Chinese Association of Automation.

Adaptive Fuzzy Backstepping Tracking Control for Flexible Robotic Manipulator

In this paper,an adaptive fuzzy state feedback control method is proposed for the single-link robotic manipulator system.The considered system contains unknown nonlinearfunction and actuator saturation.Fuzzy logic systems(FLSs)and a smooth function are used to approximate the unknownnonlinearities and the actuator saturation,respectively.By com-bining the command-filter technique with the backsteppingdesign algorithm,a novel adaptive fuuzy tracking backsteppingcontrol method is developed.It is proved that the adaptive fuuzycontrol scheme can guarantee that all the variables in the closed-loop system are bounded,and the system output can track thegiven reference signal as close as possible.Simulation results areprovided to illustrate the effectiveness of the proposed approach.

Dynamic modeling and analysis of 3-■RS parallel manipulator with flexible links

The dynamic modeling and solution of the 3-RRS spatial parallel manipulators with flexible links were investigated. Firstly, a new model of spatial flexible beam element was proposed, and the dynamic equations of elements and branches of the parallel manipulator were derived. Secondly, according to the kinematic coupling relationship between the moving platform and flexible links, the kinematic constraints of the flexible parallel manipulator were proposed. Thirdly, using the kinematic constraint equations and dynamic model of the moving platform, the overall system dynamic equations of the parallel manipulator were obtained by assembling the dynamic equations of branches. FtLrthermore, a few commonly used effective solutions of second-order differential equation system with variable coefficients were discussed. Newmark numerical method was used to solve the dynamic equations of the flexible parallel manipulator. Finally, the dynamic responses of the moving platform and driving torques of the 3-RRS parallel mechanism with flexible links were analyzed through numerical simulation. The results provide important information for analysis of dynamic performance, dynamics optimization design, dynamic simulation and control of the 3-RRS flexible parallel manipulator.

Rotation Angle Control Strategy for Telescopic Flexible Manipulator Based on a Combination of Fuzzy Adjustment and RBF Neural Network

The length of fexible manipulators with a telescopic arm alters during movement.The dynamic parameters of telescopic fexible manipulators exhibit signifcant time-varying characteristics owing to variations in length.With an increase in the manipulators’length,the nonlinear terms caused by fexibility in the manipulators’dynamic equations cannot be ignored.The time-varying characteristics and nonlinear terms of telescopic fexible manipulators cause fuctuations in rotation angles,which afect the operation accuracy of end-efectors.In this study,a control strategy based on a combination of fuzzy adjustment and an RBF neural network is utilized to improve the control accuracy of fexible telescopic manipulators.First,the dynamic equation of the manipulators is established using the assumed mode method and Lagrange’s principle,and the infuence of nonlinear terms is analyzed.Subsequently,a combined control strategy is proposed to suppress the fuctuation of the rotation angle in telescopic fexible manipulators.The variation ranges of the feedforward PD controller parameters are determined by the pole placement strategy and length of the manipulators.Fuzzy rules are utilized to adjust the controller parameters in real-time.The RBF neural network is utilized to identify and compensate the uncertain part of the dynamic model of the fexible manipulators.The uncertain part comprises time-varying parameters and nonlinear terms.Finally,numerical simulations and prototype experiments prove the efectiveness of the combined control strategy.The results prove that the proposed control strategy has a smaller standard deviation of errors.Therefore,the combined control strategy is more suitable for telescopic fexible manipulators,which can efectively improve the control accuracy of rotation angles.

Active Control of Elastodynamic Response of Flexible Redundant Robot Manipulators

This paper presents an analytical investigation into activevibration control of flexible redundant robot manipulators featuringpiezoelectric actuators and strain gage sensors. The state-sp- aceexpression of the discrete time-varying dynamic system is developedfirstly. The LQR optimal control law is presented based upon thediscrete Minimum Principle. Moreover, an approximate method isproposed for estimating the state information of the system. Finally,a planar 3R flexible redundant manipulator is utilized as anillustration example. The simulation results show that the dy- namicperformance of the manipulator has been improved significantly.

