Two-link Flexible Manipulator Research Articles

Boundary Torque Control of a Flexible Two-Link Manipulator and Its Experimental Investigation

This article focuses on a two-dimensional flexible two-link manipulator that moves in a plane. The two links are simplified into Euler-Bernoulli beams and the coupled partial differential equation-ordinary differential equation dynamic model is established via Hamiltonian's principle. Two torque controllers acting on two motors, respectively, are designed for the simultaneous angular position control of two motors and suppression of the elastic vibrations of the links. The Lyapunov direct method and extended LaSalle invariance principle are used to prove the asymptotic stability of the system. In addition, numerical simulations illustrate the correctness and reasonability of the theoretical proof for the stability analysis and boundary control design, and the experimental verification on the platform of the Quanser laboratory also reaches the same conclusion.

Reliability optimization of two-link flexible manipulator

To address the low computational efficiency and accuracy for reliability optimization of flexible mechanisms, the mean-probability decomposition-coordination-based extreme support vector machine regression (MPDC-ESVR) method based on the dynamics and uncertainty is proposed. Firstly, a dynamical model is built to calculate the maximum deformation. Then, the ESVR is used as a surrogate model to study the reliability of the flexible mechanisms. Finally, the MPDC are adopted to optimize the weight of the flexible mechanisms considering multiple failure modes. It is proved that the computational efficiency and accuracy of the present methodology are superior to those of Monte Carlo simulation (MCS) and quadratic polynomial-Monte Carlo simulation (QP-MCS) through exemplification with a two-link flexible manipulator. The results indicate the two-link flexible manipulator optimized by current MPDC is lighter than that by the equal distribution probabilistic method and the original manipulator, which is essential for low cost-effectiveness without compromise to safety.

Fault-Tolerant Optimal Control for Discrete-Time Nonlinear System Subjected to Input Saturation: A Dynamic Event-Triggered Approach.

This paper investigates the dynamic event-triggered fault-tolerant optimal control strategy for a class of output feedback nonlinear discrete-time systems subject to actuator faults and input saturations. To save the communication resources between the sensor and the controller, the so-called dynamic event-triggered mechanism is adopted to schedule the measurement signal. A neural network-based observer is first designed to provide both the system states and fault information. Then, with consideration of the actuator saturation phenomenon, the adaptive dynamic programming (ADP) algorithm is designed based on the estimates provided by the observer. To reduce the computational burden, the optimal control strategy is implemented via the single network adaptive critic architecture. The sufficient conditions are provided to guarantee the boundedness of the overall closed-loop systems. Finally, the numerical simulations on a two-link flexible manipulator system are provided to verify the validity of the proposed control strategy.

Vibration Control of a Constrained Two-Link Flexible Robotic Manipulator With Fixed-Time Convergence.

With the more extensive application of flexible robots, the expectation for flexible manipulators is also increasing rapidly. However, the fast convergence will cause the increase of vibration amplitude to some extent, and it is difficult to obtain vibration suppression and satisfactory transient performance at the same time. In order to deal with the problem, a fixed-time learning control method is proposed to realize the fast convergence. The constraint on system outputs, system uncertainty, and input saturation is addressed under the fixed-time convergence framework. A novel adaptive law for neural networks is integrated into the backstepping method, which enhances the learning rate of neural networks. The imposed constraint on the vibration amplitude is guaranteed by using the barrier Lyapunov function (BLF). Moreover, the chattering problem is addressed by approximating the sign function smoothly. In the end, some simulations have been carried out to show the effectiveness of the proposed method.

Design and Analysis of Two-Link Discrete Flexible Manipulator

Proposed two-link flexible manipulators suit the requirement of larger work volume than the traditional flexible manipulators and handle high payloads equal to that of rigid manipulators. The simulation was performed on the Computer-Aided Design (CAD) model of the Motoman HC-10DT, a Human-Collaborative robot. During the analysis, one link of the manipulator was modified as a flexible manipulator for which static and modal analysis was done and compared the results with the actual link of the robot to validate the proposed design. The kinematic analysis was also done to find the reach of the modified robot. Total deformation on both the flexible manipulator and the actual link of the robot was 0.2mm but the maximum von Mises stress acting on the flexible manipulator was 2.97% lesser than that of the rigid link of the robot. Eventually, the safety factor of the flexible manipulator was higher compared to the rigid link. The factor of safety of the upper link is 1.41 and the lower link is 1.51 whereas the actual link of the robot has the safety factor of 1.30.

