Flexible Link Robot Research Articles

Determining maximum load carrying capacity of planar flexible-link robot: closed-loop approach

SUMMARYMaximum load carrying capacity (MLCC) of flexible robot manipulators is computed based on closed-loop approach. In open-loop approach, controller is not considered, so the end effector deviation from the predefined path is significant and the accuracy constraint restrains the maximum payload before actuators go into saturation mode. In order to improve the MLCC, a method based on closed-loop strategy is presented. Since in this case the accuracy is improved the actuators constraint is not a major concern and full power of actuators can be used. Since controller can play an important role in improving the maximum payload, a sliding mode based partial feedback linearization controller is designed. Furthermore, a fuzzy variable layer is used in sliding mode design to boost the performance of the controller. However, the control strategy required measurements of elastic variables velocity that are not conveniently measurable. So a nonlinear observer is designed to estimate these variables. Stability analysis of the proposed controller and state observer are performed on the basis of Lyapunov's direct method. In order to verify the effectiveness of the presented method, simulation is done for a two-link flexible manipulator. The obtained maximum payload in open-loop and closed-loop cases is compared and the superiority of the method is illustrated and the results are discussed.

A fault-tolerant control framework for a class of non-linear networked control systems

In this article, a novel fault-tolerant control (FTC) framework is presented for a class of non-linear networked control systems (NCSs) with Markov transfer delays. First, the NCSs are modelled by non-linear discrete Takagi–Sugeno fuzzy model using Euler approximate method. Then, a sliding mode-based fault estimation technique is developed for such model. With the estimated state and fault information, the proposed FTC framework can maintain the input-to-state stability of the faulty NCSs. A flexible joint robot link example is included to show the efficiency of the proposed method.

Adaptive trajectory control and friction compensation of a flexible-link robot

An adaptive trajectory-tracking controller is developed for a single flexible-link manipulator with presence of friction in the joint and parametric uncertainties. The distributed-parameter dynamic modeling approach is used to design the controller. To eliminate large steady-state tracking error, an adaptive friction compensation technique is proposed based on general static friction model. Reduction of effects of data corruption by noise is obtained using a filtering technique. The global asymptotic stability is guaranteed using the Lyapunov stability theorem. The position tracking performance and link vibration attenuation is verified through experimental results. It also shows that the steady-state joint error is significantly eliminated and the noise effect in the control signal is efficiently reduced.

Model-based and model-free control of flexible-link robots: A comparison between representative methods

The paper presents a comparative study on representative methods for model-based and model-free control of flexible-link robots. Model-based techniques for the control of flexible-link robots can come up against limitations when an accurate model is unavailable, due to parameters uncertainty or truncation of high order vibration modes. On the other hand, several research papers argue that suitable model-free control methods result in satisfactory performance of flexible-link robots. In this paper two model-free approaches of flexible-link robot control are examined: (i) energy-based control, and (ii) neural adaptive control. The performance of the aforementioned methods is compared to the inverse dynamics model-based control, in a simulation case study for planar 2-DOF manipulators.

Flatness-based and energy-based control for distributed parameter robotic systems

The paper presents a comparative study between flatness-based control and energy-based control when applied to flexible link robots. Flatness-based control is an open-loop nonlinear control method which is suitable for differentially flat systems i.e. systems the behavior of which is determined by a finite collection of quantities, consisting of the flat output and its derivatives. On the other hand energy-based control is a closed-loop control method, which unlike the absence of an explicit mathematical model of the flexible-link dynamics can succeed satisfactory performance of the associated control loop. The performance of flatness-based control is tested against energy-based control through simulation experiments.

A recursive, numerically stable, and efficient simulation algorithm for serial robots with flexible links

A methodology for the formulation of dynamic equations of motion of a serial flexible-link manipulator using the decoupled natural orthogonal complement (DeNOC) matrices, introduced elsewhere for rigid bodies, is presented in this paper. First, the Euler Lagrange (EL) equations of motion of the system are written. Then using the equivalence of EL and Newton–Euler (NE) equations, and the DeNOC matrices associated with the velocity constraints of the connecting bodies, the analytical and recursive expressions for the matrices and vectors appearing in the independent dynamic equations of motion are obtained. The analytical expressions allow one to obtain a recursive forward dynamics algorithm not only for rigid body manipulators, as reported earlier, but also for the flexible body manipulators. The proposed simulation algorithm for the flexible link robots is shown to be computationally more efficient and numerically more stable than other algorithms present in the literature. Simulations, using the proposed algorithm, for a two link arm with each link flexible and a Space Shuttle Remote Manipulator System (SSRMS) are presented. Numerical stability aspects of the algorithms are investigated using various criteria, namely, the zero eigenvalue phenomenon, energy drift method, etc. Numerical example of a SSRMS is taken up to show the efficiency and stability of the proposed algorithm. Physical interpretations of many terms associated with dynamic equations of flexible links, namely, the mass matrix of a composite flexible body, inertia wrench of a flexible link, etc. are also presented.

