Flexible Link Robot Research Articles

Сравнение результатов работы алгоритмов обратной кинематики на основе FABRIK для многосекционных непрерывных роботов

Flexible bend link robots, also called continuum or soft robots, are an urgent research topic. Various algorithms were developed to solve the inverse problem of the multi-section continuum robot kinematics including those based on the FABRIK (Forward And Backward Reaching Inverse Kinematics) algorithm. This algorithm was originally created to solve the inverse kinematics problem of robots consisting of rigid links connected by spherical joints and could also be used in regard to continuum robots, which are arcs smoothly transiting into each other. To work with the FABRIK algorithm, each bend section is approximated to the virtual rigid link. Two known approaches are known to solve the inverse kinematics problem: the first is based on constructing the tangents (bend section transformation into two tangents), and the second is based on constructing the chords (bend section reduction to a chord). Both approaches demonstrate good results in solving the inverse kinematics problem compared to algorithms based on the Jacobian matrix construction. However, scientific literature misses data on comparing methods that use the FABRIK algorithm. In this regard, two approaches were compared to solve the inverse kinematics problem based on implementing the FABRIK algorithm. Results of numerical experiments with three-, five- and ten-sectional robots are presented. Characteristics of the algorithms and boundaries of their application were determined.

End-effector trajectory tracking of flexible link parallel robots using servo constraints

We apply the concept of servo constraints to end-effector trajectory tracking control of parallel robots with structural link flexibilities. Such servo constraints deliver the inverse robot model where solution approaches via projections are proposed, which transform the resulting differential-algebraic equations to ordinary differential equations. The applicable solution process depends on the existence and stability of the internal dynamics. When using the exact end-effector of flexible link robots as output, this internal dynamics is usually unstable. Then a two-point boundary value problem is considered in the framework of stable inversion to obtain the noncausal solution offline. This solution is used as a feedforward control, which is initially combined only with actuator feedback control. To also account for errors within the link flexibility, the well-known linear–quadratic regulator is adapted to end-effector trajectory tracking based on differential-algebraic equations. Finally, we propose a systematic input–output feedback linearization approach, which uses servo constraints for flexible link parallel robots. Here a minimum phase system is obtained by tracking a redefined end-effector output, which is an approximation of the exact end-effector position. All control concepts are validated experimentally with a parallel robot having a highly flexible link. The results allow us to compare different control approaches and show the superior performance of controllers that rely on a flexible multibody model in contrast to classical rigid multibody modeling.

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.

A numerical algorithm to find optimum parameters of a flexible-link manipulator arm for performing payload launching

PurposeThe aim of the current study is proposing a novel framework to attain the optimum value of a flexible arm manipulator parameters for payload launching missions.Design/methodology/approachThe proposed scheme is based on optimal control approach and combines direct and indirect search methods while considering the actuator capacity.FindingsThree nonlinear parameter-optimization problems will be solved to illustrate how the proposed algorithm can be exploited. Employing variational based nonlinear optimal control within the suggested framework, the answer of these problems is highly intertwined to the solution of a set of differential equations with split boundary values. To solve the obtained boundary value problem (BVP), the related solver of MATLAB® software, bvp6c, will be employed. The achieved simulation results support the worth of the developed procedure.Originality/valueFor the first time, the optimal parameters of a flexible link robot for object launching are found in the current research. In addition, the actuator saturation limits are considered which enhances the applicability of the suggested method in the real world applications.

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.

Dynamic modelling and control of flexible link manipulators: methods and scope- Part-1

Objectives: This paper addresses two key issues in the area of flexible robotics. The issues are dynamic modelling and control of flexible link robots. A brief, yet, significant review is provided that addresses these issues. Methods: The various approaches used by researchers for dynamic modelling and control of flexible robots are presented. Besides that, methods used for achieving optimal control are also discussed. Findings: After a review of 153 research papers from the year 1975 to 2021, it has been found that a good dynamic model of flexible manipulator helps in reducing the control and computational efforts. Recent trends in research in the area of flexible manipulators are towards the use of sliding mode control and vision-based control techniques. Novelty: Inclusion of the effect of torsional vibrations besides lateral vibrations on the positional accuracy of flexible manipulators makes the current research work novel. Keywords: Flexible manipulator; modelling; dynamics; control

Impulsive observer-based design for state estimation of a class of nonlinear singularly perturbed systems with discrete measurements

