Multi-link Flexible Manipulators Research Articles

Nonlinear dynamic analysis of a multi-link manipulator with flexible links-joints mounted on a mobile platform

The present work theoretically demonstrates the dynamic analysis of a planar multi-link manipulator considering flexible links and joints mounted on a moving base. A nonlinear model of a multi-manipulator (N-links) has been developed accounting for an equivalent bi-directional mobile base. The nonlinear Euler-Bernoulli beam and spring-inertia/mass system have been introduced to demonstrate the flexibilities of links and joints, respectively. Modal analysis followed by trajectory analysis has been performed to investigate the behaviors of manipulator taking into account of accurate boundary conditions. Further, vibration characteristics, steady-state responses, and their stability at resonant situations due to joint motions and inertial coupling have been studied. Results of exploiting geometric and inertial coupling due to flexible arms on stability analysis of steady-state responses have been investigated and have been subsequently verified with the findings by directly solving the governing equations. Steady-state response characteristics to explore the dynamics of the multi-link manipulators under resonant states have been studied with the varying actuator mass, the flexibility of links, lifted payload, and joint parameters. The results thus obtained, deliver a useful insight into the position analysis and long-term behavior of multi-link flexible manipulators under harmonic hub-joint motions that shall further enable its proper vibration attenuation and control.

Robust Adaptive Dynamic Surface Control of Multi-link Flexible Joint Manipulator with Input Saturation

Robust Adaptive Dynamic Surface Control of Multi-link Flexible Joint Manipulator with Input Saturation

Static Deflection Compensation of Multi-Link Flexible Manipulators Under Gravity

The static deflection compensation method of a planar multi-link flexible manipulator is proposed using the feedback from inertial sensors mounted at the tip of each link. The proposed compensation technique is validated experimentally using a high-precision laser tracker. The proposed strategy is experimentally verified using a three-link flexible manipulator. A strategy to compensate for the centripetal and tangential acceleration induced on the accelerometer mounted on the rotating link is proposed for correct inclination estimation. The improvement in the inclination estimation using the proposed compensation technique is verified both in simulation and experimental studies.

Generalized Input Preshaping Vibration Control Approach for Multi-Link Flexible Manipulators using Machine Intelligence

In this study, an open-loop vibration control through parameter tuning method for multi-link flexible manipulators is generalized using the machine learning paradigm. The experimental studies part of the study consists of two stages. In the first stage, a decision tree model is created using the C4.5 algorithm to predict transient (during motion) and residual (stationary) vibration levels, and decision rules are derived from this model. The paper utilizes the C4.5 (decision tree) algorithm on a broad experimental dataset and compares its performance to that of other four well-known traditional machine learning algorithms (Naive Bayes (NB), Multilayer Perceptron (MLP), Support Vector Machine (SVM), and k-Nearest Neighbor (kNN)). The reason for choosing the decision tree method is that it has a transparent decision-making mechanism that works in tandem with the Explainable Artificial Intelligence (XAI) perspective. The experiments showed that the C4.5 algorithm achieved the best classification performance for predicting both root mean square (RMS) values of residual and transient vibrations (RMSres and RMStrans) with 92.25% and 83.75% accuracy rates. In the second stage, the generalized coefficients for use in parameter tuning were found by interpreting the rules obtained from this model. Furthermore, the rules derived from the tree in this study were applied to different systems. Control applications showed that an average of 93.9% and 84.5% suppression ratios in residual and transient vibrations could be achieved with this method. In addition, vibration settling times were shortened by an average of 41.4 seconds. Following the experimental studies, the simulation was used to compare results with the aid of Matlab Simscape-Multibody. The results prove that the rules obtained from the tree in this study generate successful results in several different systems.