Modeling and Control of Multi Flexible Link Robot: Using Classical and Intelligent controllers

Modeling and Control of Multi Flexible Link Robot: Using Classical and Intelligent controllers

Linear PID Composite Controller and its Tuning for Flexible Link Robots

This article presents both a proposal for a linear PID composite controller, composed of slow and fast sub-controllers, for flexible link robot systems modeled using the singular perturbation approach, and an efficient tuning method for the proposed controller structure. For the slow sub-controller, a PD controller with disturbance observer is used, which eventually takes on PID form. For the fast sub-controller, modal feedback PID control is utilized. The integral action in the controller removes steady state error in the joint caused by step disturbance and imperfect gravity compensation, although it also complicates the analysis. Effects of tuning the parameters of the controller to the closed loop response are investigated, and guidelines on the performance tuning for many flexible systems thus delivered. Through simulation and experiments, the adequacy and performance of the proposed method are verified.

Virtual Decomposition Control of a Planar Flexible-Link Robot

Use of flexible link robots is motivated by applications featuring lightweight or long arms. However, the control problem faces strong technical challenges resulting from the complex dynamics. In this paper, the virtual decomposition control (VDC) approach is applied for the first time to address the technical challenges of this thorny problem mainly resulting from the dynamic coupling effects among flexible links. In view of the VDC approach, the control problem of a multiple-flexible-link robot is no more complex than the control problem of individual flexible links subject to kinematics constraints. A planar beam governed by Euler-Bernoulli equation is studied as an example for simplicity. A possible extension to robots with multiple flexible links is theoretically possible by creating appropriate virtual power flows at the two ends of each beam. The validity of the theoretical results is verified by simulations with respect to two typical space systems in planar motion.

Modified PID Control of a Single-Link Flexible Robot

The use of flexible links in robots has become very common in different engineering fields. The issue of position control for flexible link manipulators has gained a lot of attention. Using the vibration signal originating from the motion of the flexible-link robot is one of the important methods used in controlling the tip position of the single-link arms. Compared with the common methods for controlling the base of the flexible arm, vibration feedback can improve the use of the flexible-link robot systems. In this paper a modified PID control (MPID) is proposed which depends only on vibration feedback to improve the response of the flexible arm without the massive need for measurements. The arm moves horizontally by a DC motor on its base while a tip payload is attached to the other end. A simulation for the system with both PD controller and the proposed MPID controller is performed. An experimental validation for the control of the single-link flexible arm is shown. The robustness of the proposed controller is examined by changing the loading condition at the tip of the flexible arm. The response results for the single-link flexible arm are presented with both the PI and MPID controller used. A study of the stability of the proposed MPID is carried out.

Comprehensive mathematical modelling of a lightweight flexible link robot manipulator

This paper deals with a comprehensive study of the application of the Timoshenko Beam Theory (TBT) concepts to the mathematical modelling of a planar lightweight single link flexible robot manipulator arm pinned at its actuated base and carrying a payload at its free end-point. The emphasis being essentially set on obtaining accurate and complete equations of the transversely vibrating motion that display the most relevant aspects of structural properties inherent to the modelled lightweight flexible link, two important damping mechanisms, internal structural viscoelasticity (Kelvin-Voigt damping) and external viscous air damping, have been included in addition to the TBT classical effects of cross section shear deformation and rotational inertia. Torsional, gravitational and longitudinal elongation effects have been neglected. Digital simulations are performed to show the free vibrational behaviour of the modelled robotic system.

Dynamic analysis of flexible-link and flexible-joint robots

The dynamic modeling and simulation of an N-flexible-link and N-flexible-joint robot is reported. Each flexible joint is modeled as a linearly elastic torsional spring and the approach of assumed modes is adopted to describe the deformation of the flexible-link. The complete governing equations of motion of the flexible-link-joint robots are derived via Kane’s method. An illustrative example is given to validate the algorithm presented and to show the effects of flexibility on the dynamics of robots.

EXPERIMENTS WITH POSITION AND INTERACTION CONTROL FOR A ROBOT WITH ONE FLEXIBLE LINK

One of the major drawbacks of flexible-link robot applications is its low tip precision, which is an essential characteristic for applications with position and interaction control with a contact surface. In this paper, position and interaction control strategies considering a rigid contact surface are applied to a flexible-link manipulator. The applied strategies are based on the closed-loop inverse kinematics algorithm (CLIK) to obtain the desired angular references to the joint position controller. The control schemes were previously tested by simulation and further implemented on a two degrees of mobility flexible-link planar robot. The obtained experimental results exhibit a good position and force tracking performance. The overall results reveal the successful implementation of the control architectures for a robot with one flexible link.