The state estimation problem of a class of nonlinear singularly perturbed systems with discrete measurements is investigated. The fast dynamics is assumed to be linear and exponentially stable. Under this assumption and some additional conditions, an asymptotic representation of the fast state is obtained in terms of the slow state and the known input. Then the full state estimation problem reduces to the slow state estimation problem. Based on this observation, an impulsive observer based estimation scheme is presented in the framework of singular perturbation. The continuous part of the proposed impulsive observer is a copy of the reduced-order slow dynamics of the observed system, while the impulse part is responsible for the implementation of the sample-triggered update of the observer state whenever a new sample of the output arrives. The estimation error is analyzed via a discontinuous Lyapunov function, and an ε-independent observer gain is designed. It is shown that the resulting estimation error exponentially converges towards an ultimate bound of order O(ε). The theoretical results are successfully applied to state estimates of Chua’s circuit and a flexible link robot. The simulation results demonstrate that the proposed state estimation scheme can achieve a desirable estimation accuracy for small enough ε>0.

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.

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.

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.

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.

Flexible-link robots with combined trajectory tracking and vibration control

This work deals with asymptotic trajectory tracking and active damping injection on a flexible-link robot by application of Multiple Positive Position Feedback. The flexible-link robot is modeled and validated by using finite element methods and experimental modal analysis, and then a reduced order model of the flexible-link robot dynamics, up to the first dominant vibration modes, is employed for experimental evaluation on a test rig. Then, a combined control scheme is synthesized in two parts: first, a Sliding-Mode Control based on a cascaded Proportional-Integral-Derivative for regulation and trajectory tracking tasks, via a direct current motor torque as the control input for the overall system dynamics, and, second, a Multiple Positive Position Feedback for active vibration control and attenuation of residual vibrations on the tip position, via the input voltage applied to a piezoelectric patch actuator attached directly on the flexible beam. The results are evaluated on an experimental platform, where the dynamic performance of the overall active vibration control scheme leads to fast and effective tracking results, with damping ratios increased up to 300%.

Synthesis of a Minimum Functional State Observer Approach for Unperturbed/Perturbed Dynamical Systems

In this paper, we investigate the synthesis of minimum functional state observer for unperturbed and perturbed linear time invariant systems. The principal contribution is the design of a minimum functional state observer, which can estimate directly the state feedback control law. Hence, for the linear time invariant systems, the existence conditions of a minimum functional state observer are obtained by verification of a special dimension condition on system matrices. As a matter of fact, the exact solution of the proposed approach is determined, and the minimum functional state observer that has the same dimension as the control vector is derived by solving a set of linear matrix inequality (LMI) constraints. Whereas, for perturbed linear systems, the proposed minimum functional state observer scheme is developed to ensure the robust quadratic stability of the augmented system. The robustness issue is given via the reconstructed control law designed using an LMI based H∞ method; so that the desired design matrices are derived through the resolution of an optimum LMI system. The effectiveness and usefulness of the proposed approach are validated through a flexible link robot example.

DESIGN OF FUZZY CONTROL FOR UNCERTAIN UNDERACTUATED MECHANICAL SYSTEMS

ABSTRACTThis study presents a fuzzy control strategy of underactuated mechanical systemswith parametric uncertainties. Underactuated mechanical systems have fewer controlinputs than degrees of freedom and arise in applications, such as space andundersea robots, mobile robots, walking, brachiating, and gymnastic robots. TheLagrangian dynamics of these systems may contain feed forward non-linear ties,non-minimum phase zero dynamics, nonholonomic constraints, and other propertiesthat place this class of systems at the forefront of research in nonlinear control. Acomplete understanding of the control of these systems is therefore lacking. First,this paper represents a brief introduction to the underactuated mechanical systems,the causes of their underactuation and parameters uncertain. Then it deals with theanalysis and design of fuzzy controller for one of the application of uncertainunderactuated mechanical systems; single flexible link robot. The parametersuncertainties of the flexible robot are presented as bounded variation in payloadmass and rotational inertia of the link.

Adaptive Unknown Input Estimation by Sliding Modes and Differential Neural Network Observer.

In this paper, a differential neural network (DNN) implemented as a robust observer estimates the dynamics of perturbed uncertain nonlinear systems affected by exogenous unknown inputs. In the first stage, the identification error converges into a neighborhood around the origin. Then, the second-order sliding mode supertwisting algorithm implemented as a robust exact differentiator reconstructed the unknown inputs. The approach proposed in this paper can be applied in the case of full access to the state vector (identification problem) and in the case of partial access to the state vector (estimation problem). In the second case, the nonlinear system under study must have well-defined full relative degree with respect to the unknown input. Numerical examples showed the effectiveness of the proposed algorithm. The first example tested the DNN working as an identifier into a mathematical model describing the dynamics of a spatial minisatellite. The second example (with a DNN implemented as an observer) tested the methodology of this paper over a single link flexible robot manipulator represented in a canonical (Brunovsky) form. In both examples, the mathematical models served as data generators in the testing of the neural networks. Even when not exact mathematical description of both models was used in the input estimation, the accuracy obtained with the DNN is comparable with the case of applying a high-order differentiator with complete knowledge of the plant.

