Single-link Flexible Robot Research Articles

Vibration of flexible robots: Dynamics and novel synthesis of unbounded trajectories

Flexible Robotic Systems, by and large, are prone to inherent vibration that recreates itself in several modal frequencies. This in-situ vibration in flexible robots or in any such complaint robotic unit becomes tricky so far as the control system architecture is concerned. Thus, customization of the design and firmware of higher-order flexible robots is highly challenging due to its inherent parameters related to real-time vibration. Vibration in flexible robots has been investigated hitherto from the standpoint of frequency & amplitude tuple, sidetracking the important paradigm of looping of the trajectories. This work has added a technological niche in bringing out the intrinsic dynamics of this vibration from a mathematical perspective of trajectory formation so as to understand the mechanics of spiraling loops while a flexible/compliant robotic system is vibrating under natural conditions. The analytical modeling of the said in-situ vibration has been experimented with through an indigenous single-link flexible robot, fitted with a miniature gripper.

Sensor fault estimation based on L∞ unknown input observer

Abstract This study investigates the fault estimation problem for a class of Lipschitz non-linear systems with sensor faults and disturbances. An augmented system consisting of system states and sensor faults is constructed to estimate sensor faults by designing an augmented state. A novel L∞ performance index is presented to reduce the influence of disturbances on fault estimation results. An unknown input observer (UIO) is proposed based on the L∞ performance index to achieve an asymptotic estimation of sensor faults. The design conditions of the L∞ UIO are deduced and solved using linear matrix inequalities. The effectiveness of the proposed L∞ UIO and the fault estimation performance are demonstrated via numerical simulations of a single-link flexible joint robot.

Frequency Response Based Extremum Seeking Control of a Single-link Flexible Robot

Frequency Response Based Extremum Seeking Control of a Single-link Flexible Robot

Adaptive PID Fault-Tolerant Tracking Controller for Takagi-Sugeno Fuzzy Systems with Actuator Faults: Application to Single-Link Flexible Joint Robot

This paper considers the problem of Fault Tolerant Tracking Control (FTTC) strategy design for nonlinear systems using Takagi-Sugeno (T-S) fuzzy models with measurable premise variables affected by actuator faults subject to unknown bounded disturbances (UBD). Firstly, the Adaptive Fuzzy Observer (AFO) is proposed to estimate the faults. Based on the information provided by this observer, an active fault tolerant tracking controller described by an adaptive Proportional-Integral-Derivative (PID) structure has been developed to compensate for the actuator fault effects and to guarantee the trajectory tracking of desired outputs to the reference model despite the presence of actuator faults. The stability and the trajectory tracking performances of the proposed approach are analyzed based on the Lyapunov theory. Sufficient conditions can be obtained and solved for the design of the controller, and the observer gains using Linear Matrix Inequalities (LMIs). Finally, the effectiveness of the proposed technique is illustrated by using a single-link flexible joint robot.

H − / L ∞ UIO‐based actuator and sensor fault diagnosis design in the finite frequency domain for discrete‐time Lipschitz nonlinear systems

This study investigates the problem of fault diagnosis observer design in the finite frequency domain for discrete-time Lipschitz nonlinear systems simultaneously subjected to actuator and sensor faults and unknown input disturbances. An augmented descriptor system is developed by constructing an augmented state consisting of system states and sensor faults. A novel H−/L∞ unknown input observer (UIO) is proposed in the finite frequency domain using the generalized Kalman–Yakubovich–Popov lemma to render the residual sensitive to actuator faults and robust against disturbances, which can achieve a better fault diagnosis result compared with existing observers in the full frequency domain. In the fault diagnosis scheme, a time-varying threshold is presented based on the L∞ performance index to detect actuator faults, and the sensor fault estimation is simultaneously achieved through an asymptotical estimation of the augmented state. Design conditions for the proposed H−/L∞ UIO are derived and converted into linear matrix inequalities to solve its design matrices together. The effectiveness of the developed H−/L∞ UIO and the fault diagnosis scheme are validated via simulations of an example of a single-link flexible joint robot.

