Fuzzy Neural Network Control of a Flexible Robotic Manipulator Using Assumed Mode Method

PDE-Based Boundary Adaptive Consensus Control of Multiagent Systems With Input Constraints

The leader-follower adaptive consensus control problem is addressed for partial differential equations (PDEs) multiagent systems (MASs), and these agents are composed of flexible manipulator systems with input nonlinearity, boundary uncertainties, and time-varying disturbances. Because of the spatial variables in the model, the design of adaptive protocols is more difficult than that of ordinary differential equation (ODE) MASs. By designing the Lyapunov function, a novel distributed boundary control (BC) protocol is constructed, which not only ensures the consensus of angular positions but also suppresses the boundary vibration of each agent. The hybrid effects of dead zones and input saturation on flexible manipulator systems are addressed using the approximation properties of neural networks (NNs). In addition, the disturbance adaptive laws are proposed to provide a control solution for bounded and time-varying disturbances. Furthermore, by applying the Lyapunov stability theory, the uniformly bounded stability of the multiflexible manipulator can be ensured. Finally, the feasibility of the presented control approach is verified using numerical examples.

Bounded Antisynchronization of Multiple Neural Networks via Multilevel Hybrid Control

The bounded antisynchronization (AS) problem of multiple discrete-time neural networks (NNs) based on the fuzzy model is studied, in consideration of the differences in quantity and communication among different NN groups, the variabilities of dynamics, and communication topological affected by environments. To reduce the energy consumption of communication, a cluster pinning communication mechanism is proposed, and an impulsive observer is designed to estimate the state of target NN. Then, a multilevel hybrid controller based on the impulsive observer is built including the AS controller and the bounded synchronization (BS) controller. Sufficient conditions for bounded AS are obtained by analyzing the stability of the BS augmented error (BSAE) and the AS augmented error (ASAE) based on the fuzzy-based Lyapunov functional (FBLF). Finally, a numerical example and an application example are given to verify the validity of the obtained results.

Backstepping Technology-Based Adaptive Boundary ILC for an Input-Output-Constrained Flexible Beam

This article focuses on vibration suppression of an Euler-Bernoulli beam which is subject to external disturbance. By integrating backstepping technique, an adaptive boundary iterative learning control (ABILC) is put forward to suppressing vibration. The adaptive law is proposed for handing the parameter uncertainty and the iterative learning term is designed to deal with periodic disturbance. An auxiliary system is utilized to compensate the effect of input nonlinearity. In addition, a barrier Lyapunov function is adopted to deal with asymmetric output constraint. With the proposed control strategy, the stability of the closed-loop system is proven based on rigorous Lyapunov analysis. In the end, the effectiveness of the proposed control is illustrated through numerical simulation results.

Broad learning control of a two-link flexible manipulator with prescribed performance and actuator faults

In this paper, we present a broad learning control method for a two-link flexible manipulator with prescribed performance (PP) and actuator faults. The trajectory tracking errors are processed through two consecutive error transformations to achieve the constraints in terms of the overshoot, transient error, and steady-state error. And the barrier Lyapunov function is employed to implement constraints on the transition state variable. Then, the improved radial basis function neural networks combined with broad learning theory are constructed to approximate the unknown model dynamics of flexible robotic manipulator. The proposed fault-tolerant PP control cannot only ensure tracking errors converge into a small region near zero within the preset finite time but also address the problem caused by actuator faults. All the closed-loop error signals are uniformly ultimately bounded via the Lyapunov stability theory. Finally, the feasibility of the proposed control is verified by the simulation results.