Elastostatic Modeling of Multi-Link Flexible Manipulator Based on Two-Dimensional Dual-Triangle Tensegrity Mechanism

Abstract The paper deals with the elastostatic modeling of a multi-link flexible manipulator based on the two-dimensional (2D) dual-triangle tensegrity mechanism and its nonlinear behavior under external loading. The main attention is paid to the static equilibriums and the manipulator stiffness behavior under the loading for the arbitrary initial configuration. It was proved that there is a quasi-buckling phenomenon for this manipulator while the external loading is increasing. In the neighborhood of these configurations, the manipulator behavior was analyzed using the enhanced virtual joint method (VJM). A relevant simulation study confirmed the obtained theoretical results.

Modeling spatial multi-link flexible manipulator arms based on system modes

Modeling spatial multi-link flexible manipulator arms based on system modes

Dynamic Modeling of Planar Multi-Link Flexible Manipulators

A closed-form dynamic model of the planar multi-link flexible manipulator is presented. The assumed modes method is used with the Lagrangian formulation to obtain the dynamic equations of motion. Explicit equations of motion are derived for a three-link case assuming two modes of vibration for each link. The eigenvalue problem associated with the mass boundary conditions, which changes with the robot configuration and payload, is discussed. The time-domain simulation results and frequency-domain analysis of the dynamic model are presented to show the validity of the theoretical derivation.

Gain Tuning for High-Speed Vibration Control of a Multilink Flexible Manipulator Using Artificial Neural Network

Abstract Flexible manipulators are associated with merits such as low power consumption, use of small actuators, high-speed, and their low cost due to fewer materials’ requirements than their rigid counterparts. However, they suffer from link vibration which hinder the aforementioned merits from being realized. The limitations of link vibrations are time wastage, poor precision, and the possibility of failure due to vibration fatigue. This paper extends the vibration control mathematical foundation from a single link manipulator to a three-dimensional, two links flexible manipulator. The vibration control theory developed earlier feeds back a fraction of the link root strain to increase the system damping, thereby reducing the strain. This extension is supported by experimental results. Further improvements are proposed by tuning the right proportion of root strain to feed back, and the timing using artificial neural networks. The algorithm was implemented online in matlab interfaced with dSPACE for practical experiments. From the practical experiment done in consideration of a variable load, neural network tuned gains exhibited a better performance over those obtained using fixed feedback gains in terms of damping of both torsional and bending vibrations and tracking of joint angles.

Two-degree-of-freedom control of a multilink flexible manipulator using filtered inverse feedforward controller and strain feedback controller

This research paper presents a hybrid solution to both residue vibration and transient vibration as addressed using filtered inverse feedforward controller and strain feedback controller on a 3D 2 links flexible manipulator. The feedforward filtered inverse will minimize on the transient vibration due to sudden starting followed sudden stopping of the manipulator arm while the strain feedback will ensure rapid decay of the residue vibrations. Transient and residue vibrations stand in the way to reaping all the numerous advantages of the flexible manipulator. Transient vibration refers to vibrations resulting from sudden changes in the direction of the links while residue vibrations means that the arm takes too long to settle to do some useful work. Modelling of the manipulator and development of the inverse controller was carried out in Maple, MapleSim and MATLAB softwares. Experiments carried out in dSPACE control desk environment considering the manipulator without load and a case where a load of 100g was attached at the distal end of link 2.

Enhanced vibration control of a multilink flexible manipulator using filtered inverse controller

Flexible manipulators have numerous advantages such as lightweight, high operation speed, and low power consumption. However, they suffer from link vibrations, especially when operated at high speeds followed by sudden stops. This limitation has been addressed using techniques such as adaptive filters, adaptive strain feedback gain, state feedback control, etc. This article presents a filtered inverse controller for the mitigation of link vibrations in a multi-link flexible manipulator. To this end, the plant model, developed and linearized in Maple/Maplesim was inverted in MATLAB. The internal dynamics of the inverse model were stabilized using the state feedback technique. For safe and high-speed operations, the inverse model was augmented with a low pass filter to form the filtered inverse which was used as feedforward controller. Practical experiments were carried out in the dSPACE environment. Results show that filtered inverse controller yield not only faster response but relatively minimal link vibration when compared with the manipulator without vibration controller.