Trajectory tracking of a single flexible-link robot using a modal cascaded-type control

The control problem of a single flexible-link robot is addressed for tip position and trajectory tracking control, with no other actuators into the mechanical system than a servomotor installed at the rigid joint. A multi-modal cascaded-type model of the robot is obtained, where the angle of the rigid joint is considered as the control input for the flexible-link rather than the torque provided by the servomotor. A Sliding-Mode Control approach is used to overcome the rigid mode dynamics and ensure a precise tracking of a flexible-state dependent trajectory at the joint level. The proposed control scheme is simple, easy to implement and yet robust against parametric uncertainties. The main results show that, trajectory tracking at the tip of the flexible-link is achieved, with guaranteed closed-loop stability, since the problem is reduced to the tracking of an adequate trajectory at the joint level. The proposed results are validated with several experimental results. Finally, the control scheme is quantitatively compared with two different controllers for flexible robots.

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.

Control of Very Lightweight 2-DOF Single-Link Flexible Robots Robust to Strain Gauge Sensor Disturbances: A Fractional-Order Approach

This article deals with the control of two degrees of freedom manipulators that have a flexible and very lightweight link. These robots have a single low-frequency and high-amplitude vibration mode. Their actuators have high friction, and their vibration sensors are often strain gauges that have offset and high-frequency noise. These problems reduce the robot precision and produce noisy control signals that saturate actuators. An efficient control system is proposed to overcome these drawbacks. Actuator friction effect is nearly removed by closing a high gain position control loop around the actuator. It causes the separation of the robot dynamics into the controlled actuator fast subsystem and the link dynamics slow subsystem. Based on that, an innovative control system is designed to remove vibrations using the singular perturbation theory combined with the input-state linearization technique. This control system includes fractional-order controllers that nearly remove unknown sensor offset and sensor ramp disturbances while reducing the high-frequency component of the control signal caused by sensor noise. Simulated and experimental results show the superior performance of these controllers over other standard integer-order controllers of similar complexity and nominal behavior.

Simultaneous state and fault estimation for Takagi-Sugeno implicit models with Lipschitz constraints

This paper presents a state and fault observer design for a class of Takagi-Sugeno implicit models (TSIMs) with unmeasurable premise variables satisfying the Lipschitz constraints. The fault variable is constituted by the actuator and sensor faults. The actuator fault affects the state and the sensor fault affects the output of the system. The approach is based on the separation between dynamic and static relations in the TSIM. Firstly, the method begins by decomposing the dynamic equations of the algebraic equations. Secondly, the fuzzy observer design that satisfies the Lipschitz conditions and permits to estimate simultaneously the unknown states, actuator and sensor faults is developed. The aim of this approach for the observer design is to construct an augmented model where the fault variable is added to the state vector. The exponential convergence of the state estimation error is studied by using the Lyapunov theory and the stability condition is given in term of only one linear matrix inequality (LMI). Finally, numerical simulation results are given to highlight the performances of the proposed method by using a TSIM of a single-link flexible joint robot.

Dynamics and control analysis of a single flexible link robot with translational joints