Motion Planning and Adaptive Neural Tracking Control of an Uncertain Two-Link Rigid-Flexible Manipulator With Vibration Amplitude Constraint

This article deals with an uncertain two-link rigid-flexible manipulator with vibration amplitude constraint, intending to achieve its position control via motion planning and adaptive tracking approach. In motion planning, the motion trajectories for the two links of the manipulator are planned based on virtual damping and online trajectories correction techniques. The planned trajectories can not only guarantee that the two links can reach their desired angles, but also have the ability to suppress vibration, which can be adjusted to meet the vibration amplitude constraint by limiting the parameters of the planned trajectories. Then, the adaptive tracking controller is designed using the radial basis function neural network and the sliding mode control technique. The developed controller makes the two links of the manipulator track the planned trajectories under the uncertainties including unmodeled dynamics, parameter perturbations, and persistent external disturbances acting on the joint motors. The simulation results verify the effectiveness of the proposed control strategy and also demonstrate the superior performance of the motion planning and the tracking controller.

Tip Position Control and Vibration Suppression of a Planar Two-Link Rigid-Flexible Underactuated Manipulator

When a flexible link manipulator lacks a joint motor, how to use the remaining motors to achieve the control objective is a challenge, and the research in this direction is limited. This article presents a tip position control and vibration suppression approach for a planar two-link rigid-flexible (TLRF) underactuated manipulator with a passive first joint. First, we establish a dynamic model of the system by using the assumed mode method (AMM) and the Lagrangian modeling method. Then, we obtain the dynamic coupling relationship of the two links based on the dynamic model. According to this dynamic coupling relationship, we find that the passive rigid link can be controlled indirectly by controlling the active flexible link. Thus, we calculate the target angles of the two links by using the inverse kinematic method and design a controller for the active flexible link to stabilize it at its target angle and to suppress its vibration. Next, we optimize the parameters of this controller by using the genetic algorithm (GA). GA helps us simultaneously stabilize the passive rigid link at its target angle while realizing the control objective of the active flexible link. The simulation results demonstrate the effectiveness of the proposed control approach.

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.

Hybrid Force and Motion Control of a Three-Dimensional Flexible Robot Considering Measurement Noises

This work addresses the end-effector trajectory-tracking force and motion control of a three-dimensional three-link robot considering measurement noises. The last two links of the manipulator are considered as structurally flexible. An absolute coordinate approach is used while obtaining the dynamic equations to avoid complex dynamic equations. In this approach, each link is modeled as if there is no connection between the links. Then, joint connections are expressed as constraint equations. After that, these constraint equations are used in dynamic equations to decrease the number of equations. Then, the resulting dynamic equations are transformed into a form which is suitable for controller design. Furthermore, the dynamic equations are divided as pseudostatic equilibrium and deviation equations. The control torques resulting from the pseudostatic equilibrium and the elastic deflections are obtained easily as the solution of algebraic equations. On the other hand, the control torques corresponding to the deviations are obtained without any linearization. Encoders, strain gauges, position sensors and force and moment sensors are required for measurements. Low pass filters are considered for the sensors. For the crossover frequencies of the sensors, low and high values are chosen to observe the filtering effect on the robot output.

Prescribed-Time Convergent Adaptive ZNN for Time-Varying Matrix Inversion under Harmonic Noise

Harmonic noises widely exist in industrial fields and always affect the computational accuracy of neural network models. The existing original adaptive zeroing neural network (OAZNN) model can effectively suppress harmonic noises. Nevertheless, the OAZNN model’s convergence rate only stays at the exponential convergence, that is, its convergence speed is usually greatly affected by the initial state. Consequently, to tackle the above issue, this work combines the dynamic characteristics of harmonic signals with prescribed-time convergence activation function, and proposes a prescribed-time convergent adaptive ZNN (PTCAZNN) for solving time-varying matrix inverse problem (TVMIP) under harmonic noises. Owing to the nonlinear activation function used having the ability to reject noises itself and the adaptive term also being able to compensate the influence of noises, the PTCAZNN model can realize double noise suppression. More importantly, the theoretical analysis of PTCAZNN model with prescribed-time convergence and robustness performance is provided. Finally, by varying a series of conditions such as the frequency of single harmonic noise, the frequency of multi-harmonic noise, and the initial value and the dimension of the matrix, the comparative simulation results further confirm the effectiveness and superiority of the PTCAZNN model.

