Flexible Joint System Research Articles

An Adaptive Control Scheme Based on Non-Interference Nonlinearity Approximation for a Class of Nonlinear Cascaded Systems and Its Application to Flexible Joint Manipulators.

Control design for the nonlinear cascaded system is challenging due to its complicated system dynamics and system uncertainty, both of which can be considered some kind of system nonlinearity. In this paper, we propose a novel nonlinearity approximation scheme with a simplified structure, where the system nonlinearity is approximated by a steady component and an alternating component using only local tracking errors. The nonlinearity of each subsystem is estimated independently. On this basis, a model-free adaptive control for a class of nonlinear cascaded systems is proposed. A squared-error correction procedure is introduced to regulate the weight coefficients of the approximation components, which makes the whole adaptive system stable even with the unmodeled uncertainties. The effectiveness of the proposed controller is validated on a flexible joint system through numerical simulations and experiments. Simulation and experimental results show that the proposed controller can achieve better control performance than the radial basis function network control. Due to its simplicity and robustness, this method is suitable for engineering applications.

A Fused Deep Fuzzy Neural Network Controller and Its Application to Pneumatic Flexible Joint

With multilayered deep neural networks (DNNs) distinguished from the traditional single-layer neural networks (SNNs) by the depth, deep learning is a powerful paradigm possessing the capability of feature learning from big data. However, as a completely deterministic model, deep learning does not perform well in dealing with uncertain information and must be pretrained before being applied, which hinders the broad application of deep learning in real-time control. In this article, we introduce the knowledge-based fuzzy logic system (FLS) into deep learning and propose a fused deep fuzzy neural network (FDFNN) controller. The FDFNN controller derives the control signal from both deep fuzzy neural networks and the knowledge-based FLS. At the beginning of control, the FDFNN controller performs like a traditional fuzzy logic controller (FLC), which eliminates the pretraining procedure of deep learning. With another FLS providing supervised signal, the network weights of DFNN's hidden layers can be updated during the control process, which endows the FDFNN controller with online learning capability. A Lyapunov-based convergence analysis is conducted to guarantee the stability of the learning procedure. Both numerical simulations and real-world experiments validate that the proposed method effectively improves the real-time tracking control performance of a pneumatic flexible joint system.

Study on Collision Dynamics Model and Multi-Body Contact Forces of Ball Cage Flexible Joint Considering Clearance

Flexible joints are widely used in ‘soft’ touching and holding, and they represent the main component of ultra-short radius drilling tools. The analysis of contact and motion characteristics is an essential issue in the design and development stage of flexible joints. In this study, a collision dynamics model of a ball cage flexible joint (BCFJ), which is suitable for the characteristics of small clearance and large load, is established. The model contains a nonlinear stiffness coefficient and can describe the contact force between the ball key and the raceways. Moreover, the computational procedure for the dynamic analysis of BCFJ with clearance is established, and the dynamic simulation for collision and contact between ball, cage, outer race, and inner race was carried out. By numerical calculation, the variation of contact force on the five contact points of the ball key and ball cage is discussed, and the influence of ball cage clearance on contact force between ball key, ball seat, and ball cage is obtained. The results indicate that the effects of the ball cage clearance on the contact force cannot be ignored, which is the main cause for the vibration of the flexible joint system, and the amplitude of the contact force will gradually increase with the increase of the clearance. The proposed model and procedure can analyze the dynamic behavior of flexible joints with small clearance and large load, providing a basis for further research on wear prediction and safety evaluation of the BCFJ with clearance.

