Two-link Manipulator Research Articles

Neural Network-Based Hybrid Position/Force Tracking Control for Robotic Systems Without Velocity Measurement

In this paper, a hybrid position/force tracking control scheme based on neural network observer is proposed for robotic systems with uncertain parameters and external disturbances. First, an observer based on neural network is designed to estimate joint velocities. Then, a neural network-based adaptive hybrid position/force controller is proposed based on the observed joint velocities. By using strict positive real method and Lyapunov stability theory, it is proved that all the signals of the closed-loop system are ultimately uniformly bounded. Finally, the simulation tests on a two-link manipulator are conducted. The simulation results show the feasibility and effectiveness of the control scheme.

Use of memristive chaotic signal as a desired trajectory for a two-link flexible manipulator using contraction theory based on a composite control technique

Flexible manipulators are being considered as bench mark control problem in the field of nonlinear dynamics. Many of their inherent advantages create challenges while dealing with the dynamics. Tracking control and vibration suppression are two main control problems considered. In this paper a composite controller is designed for the memristive chaotic system signal as trajectory tracking control of a two-link flexible robot manipulator. The dynamics of the flexible manipulator is modelled by using assumed modes method and divided into two subsystems using the singular perturbation technique. The subsystems are called as the slow subsystem involving rigid dynamics of the manipulator and the fast sub-system which incorporates flexible dynamics of the manipulator. Separate control techniques are designed for each subsystem. Contraction theory based controllers are designed for the slow sub-system and fast subsystem for fast trajectory tracking of signal of a memristive chaotic system and quick suppression of the link deflections. The simulation results confirm the better performances of the proposed composite technique.

Overcoming the Underestimation and Overestimation Problems in Adaptive Sliding Mode Control

Underestimation and overestimation problems are commonly observed in conventional adaptive sliding mode control (ASMC). These problems refer to the fact that the adaptive controller gain unnecessarily increases when the states are approaching the sliding surface (overestimation) or improperly decreases when the states are getting far from it (underestimation). In this paper, we propose a novel ASMC strategy that overcomes such issues. In contrast to the state of the art, the proposed strategy is effective even when an a priori constant bound on the uncertainty cannot be imposed. Comparative results using a two-link manipulator demonstrate improved performance as compared to the conventional ASMC. Experimental results on a biped robot confirm the effectiveness and robustness of the proposed method under various practical uncertainties.

Sliding Mode Boundary Control for a Planar Two-link Rigid-flexible Manipulator with Input Disturbances

This paper investigates the robust control problem for a planar two-link rigid-flexible coupling manipulator, whose input torques are influenced by bounded disturbances. A nonlinear partial differential equation (PDE) model which only contains measurable states in the boundary conditions is developed and based on this model, and a sliding mode control (SMC) scheme is proposed to realize joint angles reaching desired value, flexible vibration suppression and anti-interference. To overcome the difficulties brought by the inherent nonlinearity of the PDE and controller, the existence and uniqueness of the solution for the closed-loop system are proven by the Galerkin approximation sequences. The numerical simulations demonstrate the validity and effectiveness of our control design.

Dynamic modeling and extended bifurcation analysis of flexible-link manipulator

In this article, the nonlinear dynamic analysis of a flexible-link manipulator is presented. Especially, the possibility of chaos occurrence in the system dynamic model is investigated. Upon the occurrence of chaos, the system dynamical behavior becomes unpredictable which in turn brings about uncertainty and irregularity in the system motion. The importance of this investigation is pronounced in similar systems such as double pendulum and single-link flexible manipulator. What makes this study distinct from previous ones is the increase in the number of links as well as the changing the bifurcation parameters from system mechanical parameters to force and torque inputs. To this aim, the motion equations of the N-link robot, which are derived with the aid of the recursive Gibbs-Appell formulation and the assumed modes method, are used. In the end, the equations of motion are developed for a two-link flexible manipulator, and its nonlinear dynamical behavior is analyzed via numerical integration of discrete equations. The results are presented in the form of bifurcation diagrams (for variation of torque amplitude), time histories, phase-plane portraits, Poincaré sections, and fast Fourier transforms. The outcomes indicate that when there is no offset, the decrease in damping results in chaotic generalized modal coordinates. In addition, as the excitation frequency decreases from 2π to π, a limiting amplitude is created at 0.35 before which the behavior of generalized rigid and modal coordinates is different, while this behavior has more similarity after this point. An experimental setup is also used to check the torques as the system input.

