Flexible Link Manipulator Research Articles

Position control of single link flexible manipulator: a functional observer-based output feedback sliding mode approach

Position control of single link flexible manipulator: a functional observer-based output feedback sliding mode approach

A learning-based nearly optimal control framework for trajectory tracking of a flexible-link manipulator system with actuator fault

In this paper, a learning-based nearly optimal control framework with fault-tolerant capability is designed to tackle the tracking control problem of a flexible-link manipulator in the presence of actuator fault and model uncertainties. Initially, the optimal control law is obtained by adopting the dynamic programming and a critic structure as the solution of Hamilton–Jacobi–Bellman equation for the nominal model. Then, by implementing an integral sliding mode control, the robustness against actuator fault and model uncertainty is guaranteed. The adaptive laws are constructed based on radial basis functions neural networks to estimate the upper bound of uncertainty and the actuator bias fault, satisfying both optimal performance and chattering reduction of the sliding surface. Furthermore, the actuator effectiveness loss is handled. The stability of the closed-loop system is analytically proven, and the performance of the proposed framework is investigated against several practical operating conditions. This incorporates the fidelity assessment of tracking precision and trackability of control signal using performance indices such as the integral absolute error and root-mean-square error. The results of extensive simulation studies confirm the effectiveness and robustness of the proposed control framework.

Finite-time composite learning control for flexible-link manipulator based on disturbance observer

With the development of robotic technology and theory, there is an expectation for robots to operate in complex environments. This paper addresses the joint tracking control problem of flexible-link manipulator system under unknown external disturbances, modelling uncertainties, and actuator saturation constraints. A research is conducted, proposing a composite learning control scheme based on adaptive finite-time disturbance observer (AFTDO). The designed AFTDO can estimate the upper bound of unknown disturbances by adaptive laws, and a neural network controller is developed based on the AFTDO algorithm to compensate and suppress disturbances from multiple sources, ensuring the stability of all variables within a finite time. Simultaneously, a barrier Lyapunov function (BLF) is chosen to guarantee that the system satisfies constraints under flexible vibrations. Finally, through simulation comparisons with other control strategies, the feasibility and superiority of the proposed method are convincingly demonstrated.

Fixed-Time Composite Anti-Disturbance Control for Flexible-Link Manipulators Based on Disturbance Observer

Fixed-Time Composite Anti-Disturbance Control for Flexible-Link Manipulators Based on Disturbance Observer

Comparative Analysis of Spiral Dynamic Algorithm and Artificial Bee Colony Optimization for Position Control of Flexible Link Manipulators

Comparative Analysis of Spiral Dynamic Algorithm and Artificial Bee Colony Optimization for Position Control of Flexible Link Manipulators

Precision motion control of rotary flexible link manipulators using polynomial input trajectories and feedback control

This paper aims to develop a high-precision controller for a flexible link manipulator using polynomial reference, feedforward input, and feedback control. The control objective is to move the tip of the flexible link to a target position as quickly as possible without exciting its resonant modes. Upon a frequency response-based system identification, a frequency-domain feedback controller is designed for reference tracking. The controller includes a proportional-integral controller, a lead filter, and a set of notch filters to control the rigid body and the flexible link dynamics. A set of polynomial reference and feedforward input trajectories are then designed to improve the tracking performance and minimize residual vibrations. The conventional polynomial reference is generated based on the rigid body motion of the system. A revised polynomial reference generation method is then developed by adding flexible motions to the conventional reference. Simulations and experimental tests indicate significant improvements in the performance of the control system using the revised polynomial trajectories.

Tracking control of flexible link manipulator with joint space constraints

Abstract A controller design with system uncertainties, external disturbances, and joint space constraints for a flexible link manipulator (FLM) is presented in this paper. To overcome the lumped disturbance and ensure that the joint space constraints are not violated, a finite-time extended state observer (ESO) and a barrier Lyapunov function are constructed. Using Lyapunov’s theory, the error of the system is proved to be semi-globally ultimately uniformly bounded without violating the constraints. Finally, the rationality of the proposed methodology is verified by numerical simulation.