Dynamic Modeling of a Flexible-Link Flexible-Joint System with Tip Mass Considering Stiffening Effect

This paper presents the dynamic model of a flexible-link, flexible-joint manipulator system with a considerable stiffening effect of the flexible link. A gripper, along with tip mass, is attached at one end of the flexible link. By employing the extended Hamilton’s principle, a nonlinear governing equation of motion is derived along with several boundary constraints. Under the assumption of small deformation in free vibration, a simplified motion equation is deduced to determine the natural frequencies of the mechanical system. Four parameters of the system are selected to carry out the sensitivity study on frequency. The results show that the second frequency mainly depends on the mass of tip payload. Moreover, the third frequency is significantly affected by the moment inertia of tip payload. Regarding the constant angular motion, the finite element method is adopted to analyze the dynamic model by considering the stiffening effect. The frequency results are obtained which show a higher stiffness of the Single Flexible-link Flexible-joint (SFF) system with the angular velocity increasing. The influence of three factors (i.e., payload mass, length of the flexible link, and angular velocity) on the fundamental natural frequencies are discussed, which show instinct characteristics of the flexible manipulator system.

Fractional Order Linear Active Disturbance Rejection Control for Linear Flexible Joint System

A linear flexible joint system using fractional order linear active disturbance rejection control is studied in this paper. With this control scheme, the performance against disturbances, uncertainties, and attenuation is enhanced. Linear active disturbance rejection control (LADRC) is mainly based on an extended state observer (ESO) technology. A fractional integral (FOI) action is combined with the LADRC technique which proposes a hybrid control scheme like FO-LADRC. Incorporating this FOI action improves the robustness of the standard LADRC. The set-point tracking of the proposed FO-LADRC scheme is designed by Bode's ideal transfer function (BITF) based robust closed-loop concept, an appropriate pole placement method. The effectiveness of the proposed FO-LADRC scheme is illustrated through experimental results on the linear flexible joint system (LFJS). The results show the enhancement of the robustness with disturbance rejection. Furthermore, a comparative analysis is presented with the results obtained using the integer-order LADRC and FO-LADRC scheme.

Position Control of Rotary Flexible Joint System Using Adaptive Dynamic Inversion

This paper presents an adaptive generalized dynamic inversion (AGDI) control methodology to the problem of angular position tracking of the rotary flexible joint system while suppressing joint vibrations. The AGDI control is composed of an equivalent control, which is responsible to enforce the prescribed constraint dynamics that encompasses the control objectives and control expression is obtained by inverting the constraint dynamics using Moore–Penrose generalized inversion. Furthermore, robustness is achieved by integrating a switching (discontinuous) term based on the sliding mode control method. The sliding mode gain of the switching control law is made adaptive for chattering reduction and improved tracking capability. The performance of AGDI control is evaluated through both numerical simulation and experimental investigations executed on Quanser's rotary flexible joint system. Simulation and experimental results reveal that the AGDI control is quiet capable to achieve the desired response curves against set‐point tracking and disturbance rejection scenarios. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Experimental Application of Robust and Converse Dynamic Control for Rotary Flexible Joint Manipulator System

Performance evaluation of trajectory tracking for a rotary flexible joint system is demonstrated in this paper. The robust and converse dynamic (RCD) technique is proposed and implemented for this evaluation. This control methodology is of the left inversion type, i.e., the control inputs are obtained by means of plant output error feedback. RCD control encompasses the baseline inverse (BI) control and sliding mode control-based discontinuous control element. The baseline inverse controller enforces the prescribed servo (virtual) constraints that represent the control objectives. The control objectives of the baseline inverse controller are enclosed in the form of servo (virtual) constraints which are inverted using Moore–Penrose Generalized Inverse (MPGI) to solve for the baseline control law. To boost the robust attributes against parametric uncertainties and disturbances, a discontinuous control function is augmented with baseline controller such that semiglobal practical stability is guaranteed in the sense of Lyapunov. To exhibit the effectiveness of RCD control in terms of tracking performance, computer simulations are conducted in Simulink/Matlab environment. Furthermore, the practical implementation is also investigated through a real-time experiment on Quanser’s rotary flexible joint manipulator system. The experimental results obtained by RCD are compared to the conventional sliding mode and fractional-order control techniques.