Model-Free Control of Flexible Manipulator Based on Intrinsic Design

In this article, a model-free controller is proposed to suppress residual vibration caused by the linkage flexibility after the positioning process. The controller is designed to release the potential energy rapidly by repeating a sequence comprising two steps. In the first step, the controller acts as a damper to absorb the deformation energy, whereas in the second step, neural network control is introduced for the purpose of returning to the target position smoothly. The controller is simple, and the only required feedback signal is from the motor encoder. The position error is proved to converge to zero within a small neighborhood through Lyapunov stability analysis. The effectiveness of the controller is tested in three applications, an experiment study on a single-link flexible manipulator in horizontal plane and two simulation studies on a two-link flexible manipulator in horizontal plane and vertical plane, respectively. The settling time is decreased and energy efficiency is improved in all the three applications comparing with other controllers.

Transient Reliability Evaluation Approach of Flexible Mechanism with GA-Extremum Neural Network

Efficient analytical model directly enhances the reliability evaluation of flexible mechanism under operation. In this paper, genetic algorithm-based extremum neural network (GA-ENN) is developed as reliability model by introducing the thoughts of extremum and genetic algorithm (GA) into artificial neural network to address the key problems comprising transient response and modeling precision in the dynamic reliability analysis of flexible mechanism in a time domain. The thought of extremum is adopted to simplify transient response process as one extremum value to the difficulty of dynamic reliability analysis induced by transient process response, and the GA is applied to find the optimal model parameters of reliability model. The dynamic reliability analysis of two-link flexible robot manipulator (TFRM) (a typical flexible mechanism) was implemented based on the GA-ENN method, regarding the input random variables of material density, elastic modulus, section sizes of components, and the output response of components’ deformations. From the analysis, the comprehensive reliability of the TFRM is 0.951 when the allowable deformation is 1.8 × 10−2 m. Besides, the maximum deformations of the two components follow the normal distributions with the means of 1.45 × 10−2 m and 1.69 × 10−2 m and the standard variances of 6.77 × 10−4 m and 4.08 × 10−4 m, respectively. Through the comparison of methods, it is illustrated that the developed GA-ENN improves the simulation efficiency and modeling accuracy by overcoming the problems of transient response and model parameter optimization in the dynamic reliability analysis of TFRM.

Enhanced network learning model with intelligent operator for the motion reliability evaluation of flexible mechanism

The evaluation of flexible mechanism involving multi-body dynamics with high nonlinearity and transients urgently requires an efficient evaluation method to enhance its reliability and safety. In this work, an enhanced network learning method (ENLM) is proposed to improve the modeling precision and simulation efficiency in flexible mechanism reliability evaluation, by introducing generalized regression neural network (GRNN) and multi-population genetic algorithm (MPGA) into extremum response surface method (ERSM). In the ENLM modeling, the ERSM is adopted to reasonably handle transients (time-varying) problem in motion reliability analysis by considering one extreme value in whole response process; the GRNN is applied to address high-nonlinearity in surrogate modeling; the MPGA is utilized to find the optimal model parameters in ENLM modeling. In respect of the developed ENLM, the motion reliability of two-link flexible robot manipulator (TFRM) was evaluated, with regard to the related input random parameters to material density, elastic modulus, section sizes, and deformations of components. In term of this study, it is illustrated that (i) the comprehensive reliability of flexible robot manipulator is 0.951 when the allowable deformation is 1.8×10−2 m; (ii) the maximum deformations of member-1 and member-2 obey normal distributions with the means of 1.45×10−2 m and 1.69×10−2 m as well as the standard variances of 6.77×10−4 m and 4.08×10−4 m, respectively. The comparison of methods demonstrates that the ENLM improves the modeling precision by 3.29% and reduces the simulation efficiency by 1.19 s under 10000 simulations, and the strengths of the ENLM with high modeling precision and high simulation efficiency become more obvious with the increase of simulations. The efforts of this study provide a learning-based reliability analysis way (i.e., ENLM) for the motion reliability design optimization of flexible mechanism and enrich mechanical reliability theory.