An intelligent control method for a flexible-link manipulator with uncertain backlash and model uncertainty

This study examines a new intelligent control method for a single-link flexible manipulator that addresses backlash and model uncertainty. First, a smooth backlash inverse model is constructed to mitigate backlash nonlinearity. Subsequently, a ‘disturbance-like’ term is formulated to recharacterize the coupled term composed of external disturbances and model uncertainty. A new adaptive controller is proposed to compensate for the unknown ‘disturbance-like’ term. Using the proposed control method, the stability of the system is evaluated using the direct Lyapunov theory, ensuring uniform ultimate boundedness. Finally, numerical simulations and experiments are conducted using the Quanser platform. The numerical simulation and experimental results show that the proposed control can ensure a faster convergence rate and effectively reduce actuator input chattering.

Effect of nonlinear stiffness on single link flexible joint robotic manipulator and its control

This study aims to investigate the significant dynamics of a Single Link Flexible Joint (SLFJ) Robotic Manipulator and implement chaotic control using the Adaptive Sliding Mode Control (ASMC) algorithm. The mathematical model of the system incorporates stiffness nonlinearity by introducing the function (x-x3) Various dynamical tools such as stability analysis of equilibrium points, sensitivity to initial conditions, orbit diagrams for parameter variations, Lyapunov spectrum, and frequency spectrum analysis are employed. The ASMC algorithm is utilized to suppress the chaotic behavior of the system. The equilibrium points are determined for critical parameter values, with the Jacobian matrix and corresponding eigenvalues exhibiting conjugate complex with negative real parts, indicating stability resembling a spiral saddle. Phase portraits illustrate the location and range of the chaotic attractor. Investigation of parameter ′a′ using orbit diagrams and Lyapunov spectrum reveals the transition from periodic to chaotic oscillations. The frequency spectrum confirms the chaotic nature of the system. Parameter estimation, state trajectories, and sliding surface analysis demonstrate that the ASMC scheme can effectively control the system in less than 0.3 s. Nonlinear stiffness has not been previously considered in SLFJ Robotic Manipulators, highlighting a novel aspect of this study. The results unveil new chaotic ranges for parameter variation previously undocumented. Frequency spectrum analysis is employed to distinguish between noise and chaotic oscillations, addressing a significant challenge in real-time systems. The ASMC algorithm is specifically designed to control chaotic oscillations, demonstrating its effectiveness in this context.

Design of the high-speed cam profile for the multi-DOF follower

The multi-degree-of-freedom (multi-DOF) follower may suffer from unwanted vibrations when the cam works at the high speed. The vibrations will cause significant problems of positioning accuracy, noise, wear, forces, and operating costs for the cam-follower mechanism. It is challenging to design high-speed cam profiles for multi-DOF followers because of the complicated dynamics. A novel method is presented to design the cam profile in this article. A polynomial profile filters through a continuous-piecewise smoother to produce the cam profile. While the profile and their derivatives are continuous, the profile provides good performance on the vibration reduction for multi-DOF followers. Simulated and experimental results from a flexible-link manipulator validate the effectiveness of the cam profiles created by the new method.

Finite-Time Tracking Control of a Flexible Link Manipulator Based on an Extended State Observer

In this paper, the finite-time trajectory tracking control problem of a flexible link manipulator (FLM) system with unknown parameters is investigated in joint space. An adaptive nonsingular terminal sliding mode (ANTSM) controller based on an extended state observer (ESO) is proposed to ensure that the tracking error converges to a small neighborhood of zero. Firstly, an adaptive ESO is introduced, which is used to estimate unknown system parameters, including the unknown rigid-flexible coupling coefficient and the unknown control gain. Then, an ESO based on the parameters estimated above is proposed to estimate the unmodeled dynamics and external disturbances of the system in real-time. Finally, an ANTSM controller based on ESO is studied to achieve finite-time trajectory tracking control and vibration suppression without any prior knowledge of system uncertainties and external disturbances. The finite-time convergence ability of the closed-loop system is proved by Lyapunov theory. Experimental results on the Quanser Flexible Link System verify the effectiveness of the proposed controller.