Fractional data-driven control for a rotary flexible joint system

As one of the most promising topics in complex control processes, data-driven techniques have been widely used in numerous industrial sectors and have developed over the past two decades. In addition, the fractional-order controller has become more attractive in applied studies. In this article, a fractional integral control is implemented for a rotary flexible joint system. Moreover, an adjusted virtual reference feedback tuning (VRFT) technique is used to tune the fractional-order integrator. In this method, fractional integral control is designed based on state feedback control. Then, VRFT is adjusted and applied to the fractional integral controller. The effectiveness of the proposed adjusted VRFT method is discussed and presented through simulation and experimental results. The tracking performance of the rotary arm and the minimization of the vibration tip is evaluated based on the proposed method. In this article, the comparison of our proposed VRFT fractional scheme is made with the classical state feedback as well as a recently developed state feedback-based fractional order integral (SF-FOI) controller. The current investigations determine the performance improvement of our proposed scheme of comparable structure to the recent SF-FOI, with the introduction of the VRFT to the SF-FOI scheme.

Cascade Delayed Controller Design for a Class of Underactuated Systems

In this paper, a delayed control strategy for a class of nonlinear underactuated fourth-order systems is developed. The proposal is based on the implementation of the tangent linearization technique, differential flatness, and a study of the σ-stabilization of the characteristic equation of the closed-loop system. The tangent linearization technique allows obtaining a local controllability property for the analyzed class of systems. Also, it can reduce the complexity of the global control design, through the use of a cascade connection of two second-order controllers instead of designing a global controller of the fourth-order system. The stabilizing behavior of the delayed controller design is supported by the σ-stability criterion, which provides the controller parameter selection to reach the maximum exponential decay rate on the system response. To illustrate the efficiency of the theoretical results, the proposal is experimentally assessed in two cases of study: a flexible joint system and a pendubot.

DYNAMICS MODELING, SIMULATION, AND CONTROL OF ROBOTS WITH FLEXIBLE JOINTS AND FLEXIBLE LINKS

The effects of flexible joints on the dynamic response and control of robot are studied in this paper. Firstly, the spatial robot model consisting of $n$ flexible joints and $n$ flexible links is built, and the dynamic equations of the robot system are derived via the Lagrangian's equations. The tensile deformation, bending deformation, torsional deformation, and nonlinear coupling deformation of the flexible link are considered. Furthermore, the effects of the flexible joint are also considered in order to provide an important theoretical basis for the research of the vibration suppression and control of robots. The flexible joint is simplified as a linear torsion spring with damping, and the mass effect of the flexible joint is also considered in the model. Secondly, the dynamic simulations of the spatial manipulators are done to explore the effects of the joint stiffness and damping on the dynamic response of the robot system. The results show that as the stiffness coefficient increases, the amplitude of dynamic response of the flexible robot decreases, and the vibration frequency of the system becomes larger. As the damping coefficient increases, the dynamic response of the flexible robot decreases, and the dynamic response decays faster. The vibration of the flexible robot can be suppressed by adjusting the values of the stiffness and damping of the flexible joint. Finally, in order to study the effects of the flexibility of the joint on the control system, the rigid-joint manipulator and flexible-joint manipulator are made to move under the same circular motion. Then the joint torques of the two system are obtained respectively by solving the inverse dynamics equations, and the influence of the flexibility of the joint on the dynamics control is studied. The results show that the actuating torques required in the flexible-joint system are reduced compared to that required in the rigid-joint system.

Robust Experimental Study of Data-driven Optimal Control for an Underactuated Rotary Flexible Joint

As an important component of industrial robot, the motion control of rotary flexible joint (RFJ) system is of great significance, especially when the system has unmodeled dynamics or is seriously disturbed. This paper presents an experimental robustness study on a kind data-driven optimal control approach based on an underactuated rotary flexible joint system. The data-driven approach combines the off-policy optimal control algorithm and the popular integral reinforcement learning technique. Through literature review, we find that the key step of the control design lies in that it learns the optimal value function and control policy simultaneously from the input and output (I/O) data. However, the I/O data are often disturbed by the system uncertainty or environmental noise, and then it will indirectly affect the optimal control performance. To investigate the robustness of the data-driven optimal control approach, we artificially set different experimental scenarios and take numerous control experiments on a RFJ experimental setup. The experimental results show that the data-driven optimal control method is quite robust against the system uncertainties in terms of maintaining the stability and delivering satisfactory tracking performance, even when the uncertainty is not a small quantity. In addition, the disturbance originating from environmental noise has certain impact on the controlling of RFJ system, but as long as the noise power is not too large, the control algorithm can converge to a satisfactory result. Finally, we find that the probing signal up has strong influence to this control algorithm, which reminds us to be cautious when selecting the probing signal.