Robust identification of nonlinear time-delay system in state-space form

This paper puts forward a robust identification solution for nonlinear time-delay state-space model (NDSSM) with contaminated measurements. To enhance the robustness of the developed method for outliers, the heavy-tailed Laplace distribution is employed to describe and protect the output measurement process. The undetermined time-delay is considered to be uniformly distributed and the boundary of it is known as a priori. In the developed solution, the uncertain time-delay is treated as a latent process variable and it is iteratively calculated with the expectation–maximization (EM) algorithm. The EM algorithm is actually an iterative optimization algorithm and it is effective for the hidden variable problems. The particle filter is introduced to numerically approximate the cost function (Q-function) in the EM algorithm since it is difficult to calculate directly. The efficacy of the developed solution is evaluated via a numerical test and a two-link robotic manipulator.

Robust state and fault estimation for non‐linear stochastic systems with unknown disturbances: a multi‐step delayed solution

A study on the simultaneous state and fault estimation for non-linear discrete-time stochastic systems subjected to unknown disturbances is presented. The augmented system approach, system reformation using the state-dependent coefficient (SDC) factorisation, and unknown input filtering method are integrated to simultaneously estimate the state of the system and actuator and/or sensor faults. To achieve this aim, the non-linear system with faults and unknown disturbances is first transformed into an equivalent augmented system by using delayed measurements and the SDC factorisation. Next, within the SDC factorised linear-like augmented system and inspired by the robust two-stage Kalman filter, a novel multi-step estimator named as the robust simultaneous state and fault estimator is proposed to yield a robust state and fault estimation with a multi-step delay. Moreover, a novel real-time state estimator is designed based on the proposed hybrid fault reconstruction model in order to address the inherent time-delay problem. A comparison of the performance of the proposed filters with those of existing methods from the literature is demonstrated using a non-linear two-link manipulator system with friction forces acting simultaneously at each joint.

Design of an Optimal Fuzzy Controller of an Under-Actuated Manipulator Based on Teaching-Learning-Based Optimization

Abstract In this paper, an optimal fuzzy controller based on the Teaching-Learning-Based Optimization (TLBO) algorithm has been presented for the stabilization of a two-link planar horizontal under-actuated manipulator with two revolute (2R) joints. For the considered fuzzy control method, a singleton fuzzifier, a centre average defuzzifier and a product inference engine have been used. The TLBO algorithm has been implemented for searching the optimum parameters of the fuzzy controller with consideration of time integral of the absolute error of the state variables as the objective function. The proposed control method has been utilized for the 2R under-actuated manipulator with the second passive joint wherein the model moves in the horizontal plane and friction forces have been considered. Simulation results of the offered control method have been illustrated for the stabilization of the considered robot system. Moreover, for different initial conditions, the effectiveness and the robustness of the mentioned strategy have been challenged.

Adaptive Motion Planning for a Collaborative Robot Based on Prediction Uncertainty to Enhance Human Safety and Work Efficiency

Industrial robots are expected to share the same workspace with human workers and work in cooperation with humans to improve the productivity and maintain the quality of products. In this situation, the worker's safety and work-time efficiency must be enhanced simultaneously. In this paper, we extend a task scheduling system proposed in the previous work by installing an online trajectory generation system. On the basis of the probabilistic prediction of the worker's motion and the receding horizon scheme for the trajectory planning, the proposed motion planning system calculates an optimal trajectory that realizes collision avoidance and the reduction of waste time simultaneously. Moreover, the proposed system plans the robot's trajectory adaptively based on updated predictions and its uncertainty to deal not only with the regular behavior of workers but also with their irregular behavior. We apply the proposed system to an assembly process where a two-link planar manipulator supports a worker by delivering parts and tools. After implementing the proposed system, we experimentally evaluate the effectiveness of the adaptive motion planning system.