Performance analysis of input shaped model reference adaptive control for a single-link flexible manipulator

Motion control for flexible link manipulators will have a great influence on their overall performance. Conventional control systems have the problem that they cannot compensate for the presence of uncertainty due to a variety of factors such as a change in the system itself-payload variations, degradation and modelling uncertainty. In addition, the underdamped structure of these systems entails motion-induced transient deflection and residual vibration. On the contrary, adaptive control, in particular Model Reference Adaptive Control (MRAC), has therefore been proposed to handle problems of this type dealing with other systems such as cranes, steering stability control for ground vehicles, airplanes and so on. This study presents a review and discussion on the MRAC and some individual issues of MRAC for these flexible link manipulators are addressed to specify: the state tracking error, the limitation of the adaptation values corresponding to the control gains and the control effort. Dealing with the last one, this work proves that shaping the command input to a Model Reference Adaptive Control (IS-MRAC) reduces the control effort necessary for the plant to follow the reference model and also mitigates the detrimental effects of flexibility. The IS-MRAC is implemented in a Single-Link Flexible Manipulator whose natural frequencies, experimentally and analytically estimated using the Transfer Matrix Method plus symbolic computation, vary significantly depending on payload mass and position. To this structured or parametric uncertainty, the proposed Lyapunov control law using the states associated with the low mode is designed for asymptotic stability and accommodates correctly. The state tracking, vibration suppression and control effort reduction performances of the proposed IS-MRAC combined controller are analysed via numerical simulations and experiments.

High-Precision Tip Tracking of a Flexible Link Manipulator Using Two-Time Scale Adaptive Robust Control

A flexible link manipulator (FLM) has advantages of greater payload-to-manipulator-weight ratio, safer operation, and lower energy consumption compared with the rigid manipulator, which has promising demands in various industrial and aerospace applications. However, the internal dynamics of the system is easy to be unstable due to its nonminimum phase characteristics, and there exists severe parametric uncertainties and uncertain nonlinearities in its dynamics, which has brought many difficulties in the precise tip tracking control and effective vibration suppression. In this article, the entire mathematical model of the FLM is established with assumed mode method and actuator dynamics. Then, the system is decomposed into a slow subsystem and a fast subsystem through introducing an adjustable time-scale factor according to a new output redefined dynamics with uncertainties from truncated vibration modes and unknown disturbances of system. A two-time scale adaptive robust control (TTSARC) scheme, which consists of an adaptive robust control for the slow subsystem and a state feedback control for the fast subsystem, is proposed to effectively handle parametric uncertainties and uncertain nonlinearities as well as improve behavior of internal dynamics. Moreover, the clear connection of achievable performances and control parameters based on the stability analysis of the entire system is addressed. The experimental results indicate that precise tip tracking with small link deflection for the FLM working on different conditions can be achieved with the proposed TTSARC.

Deep reinforcement learning with reward shaping for tracking control and vibration suppression of flexible link manipulator

This paper puts forward a novel deep reinforcement learning control using deep deterministic policy gradient (DRLC-DDPG) framework to address the reference tracking and vibration suppression problem of rotary flexible link (RFL) manipulator. Specifically, this study attempts to address the continuous action space DRLC problem through DDPG algorithm and presents a Lyapunov function based reward shaping approach for guaranteed deep reinforcement learning (DRL) convergence and enhanced speed of training. The proposed approach synthesizes the hard and soft constraints of the flexible manipulator as a constrained Markov decision problem (MDP) and evaluates the performance of DRLC-DDPG framework through hardware in loop (HIL) testing to realize precise servo tracking and suppressed vibration of the flexible manipulator. For identifying the dynamical model of the RFL, an empirical Auto-Regressive eXogenous (ARX) model using the closed loop identification technique is built. Moreover, to extract the true states (servo angle and deflection angle) from the actual measurements, which typically have the influence of sensor noise, an adaptive Kalman filter (AKF) is augmented with the DRLC scheme. The experimental results of DRLC-DDPG scheme compared with those of the model predictive control (MPC) for several test cases reveal that the proposed scheme is superior to MPC both in terms of trajectory tracking and robustness against the external disturbances and model uncertainty.