Numerical Analysis of Robotic Manipulator Subject to Mechanical Flexibility by Lagrangian Method

In this work, a systematic approach is presented for the development of dynamic equations of motion of a robot manipulator with mechanical flexibility. A simple structural lightweight rotating manipulator with joint elastic flexibility is considered for the mechanical flexibility study. The complexity of mathematical equations involved in mechanical flexibility is analyzed. The analytical approach helps the design for controls of flexible manipulator. A set of decoupled dynamic equations are derived incorporating both the structural and joint flexibility. The dynamic equations are compared with a detailed model, and the results are showing that equations are accurate for small joints. Also the results from the simulation show that in a flexible joint system, there is no rigid mode.

Cooperative tracking for high‐order non‐linear multi‐agent systems via adaptive control

This work studies the cooperative tracking problem for high-order non-linear multi-agent systems under a directed communication topology. The state and input of the leader are bounded. Distributed adaptive non-linear protocols based on the relative states of neighbouring agents are proposed, which can ensure the states of the followers converge to the state of the leader under the assumption that the directed communication topology contains a spanning tree with the root node being the leader agent. The distinctive features of this work are that the authors do not put Lipschitz restrictions (globally Lipschitz or Lipschitz-like condition) on non-linear functions and the adaptive protocols here can be implemented in a fully distributed fashion without using any global information (such as the knowledge of eigenvalue information of the Laplacian matrix associated with the whole communication topology). The effectiveness of the proposed distributed controller is illustrated by simulating a flexible joint system.

An experimental and numerical investigation of the effect of geometric parameters on the flexible joint nonlinear behavior for thrust vector control

Solid-propellant motors are used in a variety of space systems. This type of motor requires a guidance system, and a thrust vector control to function properly. One of the most effective methods for thrust vector control can be achieved by utilizing a flexible joint system. The flexible joint is the most widely used device in advanced nozzle system, such as space shuttle boosters, Vega, and Ariane 5. This setup includes multiple layers of elastomers to provide the flexibility, and a few metallic or composite rings as the scaffold of the system. In this study, a nonlinear simulation of the flexible joint is investigated using finite element method. These results are verified by construction and hydrostatic test, and there is a good consistency between predictions and empirical data. To the best of our knowledge, contemporary architecture does not provide the optimum result. Therefore, we propose delicately designed configuration, which can be mentored in a variety of motors, to improve the functionality of the flexible joints. A detailed study on the alteration of geometric parameters has been done to unravel its effect on the behavior of the flexible joint.

Rotary flexible joint control by fractional order controllers

In this paper, a fractional order control law is proposed and implemented for the evaluation of trajectory tracking performance of a rotary flexible-joint system. A state feedback based fractional integral control scheme is used in this proposed method. In this scheme, state feedback is responsible for stabilizing the system. The compensator, in series with the fractional integrator leads to obtain a similar closed-loop transient response like Bode’s ideal transfer function. The effectiveness of the proposed controller in tracking and being robust against parameter uncertainties is demonstrated through simulation. In addition, to show the usefulness of the proposed control scheme, the fractional controller is compared to an integer state feedback control by simulation and through experimentation on the Quanser’s rotary flexible-joint system.

Elastomeric Concrete Plug Joints: A New Durable Bridge Expansion Joint Design

Expansion joints are important components of bridges that accommodate the movements between deck spans that result from thermal loads, traffic loads, and other environmental factors. Experience shows that joints undergo premature deterioration on a regular basis, which leads to unexpected problems caused by leakage of water and other corrosive chemicals over the components of the superstructure and substructure, which in turn leads to premature deterioration of those components. The Virginia Department of Transportation (DOT) has spent millions of dollars over more than 50 years for repair and replacement of joints. Several types of closed joints have been developed and installed in the past three decades to combat this problem. Jointless details at piers and abutments have also been developed and installed in the past three decades to eliminate the need for joints and the associated deterioration. However, the issue persists. The Virginia DOT’s Structure and Bridge Division has developed a new design for a flexible joint system with bonded and debonded zones. An elastomeric concrete material acts as the load-bearing surface as well as the component that allows free expansion and contraction. This joint system has been installed in selected pilot bridges on secondary roads for observation. The performance of this joint system and the challenges faced in its development are discussed.