Delay-range-dependent static anti-windup compensator design for nonlinear systems subjected to input-delay and saturation

This paper presents the novel delay-range-dependent schemes for computing the static anti-windup compensator (AWC) gain for nonlinear systems with input time-delay and saturation constraints. By utilizing the Lyapunov–Krasovskii functional, sector conditions, Lipschitz inequality, and Wirtinger-based inequality and by employing the range of input lags, time-derivative bound of delay, and L2 gain reduction for exogenous input, sufficient conditions are derived in order to ensure global and local stability of the overall closed-loop system. In contrast to the conventional approaches, the resulting AWC design methodology can be applied to nonlinear systems with input delays (due to distant placement of a system from the controller), supports static AWC design (computationally straightforward for implementation), and employs range of the input delay (rather than trivial selection of the lower delay bound as zero). Simulations are carried out for two electro-mechanical systems, namely, a nonlinear DC motor and a nonlinear flexible-link robot under input time-delay and input saturation constraints.

Computationally efficient dynamic modeling of robot manipulators with multiple flexible-links using acceleration-based discrete time transfer matrix method

Abstract This paper presents a novel and computationally efficient modeling method for the dynamics of flexible-link robot manipulators. In this method, a robot manipulator is decomposed into components/elements. The component/element dynamics is established using Newton–Euler equations, and then is linearized based on the acceleration-based state vector. The transfer matrices for each type of components/elements are developed, and used to establish the system equations of a flexible robot manipulator by concatenating the state vector from the base to the end-effector. With this strategy, the size of the final system dynamic equations does not increase with the number of joints or the number of link beam elements that each link is decomposed. The developed method intends to avoid the traditional computation of the global system dynamic equations that usually have large size for flexible robot manipulators, and only involves calculating and transferring component/element dynamic equations that have small size. The numerical simulations and experimental testing of flexible-link manipulators are conducted to validate the proposed methodologies.

Nested Saturation Based Control of Ultra-Compliant Cantilever with Tip Mass mounted on a Cart

Ultra-compliant mechanical systems are widely deployed in flexible link robots, compliant mechanisms, antenna structures, and so on for their advantages such as lower inertia, low energy requirement, and high speeds. Mathematically however, they represent a class underactuated of systems with both compliant and distributed parameters and pose challenges for control. A representative system in this class: a vertical inverted ultra-flexible beam with tip mass on cart, exhibiting highly nonlinear dynamics, is considered here. Control task is defined to be stabilization of central unstable equilibrium along with regulation of cart to a desired position. Two coordinate transformations are proposed to obtain a mathematical structure suitable to employ nested saturation based control. Asymptotic stability of the unstable equilibrium is established with the proposed controller and is demonstrated in simulation as well as in the experimental implementation. Nested saturation based controller is found to be relatively robust in experiments although system dynamics is very sensitive to parametric uncertainities.

Inverse dynamic analyzing of flexible link manipulators with translational and rotational joints

Inverse dynamic problem analyzing of flexible link robot with translational and rotational joints is presented in this work. The new model is developed from single flexible link manipulator with only rotational joint. The dynamic equations are built by using finite element method and Lagrange approach. The approximate force of translational joint and torque of rotational joint are found based on rigid model. The simulation results show the values of driving forces at joints of flexible robot with desire path and errors of joint variables between flexible and rigid models. Elastic displacements of end-effector are shown, respectively. There are remaining issues which need be studied further in future work because the error joints variables in algorithm to solve inverse dynamic problem of flexible with translational joint has not been mentioned yet.

Output feedback control for a class of nonlinear systems with actuator degradation and sensor noise

This paper investigates the output feedback control problem of a class of nonlinear systems with sensor noise and actuator degradation. Firstly, by using the descriptor observer approach, the origin system is transformed into a descriptor system. On the basis of the descriptor system, a novel Proportional Derivative (PD) observer is developed to asymptotically estimate sensor noise and system state simultaneously. Then, by designing an adaptive law to estimate the effectiveness of actuator, an adaptive observer-based controller is constructed to ensure that system state can be regulated to the origin asymptotically. Finally, the design scheme is applied to address a flexible joint robot link problem.