Adaptive global super-twisting sliding mode control-based filter for trajectory synchronisation of two-link flexible manipulators

A projective synchronisation strategy is designed in this paper to synchronise a master manipulator having 12 states modelled using the assumed modes method and the slave manipulator with 8 states modelled using the lumped parameter method. The first objective is to design an adaptive SMC-based filter and the second objective is to design an adaptive global super-twisting sliding mode-based filter algorithm. In the first controller, a filter is designed to estimate the angular velocity errors of the master manipulator then for the second, a filter is designed to estimate the angular and link deflection velocity errors of the slave manipulator. Both the controller gains for the switching laws of the SMC are simultaneously updated online and super-twisting algorithm is designed to reduce the chattering problem. This approach is designed to reduce the time of reaching phase and to increase the robustness. The effectiveness and performances of the proposed controller are validated in MATLAB simulation environment and compared with a latest reported adaptive global SMC controller. The proposed scheme of synchronisation is found to be better than the existing controller.

Influences of generic payload and constraint force on modal analysis and dynamic responses of flexible manipulator

This article presents the dynamic modeling and nonlinear analysis of two-link flexible manipulator with generic payload whose center of gravity is different than the point of attachment with the link. The manipulator is driven by harmonic joint motions and subjected to a constraint force at the terminal end due to its interaction with working environment. Hamilton’s approach is adopted to dynamically model the multi-link manipulator for longitudinal and transverse vibrations incorporating the nonlinearities associated with axial stretching. The resulting set of eigenfrequency equations are solved numerically with subsequent generation of eigenspectrums. Further, this paper investigates the resonant behavior of manipulator links for the subharmonic and primary resonance conditions due to end follower force and revolute joint motions, respectively. The resonant responses show the jump phenomenon and existence of multi-valued solutions at pitchfork and saddle-node bifurcation points. The numerical and graphical results thus obtained, clearly indicate the significant influence of variation of system configurations and generic payload on eigencharacteristics and nonlinear responses, and hence must be given consideration during dynamic modeling of a manipulator in order to attenuate undesirable vibrations.

Vision‐based tip position tracking control of two‐link flexible manipulator

Owing to the non-collocation of actuators and sensors in a flexible-link manipulator (FLM) it becomes difficult to achieve accurate tip position tracking. To resolve this issue, a vision sensor is used for direct measurement of the tip position instead of employing the traditional mechanical sensors. Among the different visual servoing (VS) control schemes, image-based VS (IBVS) is more effective. However, there are many challenges in the IBVS scheme such as singularities in the interaction matrix and local minima in trajectories that affect the system performance in real-time applications. In this study, the moment-based new visual feature is selected to address the aforesaid issues that arise in the IBVS scheme. Furthermore, a new two-time scale IBVS controller is developed for addressing the tip-tracking control problem of the two-link flexible manipulator (TLFM). In the proposed control scheme, the dynamics of the FLM is decomposed into two-time scale models, namely a slow subsystem and a fast subsystem. The performance and robustness of the proposed new two-time scale IBVS controller for TLFM are verified by pursuing simulation studies. It is observed from the obtained results that the proposed controller effectively stabilises the oscillatory dynamics and tracks the reference trajectory accurately.

