Two-link Flexible Manipulator Research Articles

Adaptive composite learning control of a flexible two‐link manipulator with unknown spatiotemporally varying disturbance

AbstractThis article presents a novel adaptive composite learning (ACL) control strategy combining reinforcement learning and a disturbance observer (DOB) to address vibration issues in a flexible two‐link manipulator (FTLM) system affected by unknown spatiotemporally varying disturbances. Based on the assumed mode method, the FTLM system is initially transformed into an ordinary differential equation model, while effectively capturing the elastic deformation and vibration characteristics of the flexible link. A composite learning controller, based on the actor‐critic algorithm and DOB, is then developed to achieve trajectory tracking and vibration suppression in the FTLM system. The DOB in the controller compensates for unknown disturbances resulting in reduced system error. It is noting that the proposed optimal control strategy is continuously gathering system experience and evaluating the current policy's effectiveness. The stability and robustness of the closed‐loop system incorporating the composite controller are analyzed using Lyapunov's direct method, and the semi‐global uniform ultimate boundedness of the tracking and vibration errors are also demonstrated. To validate the effectiveness and superiority of the proposed ACL controller, comparative simulations and experiments are conducted on the Quanser experimental platform.

Sliding mode control of a two-link flexible manipulator for reduced vibration in the presence of unmatched uncertainty and time-varying external disturbance

Sliding mode control of a two-link flexible manipulator for reduced vibration in the presence of unmatched uncertainty and time-varying external disturbance

Sliding mode control of Two-link Flexible Manipulator for reduced vibration in the presence of unmatched uncertainty and time-varying external disturbance

Sliding mode control of Two-link Flexible Manipulator for reduced vibration in the presence of unmatched uncertainty and time-varying external disturbance

Command shaped trajectory tracking control for a two-link flexible manipulator

Command shaped trajectory tracking control for a two-link flexible manipulator

Vibration and Position Control of a Two-Link Flexible Manipulator Using Reinforcement Learning

In recent years, industries have increasingly emphasized the need for high-speed, energy-efficient, and cost-effective solutions. As a result, there has been growing interest in developing flexible link manipulator robots to meet these requirements. However, reducing the weight of the manipulator leads to increased flexibility which, in turn, causes vibrations. This research paper introduces a novel approach for controlling the vibration and motion of a two-link flexible manipulator using reinforcement learning. The proposed system utilizes trust region policy optimization to train the manipulator’s end effector to reach a desired target position, while minimizing vibration and strain at the root of the link. To achieve the research objectives, a 3D model of the flexible-link manipulator is designed, and an optimal reward function is identified to guide the learning process. The results demonstrate that the proposed approach successfully suppresses vibration and strain when moving the end effector to the target position. Furthermore, the trained model is applied to a physical flexible manipulator for real-world control verification. However, it is observed that the performance of the trained model does not meet expectations, due to simulation-to-real challenges. These challenges may include unanticipated differences in dynamics, calibration issues, actuator limitations, or other factors that affect the performance and behavior of the system in the real world. Therefore, further investigations and improvements are recommended to bridge this gap and enhance the applicability of the proposed approach.

Adaptive intelligent vision-based control of a flexible-link manipulator

Present space robots such as planetary robots and flexible robots have structural flexibility in their arms and joints that leads to an error in the tip positioning owing to tip deflection. The flexible-link manipulator (FLM) is a non-collocated system that has unstable and inaccurate system performance. Thus, tip-tracking of FLM possesses difficult control challenges. The purpose of this study is to design adaptive intelligent tip-tracking control strategy for FLMs to deal with this control challenges of FLM. A vision sensor is utilized in conjunction with a traditional mechanical sensor to directly measure tip-position in order to address the aforementioned problem. Image-based visual servoing (IBVS), one of several visual servoing control techniques, is more efficient. However, the IBVS scheme faces numerous difficulties that impair the system’s performance in real-time applications, including singularities in the interaction matrix, local minima in trajectory, visibility issues. To address the issues with the IBVS scheme, a novel adaptive intelligent IBVS (AI-IBVS) controller for tip-tracking control of a two-link flexible manipulator (TLFM) is designed in this study. In particular, this paper addresses the IBVS issues along-with retention of visual features in the field-of-view (FOV). First, in order to retain object within the camera FOV, an intelligent controller with off-policy reinforcement learning (RL) is proposed. Second, a composite controller for TLFM is developed to combine RL controller and IBVS controller. The simulation has been conducted to examine the effectiveness and robustness of the proposed controller. The obtained results show that the AI-IBVS controller developed here possesses the capabilities of self-learning and decision-making for robust tip-tracking control of TLFM. Further, a comparison with other similar approach is presented.