A Variable-Parameter Noise-Tolerant Zeroing Neural Network for Time-Variant Matrix Inversion With Guaranteed Robustness

Matrix inversion frequently occurs in the fields of science, engineering, and related fields. Numerous matrix inversion schemes are often based on the premise that the solution procedure is ideal and noise-free. However, external interference is generally ubiquitous and unavoidable in practice. Therefore, an integrated-enhanced zeroing neural network (IEZNN) model has been proposed to handle the time-variant matrix inversion issue interfered with by noise. However, the IEZNN model can only deal with small time-variant noise interference. With slightly larger noise interference, the IEZNN model may not converge to the theoretical solution exactly. Therefore, a variable-parameter noise-tolerant zeroing neural network (VPNTZNN) model is proposed to overcome shortcomings and improve the inadequacy. Moreover, the excellent convergence and robustness of the VPNTZNN model are rigorously analyzed and proven. Finally, compared with the original zeroing neural network (OZNN) model and the IEZNN model for matrix inversion, numerical simulations and a practical application reveal that the proposed VPNTZNN model has the best robust property under the same external noise interference.

A Trajectory Tracking Control Based on a Terminal Sliding Mode for a Compliant Robot with Nonlinear Stiffness Joints

A nonlinear stiffness actuator (NSA) can achieve high torque/force resolution in the low stiffness range and high bandwidth in the high stiffness range. However, for the NSA, due to the imperfect performance of the elastic mechanical component such as friction, hysteresis, and unmeasurable energy consumption caused by former factors, it is more difficult to achieve accurate position control compared to the rigid actuator. Moreover, for a compliant robot with multiple degree of freedoms (DOFs) driven by NSAs, the influence of every NSA on the trajectory of the end effector is different and even coupled. Therefore, it is a challenge to implement precise trajectory control on a robot driven by such NSAs. In this paper, a control algorithm based on the Terminal Sliding Mode (TSM) approach is proposed to control the end effector trajectory of the compliant robot with multiple DOFs driven by NSAs. This control algorithm reduces the coupling of the driving torque, and mitigates the influence of parametric variation. The closed-loop system’s finite time convergence and stability are mathematically established via the Lyapunov stability theory. Moreover, under the same experimental conditions, by the comparison between the Proportion Differentiation (PD) controller and the controller using TSM method, the algorithm’s efficacy is experimentally verified on the developed compliant robot. The results show that the trajectory tracking is more accurate for the controller using the TSM method compared to the PD controller.

Research on Robot Fuzzy Neural Network Motion System Based on Artificial Intelligence

An intelligent controller based on a self-learning interval type-II fuzzy neural network is proposed to make the motion controller of the industrial intelligent robot with good adaptability. This controller has a parallel structure and contains an interval type-II fuzzy neural network and a conventional PD controller. For the design of the interval type-II fuzzy neural network, the interval type-II fuzzy set is established using the slave design method. In the design process of the interval type-II fuzzy set of the front piece, a dual sequence symmetric trapezoidal subordinate function arrangement method is proposed, which makes the self-learning law and stability analysis of the system in an analytic form and facilitates the implementation of the algorithm in hardware. In the design of the neural network self-learning law, a parametric self-learning algorithm based on sliding mode control theory is established to adjust the structural parameters of the interval type-II fuzzy neural network online, and the stability of the system is proved by using Lyapunov’s stability theorem. Three sets of validation simulation experiments are given in conjunction with the trajectory tracking problem of the Delta parallel robot. The simulation results show that, in the presence of system uncertainty, the intelligent controller based on interval self-learning interval type-II fuzzy neural network can significantly improve the trajectory tracking accuracy and robustness of the system and make the control system highly adaptable to the environment. Experiments of intelligent control system based on self-learning interval type-II fuzzy neural network and experiments of reusable particle swarm optimal motion planning method are designed, and the effectiveness of the intelligent control system and motion planning method is verified on the experimental platform. The experimental results show that the intelligent control system based on the self-learning interval type-II fuzzy neural network can effectively improve the accuracy and stability of robot trajectory tracking control, and the reusable particle swarm optimal motion planning method can quickly solve the robot motion planning problem with complex constraints online.