Payload parameter identification method of flexible space manipulator

Purpose When a manipulator captures an unknown space object, inertia parameters of endpoint payload should be timely obtained to handle possible unexpected parameter variations and monitor the system’s operating conditions. Therefore, this study aims to present an identification method for estimating the inertia parameter of the payload carried by a flexible two-link space manipulator. Design/methodology/approach The original nonlinear dynamics model of the manipulator is linearized at a selected working point. Subsequently, the system modal frequencies with and without payload are determined using the subspace identification algorithm, and the difference of these frequencies is computed. Furthermore, by adjusting the structural configuration of the manipulator, multiple sets of frequency differences are obtained. Therefore, the inertia parameters of the payload, i.e. the mass and the moment of inertia, can be derived from the frequency differences by solving a least-squares problem. Findings The proposed method can effectively estimate the payload parameters and has satisfactory identification accuracy. Practical implications The approach’s implementation provides a practical reference for determining inertia parameters of an unknown space target in the capture process. Originality/value The study proposes a novel method for identifying the inertia parameters of the payload of a flexible two-link space manipulator using the estimated system frequencies.

Minimum-time Trajectory Planning for Residual Vibration Suppression of Flexible Manipulator Carrying a Payload

For the purpose of eliminating residual vibration of a two-link flexible manipulator as well as minimizing time consumption, a scheme of multi-objective trajectory planning in joint space is proposed in this paper. Piecewise polynomial is applied to generate a smooth joint trajectory. Lagrangian approach and the assumed modes method is used to derive motion equations of FMs. Finally, Multi-objective particle swarm optimization (MOPSO) algorithm is implemented to solve time of each polynomial. The effectiveness of proposed algorithm is demonstrated by simulation results.

Adaptive Control of a Two-Link Flexible Manipulator Using a Type-2 Neural Fuzzy System

This paper presents a simple novel intelligent control scheme. The devised control scheme is a Takagi Sugeno Kang (TSK)- based type-2 neural fuzzy system (NFS) with a self-tuning mechanism optimized via a conjugate gradient (CG) method. Defuzzification phase of the NFS comprises T-norms rather than the conventional product–sum combination. The proposed control scheme is incorporated with a two-link flexible manipulator (TLFM), which belongs to the class of multi-body discrete/distributed, nonlinear, infinite-dimensional and highly coupled systems. The finite-dimensional model is acquired by using an assumed mode method (AMM). The truncated model has uncertainties, which makes it a difficult control problem. The control objective is to accomplish angular maneuvering of the TLFM links while regulating their intrinsic fluctuations. For an extensive analysis, the proposed control scheme is compared with a TSK model-based type-1 NFS and an adaptive proportional integral derivative (APID) control scheme. The simulation results demonstrate that the proposed control scheme exhibits better position tracking and vibration regulation capabilities compared to the other intelligent control schemes.

Boundary Output Feedback Control for a Flexible Two-Link Manipulator System With High-Gain Observers

This brief focuses on the boundary output feedback control for a flexible two-link manipulator (FTLM) system with input saturation. For the purpose of suppressing elastic vibration and regulating manipulator’s angular position, boundary output feedback controllers (BOFCs) are proposed. When the system states cannot be directly measured, a set of high-gain observers are designed to reproduce these immeasurable system states. Simultaneously, in order to solve the problem of excessive control input caused by high-gain observers, two auxiliary systems are designed to compensate for the input saturation. The stability of the FTLM system is obtained through mathematical analysis. Furthermore, the effectiveness of the designed controllers is proved by numerical simulations.

Intelligent Control of Flexible Joint Manipulator Based on Dynamic Pattern Recognition

With the rapid development of intelligent manufacturing and Internet technology, the industrial system has entered a new stage of development. As an indispensable carrier for intelligent manufacturing and industrial development, robots are expanding their applications. Among them, the flexible mechanical arm has the advantages of light weight, low energy consumption and low inertia compared with the bulky rigid mechanical arm, and has been increasingly valued. The flexible manipulator is a very complex dynamic system whose dynamic equations are characterized by nonlinearity, strong coupling and time-varying. Therefore, this paper uses the most common and effective method to establish the dynamic model of the flexible manipulator using the Lagrange equation. Due to the uncertain system parameters, lack of control of the trajectory and the influence of load changes and external disturbances, the flexible manipulator has great uncertainty in its control process, and the traditional control methods have not very good control effect. Based on this, this paper proposes a combination of dynamic pattern recognition theory and flexible joint manipulator intelligent control method for the two-link flexible manipulator, and uses the new GA-RBF neural network closed-loop adaptive control method to achieve high precision. Trajectory tracking ensures stability in a shorter time. The simulation results show that the intelligent joint control method based on dynamic pattern recognition has better trajectory tracking and autonomous fast recognition dynamic mode.