Stability analysis of nonlinear dynamic system with linear observer for a multilink flexible manipulator

In this paper, the stability of nonlinear dynamic system for a multilink flexible manipulator (MLFM) is investigated by designing of linear observer to construct a closed-loop system such that for all admissible parameter uncertainties, unknown nonlinearities, and exogenous disturbances input. In a Lagrangian approach, one closed-loop augmented system is unfolded and proven to be asymptotically stable in the mean square (ASMS) by utilizing a Lyapunov theory. Further, if the stability of dynamic closed-loop system of the manipulator is maintained, a desired linear observer will be obtained by solving several algebraic Riccati inequalities. Simulation studies are used to verify the effectiveness of the proposed approach.One of the main contributions of this work is in the derivation of dynamic system stability with a suitable linear observer for the MLFM, based on Lyapunov theory, which: (1) explains physical mechanism for flexible-link movements and dynamics in a Lagrangian approach and (2) sufficient and necessary conditions of the dynamic system stability are derived through seeking the optimal feasible solutions of several algebraic Riccati matrix inequalities.

Strain feedback gain tuning using neural network for the vibration control in a multilink flexible manipulator

Strain feedback gain tuning using neural network for the vibration control in a multilink flexible manipulator

A regularized approach for frictional impact dynamics of flexible multi-link manipulator arms considering the dynamic stiffening effect

The present study offers a regularized approach for multi-link flexible manipulator arms with frictional impacts. The complex risks of global dynamics simulation, which involve nonlinear frictional impact, stick–slip, and foreshortening deformation, as well as multi-scale numerical problems, were implemented. The system is described as an assembly of $n$ flexible links connected by $n$ rotary joints. The stretching, bending, and the torsional deformations of the flexible links were considered in addition to the flexibility and mass of the joint. The introduction of a contact force potential energy approach transformed the non-differentiable functions of the normal and tangential frictions into differentiable ones, thereby generating Lagrange equations for the general recursive formulation of the systems. A numerical simulation for the double pendulum and spatial manipulator arms collision with targets was generated, thereby allowing the calculation of the frequent switching between the stick/sliding and forward/backward sliding. Several normal contact and friction models were adopted, and their corresponding results were analyzed. The generated ordinary differential equations of the proposed smoothed algorithm were solved using explicit solvers to verify any improvements in the global computational efficiency of the frictional collision dynamics for the flexible manipulator arms.

Decentralized vibration control of a multi-link flexible robotic manipulator using smart piezoelectric transducers

The work in this paper is aimed to investigate the use of a decentralized control system for suppressing vibration of a multi-link flexible robotic manipulator using embedded smart piezoelectric transducers. To achieve this, a non-linear dynamic model of a flexible robotic manipulator with smart piezoelectric actuators/sensors, is developed based on the co-rotational finite element method. The method incorporates multiple co-ordinate (co-rotational) systems which rotate and translate with each element, so that the geometric non-linearity present in rotating manipulator system can be dealt with efficiently. The placement of piezoelectric actuators and sensors over the flexible links are considered for the application of decentralized control system. A numerical study shows that the developed co-rotational finite element method can be utilized to investigate the piezoelectric actuator/sensor placement and vibration control performances for a multi-link flexible manipulator undertaking complicated motion.

Dynamic modeling of multi-flexible-link planar manipulators using curvature–based finite element method

In conventional displacement-based finite element formulation, the nodal transverse deflections and slopes of a beam element are used to approximate its transverse deflection distribution. In this paper, a curvature-based finite element formulation is presented for dynamic modeling of planar multi-link flexible manipulators. This formulation approximates the curvature distribution of the Euler-Bernoulli beam element by using its nodal curvatures. Therefore, in the curvature-based finite element formulation, fewer numbers of total elastic degrees of freedom for the system are needed. In addition, while the displacement-based finite element formulation yields discontinuous bending stresses at the inter-element nodes, this modeling provides continuous bending stress at those nodes. The proposed modeling will be verified and the dynamic behavior of the flexible planar manipulators will be studied.

