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.

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.

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.

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.

Dynamic analysis of multi-link spatial flexible manipulator arms with dynamic stiffening effects

The dynamics for multi-link spatial flexible manipulator arms is investigated. The system considered here is an N-flexible-link manipulator driven by N DC-motors through N revolute flexiblejoints. The flexibility of each flexible joint is modeled as a linearly elastic torsional spring, and the mass of the joint is also considered. For the flexibility of the link, all of the stretching deformation, bending deformation and the torsional deformation are included. The complete governing equations of motion of the system are derived via the Lagrange equations. The nonlinear description of the deformation field of the flexible link is adopted in the dynamic modeling, and thus the dynamic stiffening effects are captured. Based on this model, a general-purpose software package for dynamic simulation of multi-link spatial flexible manipulator arms is developed. Several illustrative examples are given to validate the algorithm presented in this paper and to indicate that not only dynamic stiffening effects but also the flexibility of the structure has significant influence on the dynamic performance of the manipulator.

Finite-time State Feedback Stabilization Method for a Class of Flexible Manipulators

Aimed at the finite-time stabilization problem of a class of flexible manipulators,a finite-time state feedback stabilization controller was proposed in this paper.Firstly,the nonlinear model of flexible manipulators was transformed into linear system through the exact state feedback linearization,and then using the finite time stabilization control method of the linear system,a finite-time state feedback stabilization controller was designed for the flexible manipulators.Furthermore,it was proved that all the states of flexible manipulators could be stabilized to equilibrium in finite-time under the proposed controller.The simulation results show that the performance of the flexible manipulators under the proposed finite-time state feedback controller is better than the traditional state-feedback controller.The proposed finite-time stabilization controller can improve the performance of the flexible manipulators.

DYNAMICS OF A ROTATING FLEXIBLE MANIPULATOR WITH TIP LOAD

The dynamics of a flexible manipulator is investigated in this paper. From the point of view of dynamic balance, the motion equations of a rotating beam with tip load are established by us ing Hamilton' s principle. By taking into account the effects of dynamic stiffening and dynamic softening, the stability of the system is proved by employing Lyapunov' s approach. Furthermore, the method of power series is proposed to find the exact solution of the eigenvalue problem The effects of rotating speed and tip load on the vibration behavior of the flexible manipulator are shown in numerical results.

Dynamic modeling and RBF neural network compensation control for space flexible manipulator with an underactuated hand

In space operation,flexible manipulators and gripper mechanisms have been widely used because of light weight and flexibility.However,the vibration caused by slender structures in manipulators and the parameter perturbation caused by the uncertainty derived from grasping mass variation cannot be ignored.The existence of vibration and parameter perturbation makes the rotation control of flexible manipulators difficult,which seriously affects the operation accuracy of manipulators.What’s more,the complex dynamic coupling brings great challenges to the dynamics modeling and vibration analysis.To solve this problem,this paper takes the space flexible manipulator with an underactuated hand(SFMUH)as the research object.The dynamics model considering flexibility,multiple nonlinear elements and disturbance torque is established by the assumed modal method(AMM)and Hamilton’s principle.A dynamic modeling simplification method is proposed by analyzing the nonlinear terms.What’s more,a sliding mode control(SMC)method combined with the radial basis function(RBF)neural network compensation is proposed.Besides,the control law is designed using a saturation function in the control method to weaken the chatter phenomenon.With the help of neural networks to identify the uncertainty composition in the SFMUH,the tracking accuracy is improved.The results of ground control experiments verify the advantages of the control method for vibration suppression of the SFMUH.

Hybrid vibration isolation optimization of a flexible manipulator based on neural network agent model

Segmented Active Constrained Layer Damping(SACLD)is an intelligent vibration-damping structure,which could be applied to the sectors of aviation,aerospace,and transportation engineering to reduce the vibration of flexible structures.Moreover,machine learning technology is widely used in the engineering field because of its efficient multi-objective optimization.The dynamic simulation of a rotational segmental flexible manipulator system is presented,in which enhanced active constrained layer damping is carried out,and the neural network model of Genetic Algorithm-Back Propagation(GA-BP)algorithm is investigated.Vibration suppression and structural optimization of the SACLD manipulator model are studied based on vibration mode and damping prediction.The modal responses of the SACLD manipulator model at rest and rotation are obtained.In addition,the four model indices are optimized using the GA-BP neural network:axial incision size,axial incision position,circumferential incision size,and circumferential incision position.Finally,the best model for vibration suppression is obtained.

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.

Impact vibration reduction for flexible manipulators via controllable local degrees of freedom

When performing operation tasks, the interaction between a flexible manipulator and a grasped object usually results in an impact. In this paper, a new way is suggested to alleviate impact vibration of a flexible manipulator via its structural characteristic when capturing a moving object. Controllable local degrees of freedom are introduced to the topological structure of the flexible manipulator, and used as an effective tool to combat impact vibration through dynamic coupling. A corresponding method is put forward to reduce impact vibration responses of the flexible manip- ulator via the controllable local degrees of freedom. By planning motion of the controllable local degrees of freedom, appropriate control force can be constructed to increase the modal damping and stiffness and eliminate the exciting force simultaneously, thereby reducing impact vibration responses of the flexible manipulator. Simulations are conducted and results are shown to prove the presented method.