Modern design always aims at reducing mass, simplifying the structure, and reducing the energy consumption of the system especially in robotics. These targets could lead to lowing cost of the material and increasing the operating capacity. The priority direction in robot design is optimal structures with longer lengths of the links, smaller and thinner links, more economical still warranting ability to work. However, all of these structures such as flexible robots are reducing rigidity and motion accuracy because of the effect of elastic deformations. Therefore, taking the effects of elastic factor into consideration is absolutely necessary for kinematic, dynamic modeling, analyzing, and controlling flexible robots. Because of the complexity of modeling and controlling flexible robots, the single-link and two-link flexible robots with only rotational joints are mainly mentioned and studied by most researchers. It is easy to realize that combining the different types of joints of flexible robots can extend their applications, flexibility, and types of structure. However, the models consisting of rotational and translational joints will make the kinematic, dynamic modeling, and control becomes more complex than models that have only rotational joints. This study focuses on the dynamics model and optimal controller based on genetic algorithms (GA) for a single flexible link robot (FLR) with a rigid translational joint. The motion equations of the FLR are built based on the Finite Element Method (FEM) and Lagrange Equations (LE). The difference between flexible manipulators that have only rotational joints and others with the translational joint is presented through boundary conditions. A PID controller is designed with parameters that are optimized by the GA algorithm. The cost function is established based on errors signal of translational joint, elastic displacements of the End-Point (EP) of the FLR. Simulation results show that the errors of the joint variable, the elastic displacements (ED) are destructed in a short time when the system is controlled following the reference point. The results of this study can be basic to research other flexible robots with more joint or combine joint styles.

A new estimation/decoupling approach for robust observer-based fault reconstruction in nonlinear systems affected by simultaneous time varying actuator and sensor faults

This paper presents an estimation/decoupling approach to design a fault estimation observer for nonlinear systems affected by a simultaneous actuator and sensor faults. In this approach, the sensor fault is treated as unknown inputs while the state and the actuator faults are estimated by recalling the extended state observer (ESO) idea. A Takagi-Sugeno Multiple-Integral Unknown Input Observer (TSMIUIO) is used to achieve this approach. First, the TSMIUIO estimates an extended state consists of the original system state and the actuator faults by using the ESO idea. On the other hand, the sensor faults are decoupled from the estimation of the extended state by treating such faults as unknown inputs. Then, the TSMIUIO permits an implicit estimation of sensor faults by using the output signals. The benefits earned by such an approach are: (1) the approach does not presume constraints on the time behaviour of the sensor faults. (2) By decoupling the sensor faults, the approach eliminates the bi-directional interaction (BDI) between the estimated signals. (3) It offers an implicit estimation of sensor faults by using the output signals. The design algorithm is given in a linear matrix inequality (LMI) form. The single-link flexible joint robot and the FAST 5MW benchmark wind turbine have been used to show the effectiveness of the proposed method.

Increasing the damping of oscillatory systems with an arbitrary number of time varying frequencies using fractional-order collocated feedback

This paper studies the active damping of the oscillations of lightly damped linear systems whose parameters are indeterminate or may change through time. Systems with an arbitrary number of vibration modes are considered. Systems described by partial differential equations, that yield an infinite number of vibration modes, can also be included. In the case of collocated feedback, i.e. the sensor is placed at the same location of the actuator, a simple fractional order differentiation or integration of the measured signal is proposed that provides an effective control: (1) it guarantees a minimum phase margin or damping of the closed-loop system at all vibration modes, (2) this feature is robustly achieved, i.e., it is attained for very large variations or uncertainties of the oscillation frequencies of the system and (3) it is robust to spillover effects, i.e., to the unstabilizing effects of the vibration modes neglected in the controller design (especially important in infinite dimensional systems). Moreover, the sensitivity of the gain crossover frequency to such variations is assessed. Finally, these results are applied to the position control of a single link flexible robot. Simulated results are provided.

Robust fault tolerant control based on adaptive observer for Takagi-Sugeno fuzzy systems with sensor and actuator faults: Application to single-link manipulator

In this work, we investigate the problem of control for nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models affected by both sensor and actuator faults subject to an unknown bounded disturbances (UBD). For this, we design an adaptive observer to estimate state, sensor and actuator fault vectors simultaneously despite the presence of external disturbances. Based on this observer, we develop a fault tolerant control (FTC) law not only to stabilize closed loop system, but also to compensate the fault effects. For the observer-based controller design, we propose less conservative conditions formulated in terms of linear matrix inequalities (LMIs). Moreover, both observer and controller gains are calculated via solving a set of LMIs only in single step. Finally, comparative results and an application to single-link flexible joint robot are afforded to prove the efficiency of the proposed design.