Fractional Control of a Lightweight Single Link Flexible Robot Robust to Strain Gauge Sensor Disturbances and Payload Changes

In this paper, a method to control one degree of freedom lightweight flexible manipulators is investigated. These robots have a single low-frequency and high amplitude vibration mode. They hold actuators with high friction, and sensors which are often strain gauges with offset and high-frequency noise. These problems reduce the motion’s performance and the precision of the robot tip positioning. Moreover, since the carried payload changes in the different tasks, that vibration frequency also changes producing underdamped or even unstable time responses of the closed-loop control system. The actuator friction effect is removed by using a robust two degrees of freedom PID control system which feeds back the actuator position. This is called the inner loop. After, an outer loop is closed that removes the link vibrations and is designed based on the combination of the singular perturbation theory and the input-state linearization technique. A new controller is proposed for this outer loop that: (1) removes the strain gauge offset effects, (2) reduces the risk of saturating the actuator due to the high-frequency noise of strain gauges and (3) achieves high robustness to a change in the payload mass. This last feature prompted us to use a fractional-order PD controller. A procedure for tuning this controller is also proposed. Simulated and experimental results are presented that show that its performance overcomes those of PD controllers, which are the controllers usually employed in the input-state linearization of second-order systems.

The Boundary Proportion Differential Control Method of Micro-Deformable Manipulator with Compensator Based on Partial Differential Equation Dynamic Model

It is challenging to accurately judge the actual end position of the manipulator—regarded as a rigid body—due to the influence of micro-deformation. Its precise and efficient control is a crucial problem. To solve the problem, the Hamilton principle was used to establish the partial differential equation (PDE) dynamic model of the manipulator system based on the infinite dimension of the working environment interference and the manipulator space. Hence, it resolves the common overflow instability problem in the micro-deformable manipulator system modeling. Furthermore, an infinite-dimensional radial basis function neural network compensator suitable for the dynamic model was proposed to compensate for boundary and uncertain external interference. Based on this compensation method, a distributed boundary proportional differential control method was designed to improve control accuracy and speed. The effectiveness of the proposed model and method was verified by theoretical analysis, numerical simulation, and experimental verification. The results show that the proposed method can effectively improve the response speed while ensuring accuracy.

Neural-Network-Based Sliding-Mode Control of an Uncertain Robot Using Dynamic Model Approximated Switching Gain

In this article, a new neural-network-based sliding-mode control (SMC) of an uncertain robot is presented. The distinguishing characteristic of the proposed control scheme is that the switching gain is designed as a dynamic model approximated value, which is handled by using the neural-network strategy to adapt the unknown dynamics and disturbances. In the presented control scheme, the modeling information of the robotic system is not required and only one parameter is required to be estimated in each joint of the robotic system. Subsequently, the Lyapunov method is utilized to prove that the trajectory tracking errors will eventually converge to a neighborhood of zero. Finally, the contrast simulation studies reveal that with the proposed control scheme, the problems of chattering and high-speed switching of control input, which takes place in a conventional SMC, can be addressed, and a satisfactory control precision is guaranteed.

Design and Analysis of Two Prescribed-Time and Robust ZNN Models With Application to Time-Variant Stein Matrix Equation