An Experimental Study of Robustness of Multi-Objective Optimal Sliding Mode Control

This paper presents an experimental study of robustness of multi-objective optimal sliding mode control, which is designed in a previous study. Inertial and stiffness uncertainties are introduced to a two degrees-of-freedom (DOF) under-actuated rotary flexible joint system. A randomly selected design from the Pareto set of multi-objective optimal sliding mode controls is used in the experiments. Three indices are introduced to evaluate the performance variation of the tracking control in the presence of uncertainties. We have found that the multi-objective optimal sliding mode control is quite robust against the inertial and stiffness uncertainties in terms of maintaining the stability and delivering satisfactory tracking performance as compared to the control of the nominal system, even when the uncertainty is not a small quantity. Furthermore, we have studied the effect of upper bounds of the model estimation error on the stability of the closed-loop system.

Flexible Plug Joint System with New Material

Up to now the common material used for flexible plug joints of bridges has been based on bituminous mixtures consisting of aggregates and elastomeric-modified binders. All existing national regulations and also the European Guideline for Expansion Joints ETAG 032 are restricting flexible plug joints to these traditional bituminous mixtures. All existing asphaltic mixtures are susceptible for plastic deformations at higher temperatures including rutting whereas they cause significant reaction forces at low temperatures. These properties limit the application of the traditional joints to areas with moderate climate. In practice asphaltic plug expansion joints also often fail in the intersection between adjacent pavement and joint, causing cracks and leakages. The new expansion joint system shows essential improvements in the intersection pavement/joint by mechanical means and uses a new material based on polyurethane, which does not show negative temperature affine properties and can be processed in cold condition. The new flexible plug joint system also enables new applications, both for a wider climatic range and more complicated geometries. Furthermore the new flexible plug joint allows for larger movements up to more than 100mm and addresses a longer design working life. As the new design is not covered by existing standards and verification methods in the first phase a comprehensive research had to executed after consultation with leading European experts from Germany, Switzerland and Austria. The paper covers reports on material and system tests executed during national and European approval procedures at several European testing institutes and shows examples of installation.

Delay-Induced Bogdanov–Takens Bifurcation and Dynamical Classifications in a Slow-Fast Flexible Joint System

A slow-fast delay-coupled flexible joint system is investigated in this paper. To understand the effects of time delay on the stability and oscillation of the manipulator, the geometric singular perturbation method is extended in dealing with delay differential equations. Bogdanov–Takens (BT) bifurcation of the fast subsystem is obtained, which leads to the existence of homoclinic orbits and is proved to be related to the formation of spiking. After the break of homoclinic orbits, Melnikov theory is introduced to predict the threshold curve indicating the occurrence of chaos. Numerical results show that with the increase of time delay, the stability of the system gets worse, and complicated oscillations including bursting, chaotic-bursting and complete chaos turn up. Besides, it is briefly summarized that the effect of the small parameter in the slow-fast system is to influence the convergence rate of solution trajectories, which is widely neglected in previous works.

A boundary layer sliding mode control design for chatter reduction using uncertainty and disturbance estimator

This paper proposes a new boundary layer sliding mode control design for chatter reduction. The control scheme uses a discontinuous control outside the boundary layer and switches over to uncertainty and disturbance estimator (UDE) based control inside. The problem of large initial control underlying the method of UDE, is also addressed with a modified sliding surface. The overall stability of the system is proved and the results are verified on an illustrative example and application to flexible joint system. The results show that the proposed method exhibits much better control performance than the baseline SMC using ‘sat’ function, for reduced chattering.