Adaptive Notch Filter in a Two-Link Flexible Manipulator for the Compensation of Vibration and Gravity-Induced Distortion

This paper presents a 2-link, 2-DOF flexible manipulator control using an inverse feedforward controller and an adaptive notch filter with a direct strain feedback controller. In the flexible manipulator, transient and residue vibrations inhibit the full potential of the manipulator. Vibrations caused by abrupt changes in the direction of the links are referred to as transient vibrations, whereas residual vibrations occur when the arm takes too long to settle after engaging in the intended task. The feedforward adaptive notch filter will reduce transient vibration caused by the manipulator arm beginning and halting suddenly, while the strain feedback will assure the quick decay of leftover vibrations. Maple, Maplesim, and MATLAB tools were used to model the manipulator and create the inverse controller and adaptive notch filter. The experiments took place in the dSPACE control desk environment. The experimental results of the spectral power of strain resulting from the two strategies are compared. From the results, the adaptive notch filter control had over an 80% improvement in the reduction in resonant frequencies that contribute to vibration. The results confirmed the feasibility of the approach, characterized by very minimal transient vibrations and a quick settling of the end effector.

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

AbstractIn 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.

Vibration Suppression Method for a Two-Link Flexible Manipulator Based on Adaptive Iterative Learning Algorithm

Vibration Suppression Method for a Two-Link Flexible Manipulator Based on Adaptive Iterative Learning Algorithm

Real-Time Fuzzy Logic Control of Two-Link Flexible Manipulators

This study investigates the development of a Fuzzy Logic Controller (FLC) for tracking a sinusoidal wave trajectory and suppressing the vibration of a Two Link Flexible Manipulator (TLFM). The TLFM was modeled using Lagrange's formalism and the Assumed Mode Method (AMM). A three-part apparatus consisting of a TLFM mathematical model, a real-world TLFM, and control software was designed and implemented. The FLC was applied to both the simulated and real-world TLFM. The robustness of the FLC was investigated by considering variable payload mass and link angular velocity in both constructive and destructive link interference trajectory cases. Simulation and experimental results show the effectiveness and robustness of the proposed FLC.

Cascade control of underactuated manipulator based on reinforcement learning framework

In this article, we propose a cascade control framework to attenuate the residual vibration of the underactuated manipulator. The control framework is divided into two phases. In the first phase, a path generator trained by the reinforcement learning produces the leading signal for the tracking controller. In the second phase, the leading signal stabilizes the underactuated manipulator, and the adaptive proportional derivative controller is implemented to reduce the vibration. In the process, a novel path planning method is proposed to improve exploration efficiency, and a negative reward is introduced to avoid unsafe strategies and simulation instability. The effectiveness of the proposed control scheme is verified in the simulations of the double pendulum crane and the two-link flexible manipulator.

Modeling of Flexible-Link Manipulators Under Uncertain Parameters Based on Stochastic Finite Element Method

Abstract This paper presents a novel approach to obtain the dynamic model of flexible-link manipulators based on the stochastic finite element method. The links and elements of flexible manipulators are affected by uncertainties. The main sources of uncertainties include the variation of mechanical properties. The present research study conveys the following contributions: (i) modeling the uncertain parameters such as the stiffness of the links as an extension of the finite element method based on stochastic fields and the stochastic finite element method, (ii) numerical method to simulate the dynamic response of flexible manipulation with uncertain parameters in the links based on the Monte Carlo simulation (MCS), and (iii) numerical application of the proposed method to the one-link flexible manipulator and two-link flexible manipulator. Numerical simulations illustrate the proposed approach in terms of joint responses and frequency response functions subject to uncertain parameters.