Parameter optimization of controllable local degree of freedom for reducing vibration of flexible manipulator

Parameter optimization of the controllable local degree of freedom is studied for reducing vibration of the flexible manipulator at the lowest possible cost. The controllable local degrees of freedom are suggested and introduced to the topological structure of the flexible manipulator, and used as an effective way to alleviate vibration through dynamic coupling. Parameters introduced by the controllable local degrees of freedom are analyzed and their influences on vibration reduction are investigated. A strategy to optimize these parameters is put forward and the corresponding optimization method is suggested based on Particle Swarm Optimization （PSO）. Simulations are conducted and results of case studies confirm that the proposed optimization method is effective in reducing vibration of the flexible manipulator at the lowest possible cost.

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.

Adaptive Fuzzy Control of Constrained Flexible-Link Manipulators

In this paper, a novel adaptive fuzzy control scheme is presented. The controller is constructed by using a table lookup scheme and self tuning techniques, which includes the identification block, the fuzzification, the updating rule base, the defuzzification, and the crisp controller (sub controller), etc. The adaptive fuzzy controller is designed in detail by means of a triangular membership function and the center of gravity method. The control scheme addressed here is implemented to control the motion of the end effector of a two link constrained flexible manipulator. Computer simulation results show that the novel adaptive fuzzy control scheme works quite well.

Delayed feedback control experiments on some flexible structures

In recent decades,studies on delayed system dynamics have attracted increasing attention and advances have been achieved in stability,nonlinearity,delay identification, delay elimination and application.However,most of the existing work is on the theoretical basis and little is on the experiment.This paper presents our experimental studies on delayed feedback control conducted in recent years with the focus on the discussion of a DSP-based delayed experiment system.Some phenomena in our delay experiments are discussed and a few topics of interest for further research are brought forward.

OPTIMAL CONTROL OF THE FLEXI-BLE LINK MANIPULATOR WITH CONTROLLABLE LOCAL DEGREES OF FREEDOM

Although flexible manipulators own many potential advantages, one of their major disadvantages is the deterioration of the end-effector accuracy due to the flexibility. Therefore, how to reduce vibration is a significant problem. Inspired by the observation on the motion behaviors of animals, a new idea of decreasing motion deflection of the flexible manipulator is suggested. The concept of controllable local degrees of freedom is proposed and analyzed. By way of optimizing local motion provided by the controllable local degrees of freedom, the end-effector deflection of the flexible manipulator can be effectively decreased through dynamic coupling. The corresponding optimal method for vibration control of the flexible manipulator is put forward. The kinematic simulation is carried ant on a three-link flexible manipulator The corresponding results verify the feasibility of this method.

Integrated Optimal Model of Structure and Control of the Single Arm Manipulator

The integrated optimal design of mechanical and control system is discussed in terms of the performance requirement and configuration for the single arm flexible manipulator. By combination of dynamics of flexible structure and control theory, a PD feedback control system, which minimizes the settling time, has been designed. Then, the viable region of poles of the PD dosed-loop control system is decided according to overshoot and the settling time, and an integrated optimal model of structure and control of single arm manipulator is presented. Finally, the parameters of structure and control system are simultaneously optimized with respect to objective function induding the moment of inertia and the control effort of system.

Sliding Mode Control for Flexible-link Manipulators Based on Adaptive Neural Networks

This paper mainly focuses on designing a sliding mode boundary controller for a single flexible-link manipulator based on adaptive radial basis function （RBF） neural network. The flexible manipulator in this paper is considered to be an Euler-Bernoulli beam. We first obtain a partial differential equation （PDE） model of single-link flexible manipulator by using Hamiltons approach. To improve the control robustness, the system uncertainties including modeling uncertainties and external disturbances are compensated by an adaptive neural approximator. Then, a sliding mode control method is designed to drive the joint to a desired position and rapidly suppress vibration on the beam. The stability of the closed-loop system is validated by using Lyapunov＇s method based on infinite dimensional model, avoiding problems such as control spillovers caused by traditional finite dimensional truncated models. This novel controller only requires measuring the boundary information, which facilitates implementation in engineering practice. Favorable performance of the closed-loop system is demonstrated by numerical simulations.

Neuro-Sliding-Mode Control of Flexible-Link Manipulators Based on Singularly Perturbed Model

A neuro-sliding-mode control （NSMC） strategy was developed to handle the complex nonlinear dynamics and model uncertainties of flexible-link manipulators. A composite controller was designed based on a singularly perturbed model of flexible-link manipulators when the rigid motion and flexible motion are decoupled. The NSMC is employed to control the slow subsystem to track a desired trajectory with a tradi- tional sliding mode controller to stabilize the fast subsystem which represents the link vibrations. A stability analysis of the flexible modes is also given. Simulations confirm that the NSMC performs better than the tra- ditional sliding-mode control for controlling flexible-link manipulators. The control strategy not only gives good tracking performance for the joint angle, but also effectively suppresses endpoint vibrations. The simulations also show that the control strategy has a strong self-adaptive ability for controlling manipulators with different parameters.