Three-dimensional modeling and input saturation control for a two-link flexible manipulator based on infinite dimensional model

In this paper, the modeling and controlling problem is studied for a two-link rigid-flexible manipulator in three-dimensional (3D) space under input saturation. The dynamics of the 3D manipulator is first derived in infinite dimension model, which is represented by partial differential equations (PDEs). The controller can achieve joint angle control and vibration suppression control in the presence of input constraint. The stability analysis of the closed-loop system is given based on LaSalle’s Invariance Principle. Numerical simulations illustrate the effectiveness of the proposed controller.

Use of memristive chaotic signal as a desired trajectory for a two-link flexible manipulator using contraction theory based on a composite control technique

Flexible manipulators are being considered as bench mark control problem in the field of nonlinear dynamics. Many of their inherent advantages create challenges while dealing with the dynamics. Tracking control and vibration suppression are two main control problems considered. In this paper a composite controller is designed for the memristive chaotic system signal as trajectory tracking control of a two-link flexible robot manipulator. The dynamics of the flexible manipulator is modelled by using assumed modes method and divided into two subsystems using the singular perturbation technique. The subsystems are called as the slow subsystem involving rigid dynamics of the manipulator and the fast sub-system which incorporates flexible dynamics of the manipulator. Separate control techniques are designed for each subsystem. Contraction theory based controllers are designed for the slow sub-system and fast subsystem for fast trajectory tracking of signal of a memristive chaotic system and quick suppression of the link deflections. The simulation results confirm the better performances of the proposed composite technique.

Dynamic modeling and extended bifurcation analysis of flexible-link manipulator

In this article, the nonlinear dynamic analysis of a flexible-link manipulator is presented. Especially, the possibility of chaos occurrence in the system dynamic model is investigated. Upon the occurrence of chaos, the system dynamical behavior becomes unpredictable which in turn brings about uncertainty and irregularity in the system motion. The importance of this investigation is pronounced in similar systems such as double pendulum and single-link flexible manipulator. What makes this study distinct from previous ones is the increase in the number of links as well as the changing the bifurcation parameters from system mechanical parameters to force and torque inputs. To this aim, the motion equations of the N-link robot, which are derived with the aid of the recursive Gibbs-Appell formulation and the assumed modes method, are used. In the end, the equations of motion are developed for a two-link flexible manipulator, and its nonlinear dynamical behavior is analyzed via numerical integration of discrete equations. The results are presented in the form of bifurcation diagrams (for variation of torque amplitude), time histories, phase-plane portraits, Poincaré sections, and fast Fourier transforms. The outcomes indicate that when there is no offset, the decrease in damping results in chaotic generalized modal coordinates. In addition, as the excitation frequency decreases from 2π to π, a limiting amplitude is created at 0.35 before which the behavior of generalized rigid and modal coordinates is different, while this behavior has more similarity after this point. An experimental setup is also used to check the torques as the system input.

Polyvinylidene fluoride/sulfonated graphene oxide blend membrane coated\xa0with polypyrrole/platinum electrode for ionic polymer metal composite actuator applications

A polyvinylidene fluoride, sulfonated graphene oxide composite membrane coated with polypyrrole (Ppy) and platinum metal (Pt) was fabricated. The Fourier-transform infrared (FTIR) spectroscopic analysis was done to analyze the functional groups present in the composite material. Deposition of PPy/Pt electrode and surface morphology of PVDF/SGO/Pt/PPy was confirmed by scanning electron microscopic (SEM) images. The capacity of ion exchange and proton conductivity (PC) of PVDF/SGO/Pt/PPy were 1.4 meq g−1 of dry ion exchanger and 4.251 × 10−2 S cm−1, respectively. A two-link flexible manipulator based on the fabricated ionic polymer metal composite (IPMC) membranes was also developed where the electromechanical behaviour of a polymer-based actuator provides an important step in robotics applications.