Optimal state estimation and fault diagnosis for a class of nonlinear systems

This study proposes a scheme for state estimation and, consequently, fault diagnosis in nonlinear systems. Initially, an optimal nonlinear observer is designed for nonlinear systems subject to an actuator or plant fault. By utilizing Lyapunov &#x02BC s direct method, the observer is proved to be optimal with respect to a performance function, including the magnitude of the observer gain and the convergence time. The observer gain is obtained by using approximation of Hamilton-Jacobi-Bellman &#x0028 HJB &#x0029 equation. The approximation is determined via an online trained neural network &#x0028 NN &#x0029 . Next a class of affine nonlinear systems is considered which is subject to unknown disturbances in addition to fault signals. In this case, for each fault the original system is transformed to a new form in which the proposed optimal observer can be applied for state estimation and fault detection and isolation &#x0028 FDI &#x0029 . Simulation results of a singlelink flexible joint robot &#x0028 SLFJR &#x0029 electric drive system show the effectiveness of the proposed methodology.

Precise tip-positioning control of a single-link flexible arm using a fractional-order sliding mode controller

This article presents an efficient scheme based on fractional order sliding mode control approach for precision tip position control of a single link flexible robot arm. The proposed control strategy is robust against the system parameters variations such as payload and viscous friction variations in the presence of the sinusoidal disturbance and the unknown Coulomb friction disturbances. The aim of controller design is reduction of the deviation caused by the link flexibility and then the precision tip positioning control of the single-link flexible arm. In this regard, sliding mode control strategy is performed in two stages. In the first stage, the difference between the motor angle (load angle) and the tip angle of the flexible link is reduced by applying the proposed fractional order sliding mode controller and then, in the second step, the precision tracking of the tip position of the link is done by adding another sliding mode control scheme. The feasibility and effectiveness of the proposed control scheme is demonstrated via numerical simulation results.

Similar Fault Isolation of Discrete-Time Nonlinear Uncertain Systems: An Adaptive Threshold Based Approach

In this paper, a new concept of “similar fault” is introduced to the field of fault isolation (FI) of discrete-time nonlinear uncertain systems, which defines a new and important class of faults that have small mutual differences in fault magnitude and fault-induced system trajectories. Effective isolation of such similar faults is rather challenging as their small mutual differences could be easily concealed by other system uncertainties (e.g., modeling uncertainty/disturbances). To this end, a novel similar fault isolation (sFI) scheme is proposed based on an adaptive threshold mechanism. Specifically, an adaptive dynamics learning approach based on the deterministic learning theory is first introduced to locally accurately learn/identify the uncertain system dynamics under each faulty mode using radial basis function neural networks (RBF NNs). Based on this, a bank of sFI estimators are then developed using a novel mechanism of absolute measurement of fault dynamics differences. The resulting residual signals can be used to effectively capture the small mutual differences of similar faults and distinguish them from other system uncertainties. Finally, an adaptive threshold is designed for real-time sFI decision making. One important feature of the proposed sFI scheme is that: it is capable of not only isolating similar faults that belong to a pre-defined fault set (used in the training/learning process), but also identifying new faults that do not match any pre-defined faults. Rigorous analysis on isolatability conditions and isolation time is conducted to characterize the performance of the proposed sFI scheme. Simulation results on a practical application example of a single-link flexible joint robot arm are used to show the effectiveness and advantages of the proposed scheme over existing approaches.

Estimation/decoupling approach for robust Takagi–Sugeno UIO-based fault reconstruction in nonlinear systems affected by a simultaneous time-varying actuator and sensor faults

ABSTRACTThis paper presents a robust design of Takagi–Sugeno Multiple-Integral Unknown Input Observer (TSMIUIO) for nonlinear systems affected by a simultaneous time-varying actuator and sensor faults, sensor noise and unknown input by using novel estimation/decoupling approach. In comparison to the available literature, the motivation for this approach is to: (1) attain robust fault reconstruction against the effects of bi-directional interaction accompanying the use of extended state observer (ESO) to simultaneously estimate actuator and sensor faults. (2) Guarantee accurate fault reconstruction despite the time behaviour of the fault. (3) Reduce the order of the TSMIUIO by avoiding the use of ESO for estimating all faults. The -norm minimisation has been exploited to ensure robust global stability against system disturbances. The design algorithm has been formulated using linear matrix inequality framework. Finally, the effectiveness of the proposal is illustrated by using a single-link flexible joint robot.