Smart Material Based Complex Mode Active Control of Flexible Manipulators with Kinematic Redundancy

An active control methodology is presented for suppressing the vibratoryresponse of flexible redundant manipulators with bonded piezoceramic actuators and strain gagesensors. Firstly, the dynamic equation of the manipulator is decoupled by means of the complex modetheory and the state-space expression of the controlled system is developed. Secondly, a continuouslinear quadratic regulator (LQR) state feedback controller is designed based on the minimumprinciple. Thirdly, a full-order Luenberger state observer featuring an assigned degree of stabilityis determined via the duality between control and estimation. Finally, a numerical simulation iscarried out on a planar 3R flexible redundant manipulator. The simulation results reveal that thedynamic performance of the system is improved rapidly and significantly.

Recursive Lagrangian dynamic modeling and simulation of multi-link spatial flexible manipulator arms

The dynamics for multi-link spatial flexible manipulator arms consisting of n links and n rotary joints is investigated. Kinematics of both rotary-joint motion and link deformation is described by 4 - 4 homogenous transformation matrices, and the Lagrangian equations are used to derive the governing equations of motion of the system. In the modeling the recursive strategy for kinematics is adopted to improve the computational efficiency. Both the bending and torsional flexibility of the link are taken into account. Based on the present method a general-purpose software package for dynamic simulation is developed. Dynamic simulation of a spatial flexible manipulator arm is given as an example to validate the algorithm.

Modeling and controlling of a flexible hydraulic manipulator

A mathematical model was developed combining the dynamics of an Euler-Bernoulli beam, described by the assumed-mode method and hydraulic circuit dynamics. Only one matrix, termed drive Jacobian, was needed in the modeling of interaction between hydraulic circuit and flexible manipulator mechanism. Furthermore, a new robust controller based on mentioned above dynamic model was also considered to regulate both flexural vibrations and rigid body motion. The proposed controller combined sliding mode and backstepping techniques to deal with the nonlinear system with uncertainties. The sliding mode control was used to achieve an asymptotic joint angle and vibration regulation by providing a virtual force while the backstepping technique was used to regulate the spool position of a hydraulic valve to provide the required control force. Simulation results are presented to show the stabilizing effect and robustness of this control strategy.

Adaptive Control of Flexible Redundant Manipulators Using Neural Networks

An investigation on the neural networks based active vibration control of flexible redundant manipulators was conducted. The smart links of the manipulator were synthesized with the flexible links to which were attached piezoceramic actuators and strain gauge sensors. A nonlinear adaptive control strategy named neural networks based indirect adaptive control (NNIAC) was employed to improve the dynamic performance of the manipulator. The mathematical model of the 4-layered dynamic recurrent neural networks (DRNN) was introduced. The neuro-identifier and the neuro-controller featuring the DRNN topology were designed off line so as to enhance the initial robustness of the NNIAC. By adjusting the neuro-identifier and the neuro-controller alternatively, the manipulator was controlled on line for achieving the desired dynamic performance. Finally, a planar 3R redundant manipulator with one smart link was utilized as an illustrative example. The simulation results proved the validity of the control strategy.

Adaptive nonlinear model predictive control design of a flexible-link manipulator with uncertain parameters

This paper presents a novel adaptive nonlinear model predictive control design for trajectory tracking of flexible-link manipulators consisting of feedback linearization, linear model predictive control, and unscented Kalman filtering. Reducing the nonlinear system to a linear system by feedback linearization simplifies the optimization problem of the model predictive controller significantly, which, however, is no longer linear in the presence of parameter uncertainties and can potentially lead to an undesired dynamical behaviour. An unscented Kalman filter is used to approximate the dynamics of the prediction model by an online parameter estimation, which leads to an adaptation of the optimization problem in each time step and thus to a better prediction and an improved input action. Finally, a detailed fuzzy-arithmetic analysis is performed in order to quantify the effect of the uncertainties on the control structure and to derive robustness assessments. The control structure is applied to a serial manipulator with two flexible links containing uncertain model parameters and acting in three-dimensional space.