Intelligent Tuning Control of two Link Flexible Manipulator with Piezoelectric Actuator

This paper represents an experimental study on the application of smart control represented by the use of the fuzzy logic controller. Two-link flexible manipulators that are used in airspace and military applications are made of flexible materials characterized by low frequency and damping ratio. To solve this problem, this paper proposes the use of smart materials (piezoelectric transducers), where each link is bonded with a pair of piezoelectric transducers that act as a sensor and another as an actuator. As the arm vibrates because of the movement generated by the motor, this voltage is controlled by a regulator inside the LABVIEW® 2020 software and sends the output control voltage to the piezoelectric actuator. Experimental results show that fuzzy logic control was efficient during high amplitude and led to pronounced results in suppressing vibrations within a short time. Fuzzy logic gives more flexibility to the designer and allows him to control the system through its simple implementation. This differs from classical control, which requires a mathematical model.

Optimal integral sliding mode controller controller design for 2-RLFJ manipulator based on hybrid optimization algorithm

A newly hybrid nature-inspired algorithm called HSSGWOA is presented with the combination of the salp swarm algorithm (SSA) and grey wolf optimizer (GWO). The major idea is to combine the salp swarm algorithm's exploitation ability with the grey wolf optimizer's exploration ability to generate both variants' strength. The proposed algorithm uses to tune the parameters of the integral sliding mode controller (ISMC) that design to improve the dynamic performance of the two-link flexible joint manipulator. The efficiency and the capability of the proposed hybrid algorithm are evaluated based on the selected test functions. It is clear that when compared to other algorithms like SSA, GWO, differential evolution (DE), gravitational search algorithm (GSA), particles swarm optimization (PSO), and whale optimization algorithm (WOA). The ISMC parameters were tuned using the SSA, which was then compared to the HSSGWOA algorithm. The simulation results show the capabilities of the proposed algorithm, which gives an enhancement percentage of 57.46% compared to the standard algorithm for one of the links, and 55.86% for the other.

Dynamic formulation of a two link flexible manipulator and its comparison analysis with a knuckle joint cantilever

In the present study a dynamic modelling technique for a two-link flexible planar manipulator is presented. The developed manipulator model can include an arbitrary number of flexible links. The gross equation of motion of each flexible link has been obtained by composing the rigid body motion and a small elastic deformation of each link. In order to bring the simplicity the modelling technique has been applied to model a two link flexible manipulator. The analytical derivation and final expression for the equation of motion has been shown for a two link flexible manipulator using the proposed modelling method. Later on, a comparison analysis has been studied between the proposed manipulator model and a simple cantilever with a knuckle joint. Finite element analysis of the beam has been done in ANSYS 17.1 considering different types of elements under different loading conditions. The various numerical results have been generated at different nodal points by taking the origin of the Cartesian coordinate system at the fixed end of the beam. Finally, a comparison analysis has been made to find a way to validate the proposed mathematical modelling.

Reinforcement Learning Control of a Flexible Two-Link Manipulator: An Experimental Investigation

This article discusses the control design and experiment validation of a flexible two-link manipulator (FTLM) system represented by ordinary differential equations (ODEs). A reinforcement learning (RL) control strategy is developed that is based on actor–critic structure to enable vibration suppression while retaining trajectory tracking. Subsequently, the closed-loop system with the proposed RL control algorithm is proved to be semi-global uniform ultimate bounded (SGUUB) by Lyapunov’s direct method. In the simulations, the control approach presented has been tested on the discretized ODE dynamic model and the analytical claims have been justified under the existence of uncertainty. Eventually, a series of experiments in a Quanser laboratory platform are investigated to demonstrate the effectiveness of the presented control and its application effect is compared with PD control.

Constraint-Following Servo Control for the Trajectory Tracking of Manipulator with Flexible Joints and Mismatched Uncertainty

Trajectory tracking is a common application method for manipulators. However, the tracking performance is hard to improve if the manipulators contain flexible joints and mismatched uncertainty, especially when the trajectory is nonholonomic. On the basis of the Udwadia–Kalaba Fundamental Equation (UKFE), the prescribed position or velocity trajectories are creatively transformed into second-order standard differential form. The constraint force generated by the trajectories is obtained in closed form with the help of UKFE. Then, a high-order fractional type robust control with an embedded fictitious signal is proposed to achieve practical stability of the system, even if the mismatched uncertainty exists. Only the bound of uncertainty is indispensable, rather than the exact information. A leakage type of adaptive law is proposed to estimate such bound. By introducing a dead-zone, the control will be simplified when the specific parameter enters a certain area. Validity of the proposed controller is verified by numerical simulation with two-link flexible joint manipulator.

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.