Adaptive sliding mode fault tolerant control design for uncertain nonlinear systems with multiplicative faults: Takagi–Sugeno fuzzy approach

The present article deals with adaptive sliding mode fault tolerant control design for uncertain nonlinear systems, affected by multiplicative faults, that is described under Takagi–Sugeno fuzzy representation. First, we propose to conceive robust adaptive observer in order to achieve states and multiplicative faults estimation in the presence of nonlinear system uncertainties. Under the nonlinear Lipschitz condition, the observer gains are attained by solving the multi-objective optimization problem. Second, sliding mode controller is suggested to offer a solution of the closed-loop system stability even the occurrence of real fault effects. The main objective is to compensate multiplicative fault effects based on output feedback information. Sufficient conditions are developed with [Formula: see text] performances and expressed as a set of linear matrix inequalities subject to compute controller gains. Finally, simulation results, using the nonlinear model of a single-link flexible joint robot system, are given to illustrate the capability of the suggested fault tolerant control strategy to treat multiplicative faults.

Hybrid approach to design Takagi–Sugeno observer‐based FTC for non‐linear systems affected by simultaneous time varying actuator and sensor faults

This study uses a novel approach, integrating fault estimation and fault decoupling methods, in designing a new Takagi–Sugeno multiple integral unknown input observer (TSMIUIO)-based fault tolerant control (FTC) system. The motivation is to tackle the challenges underlined in designing observer-based FTC for non-linear systems affected by simultaneous time-varying actuator and sensor faults, exogenous input, and sensor noise. In such systems, the FTC design challenges are the constraints imposed by the structure of input/output matrices, the need of extending the order of the observer to estimate simultaneous faults, the bi-directional interaction caused by the state and faults’ estimation errors, and the unpredictable time behaviour of fault signals. These challenges motivate the proposal of TSMIUIO to (i) ensure acceptable FTC performance, irrespective of the time behaviour of sensor fault; (ii) relax the complexity of TSMIUIO by avoiding the use of extended state approach for estimating simultaneous faults; and (iii) eliminate the BDI in the estimated signals that feed the controller. The effectiveness of the proposed method is illustrated using a single-link flexible joint robot and translational oscillator with an eccentric rotational proof mass actuator benchmark.

Stable force control and contact transition of a single link flexible robot using a fractional-order controller

The control of robots that interact with the environment is an open area of research. Two applications that benefit from this study are: the control of the force exerted by a robot on an object, which allows the robot to perform complex tasks like assembly operations, and the control of collisions, which allows the robot safely collaborate with humans. Robot control is difficult in these cases because: (1) bouncing between free and constrained motion appears that may cause instability, (2) switching between free motion (position) controller and constrained motion (force) controller is required being the switching instants difficult to know and (3) robot control must be robust since the mechanical impedance of the environment is unknown. Robots with flexible links may alleviate these drawbacks. Previous research on flexible robots proved stability of a PD controller that fed back the motor position when contacting an unknown environment, but force control was not achieved. This paper proposes a control system that combines a fractional-order D tip position controller with a feedforward force control. It attains higher stability robustness and higher phase margin than a PD controller, which is the integer-order controller of similar complexity. This controller outperforms previous controllers: (1) it achieves force control with nearly zero steady state error, (2) this control is robust to uncertainties in the environment and motor friction, (3) it guarantees stability (like others) but it also guarantees a higher value of the phase margin, i.e., a higher damping, and a more efficient vibration cancellation, and (4) it effectively removes bouncing. Experimental results prove the effectiveness of this new controller.