Hybrid Controller for a Single Flexible Link Manipulator

In this study, the dynamic modeling and step input tracking control of single flexible link is studied. The Lagrange-assumed modes approach is applied to get the dynamic model of a planner single link manipulator. A Step input tracking controller is suggested by utilizing the hybrid controller approach to overcome the problem of vibration of tip position through motion which is a characteristic of the flexible link system. The first controller is a modified version of the proportional-derivative (PD) rigid controller to track the hub position while sliding mode (SM) control is used for vibration damping. Also, a second controller (a fuzzy logic based proportional-integral plus derivative (PI+D) control scheme) is developed for both vibration damping and hub position tracking. A comparison is made between the performances of these two controllers. The Hybrid controller with PD and SM shows better tracking behavior than obtained from the suggested fuzzy (PI+D)2 controller for a single 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.

Addressing Model Uncertainties and External Disturbances in Optimal Robust Control for Vibration Reduction in a Flexible Link Manipulator

Addressing Model Uncertainties and External Disturbances in Optimal Robust Control for Vibration Reduction in a Flexible Link Manipulator

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.

Trajectory Tracking and Adaptive Fuzzy Vibration Control of Multilink Space Manipulators with Experimental Validation

This paper investigates the problem of modeling and controlling a space manipulator system with flexible joints and links. The dynamic model of the flexible manipulator system is derived by using the Lagrange equation and the floating frame of reference formulation, where the assumed mode method is adopted to discretize flexible links, while the flexible joints are regarded as linear torsion springs. The natural characteristics of a single flexible link manipulator, under three different boundary conditions, are compared to reveal the effect of the flexibility of joints on the manipulator system and to choose suitable assumed modes. Furthermore, singular perturbation theory is introduced to decompose the system into a slow subsystem that describes the rigid-body motion, and a fast subsystem that describes the elastic vibration. Since the system is underactuated, a compound control strategy, which consists of the underactuated computed torque controller and the adaptive fuzzy controller, is presented to improve the accuracy of the trajectory tracking of the flexible joints and to suppress the elastic vibration of the flexible links, in the meantime. Both numerical simulation and experimentation are performed to verify the effectiveness of the proposed compound controller, and a comparison with the proportional-derivative (PD) controller is provided to highlight its superiority in suppressing the residual vibration of the tip.

Vibration suppression method for flexible link underwater manipulator considering torsional flexibility based on adaptive PI controller with nonlinear disturbance observer

Achieving stable and high-precision control of underwater manipulators in complex ocean environments is one of the biggest challenges faced by the research of marine robotics at present. Flexible link manipulators can be installed on unmanned underwater vehicles to realize underwater operations such as underwater cable inspection, deep sea rescue, and marine organizational collections. The flexible link underwater manipulator will vibrate due to the influence of torsional flexibility and water flow disturbance during rotation, which will seriously affect the motion accuracy of the end actuator. In this paper, a control strategy combining the adaptive proportional-integral (PI) controller and the nonlinear disturbance observer is proposed, which indirectly suppresses vibration by improving the speed control accuracy. Firstly, according to the assumed mode method, a dynamic model of the flexible link underwater manipulator considering torsional flexibility and external disturbance is established. Next, the overload compensation control law is proposed to meet the closed-loop stability of the flexible link underwater manipulator. In addition, the PI controller's adaptive law is designed according to the Lyapunov theorem. Finally, the effectiveness of the adaptive PI controller with a nonlinear disturbance observer is proved by the simulation and control experiments of different control strategies. The results show that the proposed controller can achieve stable speed tracking and has a better vibration suppression effect.