The zeroing neural network (ZNN) activated by nonlinear activation functions plays an important role in many fields. However, conventional ZNN can only realize finite-time convergence, which greatly limits the application of ZNN in a noisy environment. Generally, finite-time convergence depends on the original state of ZNN, but the original state is often unknown in advance. In addition, when meeting with different noises, the applied nonlinear activation functions cannot tolerate external disturbances. In this article, on the strength of this idea, two prescribed-time and robust ZNN (PTR-ZNN) models activated by two nonlinear activation functions are put forward to address the time-variant Stein matrix equation. The proposed two PTR-ZNN models own two remarkable advantages simultaneously: 1) prescribed-time convergence that does not rely on original states and 2) superior noise-tolerance performance that can tolerate time-variant bounded vanishing and nonvanishing noises. Furthermore, the detailed theoretical analysis is provided to guarantee the prescribed-time convergence and noise-tolerance performance, with the convergence upper bounds of steady-state residual errors calculated. Finally, simulative comparison results indicate the effectiveness and the superiority of the proposed two PTR-ZNN models for the time-variant Stein matrix equation solving.

A Vibration Control Method for Hybrid-Structured Flexible Manipulator Based on Sliding Mode Control and Reinforcement Learning

The hybrid-structured flexible manipulator has a complex structure and strong coupling between state variables. Meanwhile, the natural frequency of the hybrid-structured flexible manipulator varies with the motion of the telescopic joint, so it is difficult to suppress the vibration quickly. In this article, the tip state signal of the hybrid-structured flexible manipulator is decomposed into elastic vibration signal and tip vibration equilibrium position signal, and a combined control method is proposed to improve tip positioning accuracy and trajectory tracking accuracy. In the proposed combined control method, an improved nominal model-based sliding mode controller (NMBSMC) is used as the main controller to output the driving torque, and an actor-critic-based reinforcement learning controller (ACBRLC) is used as an auxiliary controller to output small compensation torque. The improved NMBSMC can be divided into a nominal model-based sliding mode robust controller and a practical model-based integral sliding mode controller. Two sliding mode controllers with different structures make full use of the mathematical model and the measured data of the actual system to improve the vibration equilibrium position tracking accuracy. The ACBRLC uses the tip elastic vibration signal and the prioritized experience replay method to obtain the small reverse compensation torque, which is superimposed with the output of the NMBSMC to suppress tip vibration and improve the positioning accuracy of the hybrid-structured flexible manipulator. Finally, several groups of experiments are designed to verify the effectiveness and robustness of the proposed combined control method.

A Critical Review of Control Techniques for Flexible and Rigid Link Manipulators

There is a high demand for developing effective controllers to perform fast and accurate operations for either flexible link manipulators (FLMs) or rigid link manipulators (RLMs). Thus, this paper is beneficial for such vast field, and it is also advantageous and indispensable for researchers who are interested in robotics to have sufficient knowledge about various controllers of FLMs and RLMs as the controllers’ concepts are elaborated in detail. The paper concentrates in critically reviewing classical controllers, intelligent controllers, robust controllers, and hybrid controllers for both FLMs and RLMs. The advantages and disadvantages of the aforementioned control methods are summarized in this paper; it also has a detailed comparison for the controllers in terms of the design difficulty, performance, and the suitability for controlling FLMs or RLMs.

Event-Sampled Output Feedback Control of Robot Manipulators Using Neural Networks

In this paper, adaptive neural networks (NNs) are employed in the event-triggered feedback control framework to enable a robot manipulator to track a predefined trajectory. In the proposed output feedback control scheme, the joint velocities of the robot manipulator are reconstructed using a nonlinear NN observer by using the joint position measurements. Two different configurations are proposed for the implementation of the controller depending on whether the observer is co-located with the sensor or the controller in the feedback control loop. Besides the observer NN, a second NN is utilized to compensate the effects of nonlinearities in the robot dynamics via the feedback control. For both the configurations, by utilizing observer NN and the second NN, torque input is computed by the controller. The Lyapunov stability method is employed to determine the event-triggering condition, weight update rules for the controller, and the observer for both the configurations. The tracking performance of the robot manipulator with the two configurations is analyzed, wherein it is demonstrated that all the signals in the closed-loop system composed of the robotic system, the observer, the event-sampling mechanism, and the controller are locally uniformly ultimately bounded in the presence of bounded disturbance torque. To demonstrate the efficacy of the proposed design, simulation results are presented.