Vibration analysis of a planar multilink manipulator using a reduced-order matrix formulation

The main scope of this paper is both to provide an efficient formulation for deriving natural frequencies and mode shapes of a multilink flexible manipulator in an arbitrary posture and discuss the importance of introducing axial deformations along with transversal ones in the same postures. The free vibration problem is solved through a global transfer matrix formulation, which is obtained by opportunely assembling the transfer matrices of links and joints associated with the desired configuration of the robot. The formulation has been chosen in order to keep the same matrix order of the problem, regardless of the number of links of the manipulator. Manipulator links are treated as Timoshenko beams by accounting for both axial loading capability and mass/inertial effects due to the joint actuators. Numerical comparisons between the solutions derived herein and those obtained through existing formulations highlight the importance of the proposed model within the frame of multilink flexible manipulators. A forced vibration analysis is finally presented for a two-link manipulator.

Dynamic Modeling of Planar Flexible Multi-Link Manipulators with Accounting for both Link Foreshortening and Link Material Damping

In order to investigate dynamic performance of flexible multi-link manipulators more exactly, establishing the dynamic model with accounting for link foreshortening and link material damping is needed. In this paper, a new dynamic model for planar flexible multi-link manipulators is established by using Lagrange approach. Both link foreshortening and link material damping are accounted for in this model. As a case simulation, this model is applied to a planar flexible two-link manipulator with a tip mass, and the motion responses of the manipulator are obtained using Gear method.

Vibration Analysis of Multilink Manipulators Based on Timoshenko Beam Theory

Timoshenko's theory is adopted in order to accurately describe the freely vibrating dynamics of a multilink flexible manipulator. It is herein presented an analytical modelling strategy that extends previous works through a more refined model which accounts for elastic complicating effects along with lumped inertial loads which are typically mounted on joints of manipulators; in this regard, more accurate results are provided. The eigenproblem is presented from an analytical point of view through a matrix formulation, thus providing an essentially closed formula. Apart from the limitations of the implementing calculator, the formulation can take into account an arbitrary number of links in an arbitrary settled configuration, thus allowing relevant analytical analysis and avoiding the need to recur to nonimmediate numerical schemes. Once the analytical model is introduced, solutions are compared to both those achieved by previous models and those obtained by a finite elements method.

Maneuver control of the multilink flexible manipulators

In this paper a new controller for the end-effector trajectory tracking (EETT) of multilink flexible manipulators (MLFM) is introduced. The new controller is derived utilizing the concept of the integral manifold of the singularly perturbed differential equations. Based on the new controller, to reduce the end-effector trajectory tracking error, a corrective term of order ε 2 has to be added to the computed torque command (CTC) of the rigid link counterpart of the MLFM, where the parameter ε = 1 / 2 π f and f is the smallest non-zero natural frequency (first natural frequency) of the MLFM in the specified range of operation of the manipulator. The implementation of the new controller does not require measurement of the time derivative of the links’ lateral deflections, which may be practically impossible. This is achieved since the time derivative of the links’ lateral deflections is estimated by using an observer, which is designed based on the gain-scheduling technique. The stability of the proposed controller is proven using the Lyapunov criterion. Simulation results showed the effectiveness of the new controller. One of the main contributions of this work is in the derivation of a new EETT controller for the MLFM, based on the integral manifold concept, which: (1) requires the fewest corrective terms in addition to the CTC and (2) its calculation effort is minimized.

On a Control of Multi-link Flexible Manipulators Using Sliding Mode Observer and Its Numerical Simulations

On a Control of Multi-link Flexible Manipulators Using Sliding Mode Observer and Its Numerical Simulations