Control of a flexible manipulator within the framework of the Timoshenko beam model

A study is made of a controllable mechanical system in the form of a Timoshenko beam with a weight. The system models a flexible-link robot manipulator. A Galerkin approximation based on the solutions of the corresponding Sturm-Liouville problem is constructed for the partial differential equations of motion. Conditions of local controllability of the Galerkin approximation in the neighborhood of the system’s equilibrium state are established. The stabilizability of the equilibrium state is proved, and an explicit scheme for feedback control design is proposed

Impedance control of a two degree-of-freedom planar flexible link manipulator using singular perturbation theory

In this article, impedance control of a two link flexible link manipulators is addressed. The concept of impedance control of flexible link robots is rather new and is being addressed for the first time by the authors. Impedance Control provides a universal approach to the control of flexible robots, in both constrained and unconstrained maneuvers. The initial part of the paper concerns the use of Hamilton's principle to derive the mathematical equations governing the dynamics of joint angles, vibration of the flexible links and the constraining forces. The approximate elastic deformations are then derived by means of the Assumed-Mode-Method (AMM). Using the singular perturbation method, the dynamic of the manipulator is decomposed into fast and slow subsystems. The slow dynamic corresponds to the rigid manipulator and the fast dynamic is due to vibrations of flexible links. The sliding mode control (SMC) theory has been used as the means to achieve the 2nd order target impedance for the slow dynamics. A controller based on state feedback is also designed to stabilize the fast dynamics. The composite controller is constructed by using the slow and fast controllers. Simulation results for a 2-DOF robot in which only the 2nd link is flexible confirm that the controller performs remarkably well under various simulation conditions.

A coupled sliding-surface approach for the trajectory control of a flexible-link robot based on a distributed dynamic model

This paper proposes a coupled sliding-surface method for the design of trajectory control of a flexible-link robot. First, a sliding surface, coupling the joint velocity with the link bending moment at the joint, is defined based on the energy dynamics of the flexible link. Then a new trajectory–tracking control scheme is designed based on the coupled sliding surface, and extended to an adaptive scheme to cope with parametric uncertainties, where the Lyapunov stability theorem is used as a mathematical design tool. The proposed control is a collocated control designed based on a distributed-parameter dynamic model and hence is free from the so-called spillover instability. Using only the joint actuator, the proposed control guarantees stability throughout the entire trajectory control and asymptotic stability at desired goal positions. The proposed control is a PID control for the rigid dynamics and a proportional control for the flexible dynamics, with feed-forward and dynamics compensation. As a result, the proposed control guarantees zero steady-state joint-tracking errors even in the presence of low-frequency disturbances due to unavoidable mechanical inaccuracies in application. The theoretical results have also been proven by experimental studies.

10215 2リンク柔軟ロボットアームの運動と振動の制御((IV),OS15 知能ロボット)

The purpose of this study is to control simultaneously, motion and vibration of flexible 2-link robot arms. For this purpose, we had used modeling method called an 'extended reduced-order physical model (extended model)' to make a model of one-link flexible robot arm. The model of the flexible 2-link robot arms is made of a combination of the model of each link that is regarded as one link flexible robot arm. To connect each link, the constraint addition method is used. This is creating method of an equation of motion in multi-body systems. It is verified that the results of the simulation are effective for control of flexible 2-link robot arms.

RECURSIVE IDENTIFICATION OF PHYSICAL PARAMETERS IN A FLEXIBLE ROBOT ARM

ABSTRACTRecursive identification of a physically parameterized model of a single link flexible robot arm is considered. The parameters are estimated using a recursive prediction error method applied to a linear continuous time model structure and discrete time data. The algorithm is applied to real data from an industrial robot, and three important parameters are identified using only measurements of the motor angle. The experiments show that the particular parameter that is estimated will have big influence on the algorithm behavior.

Robot positioning of flexible-link manipulator using vision

Vision-aided flexible link robot positoning using the Camera Space Manipulation (CSM) method is developed. The primary motivation for this work is to use an autonomous vision-aided robotic system to pick-up and accurately move a flexible object that it encounters. The work consists of analytical and experimental investigation of the performance of CSM for a kinematic model of the PUMA manipulator with a flexible structure at the wrist which accounts for the gravitation. Trade-offs between camera view parameters and axial deflection model parameters were investigated. View parameter reestimation and maneuvering resulted a very accurate placement of the end-effector at the target.

A new trajectory control of a flexible-link robot based on a distributed-parameter dynamic model

The objective of this study is to develop a new trajectory-tracking control method, free from the so-called spillover instability, for a flexible-link robot. Based on a distributed-parameter dynamic model (a partial differential equation), a new moment-feedback trajectory-tracking control scheme is designed for a one-link flexible robot having a payload at the free end, in which zero geometric boundary conditions at the hub end and non-zero dynamic boundary conditions at the free end are taken into account. The proposed control is then extended to an adaptive scheme to cope with parametric uncertainties. The proposed control is stable for trajectory-tracking control and asymptotically stable at desired goal positions, which is proven by using the Lyapunov stability theorem. In addition, the proposed trajectory-tracking control, based on a distributed-parameter dynamic model, does not have the spillover problem. Furthermore, the control performance is guaranteed regardless of the magnitude of desired angle of rotation, which does not require any additional actuators such as piezoelectric actuators on the link and boundary force or moment actuators at the free end. The effectiveness of the proposed control has been shown by experiments.