Development of the concept of control system work for plaster works based on neural network

Preparation of mortar, its submission to the place of work and application to the surface is efficiently carried out by means of automated mechanical systems in tandem with concrete pumps combined with plastering machine units. The technical consistency and competitiveness of robotic plastering stations largely depends on the accepted kinematic models of the plastering robot being developed and the development of advanced control systems based on them. Simple kinematic circuits generate simple design solutions that are quickly prototyped and of low cost, but because of their design imperfection, these solutions are commonly used for limited production processes, have low precision and primitive control systems, which do not allow for deep automation production. Complex kinematic circuits of robots allow them to be used as a versatile tool in many stages of construction, but such design solutions require the creation of sophisticated control systems.The use of a neural network allows the architecture of the robot control system to be compromised, making it a versatile robot for performing various technological procedures, but requires a clear algorithm for describing the mathematical model of work and its training.This study proposes a mathematical model of a neural network based on a sigmoidal activation function for a two-link manipulator.

RBFNN-based nonsingular fast terminal sliding mode control for robotic manipulators including actuator dynamics

To achieve robust finite-time trajectory tracking control, this paper proposes a novel neural-network-based nonsingular fast terminal sliding mode (NFTSM) control strategy for n-link robotic manipulators including actuator dynamics, subject to the model uncertainty and external disturbances. The suggested NFTSM control method can improve the finite-time convergence rate of system states, owing to the introduction of nonlinear item on the sliding surface. In addition, the singular problem is settled via introducing a saturation function into the control signal. In this control scheme, the precise dynamics of the robot system are unknown completely. Considering that the radial basis function neural network (RBFNN) has a fast study convergence speed and great approximation ability, three RBFNNs are utilized to estimate the manipulator-actuator dynamic parameters, along with an adaptive weight update law. Meanwhile, by designing robust control items, the approximation errors of RBFNNs are compensated, and the external disturbances are suppressed. Then, the finite-time stability of the controlled system is proved by Lyapunov stability theory. Finally, the proposed control approach is employed to a two-link robotic manipulator. The simulation results verified the effectiveness of the proposed control method.

Boundary Control for a Rigid-Flexible Manipulator With Input Constraints Based on Ordinary Differential Equations–Partial Differential Equations Model

In this paper, the dynamic model is established for the two-link rigid-flexible manipulator, which is represented by nonlinear ordinary differential equations–partial differential equations (ODEs–PDEs). Based on the nonlinear ODE–PDE model, the boundary control strategy is designed to drive the manipulator to follow a given trajectory and eliminate the vibration simultaneously. Considering actuators saturation, smooth hyperbolic tangent function is introduced for dealing with control input constraints problem. It has been rigorously proved that the nonlinear closed-loop system is asymptotically stable by using LaSalle's invariance principle. Simulation results show that the proposed controller is effective.

Polyvinylidene fluoride/sulfonated graphene oxide blend membrane coated\xa0with polypyrrole/platinum electrode for ionic polymer metal composite actuator applications

A polyvinylidene fluoride, sulfonated graphene oxide composite membrane coated with polypyrrole (Ppy) and platinum metal (Pt) was fabricated. The Fourier-transform infrared (FTIR) spectroscopic analysis was done to analyze the functional groups present in the composite material. Deposition of PPy/Pt electrode and surface morphology of PVDF/SGO/Pt/PPy was confirmed by scanning electron microscopic (SEM) images. The capacity of ion exchange and proton conductivity (PC) of PVDF/SGO/Pt/PPy were 1.4 meq g−1 of dry ion exchanger and 4.251 × 10−2 S cm−1, respectively. A two-link flexible manipulator based on the fabricated ionic polymer metal composite (IPMC) membranes was also developed where the electromechanical behaviour of a polymer-based actuator provides an important step in robotics applications.

Adaptive disturbance cancellation for a class of MIMO nonlinear Euler–Lagrange systems under input saturation

In this paper, we develop an adaptive disturbance cancellation tracking control strategy with the asymptotically converging output tracking errors for a class of multi-input and multi-output (MIMO) nonlinear Euler–Lagrange systems with unknown time-varying disturbances under input saturation. The unknown time-varying disturbances are firstly described as the outputs of a multivariate linear unknown exosystem with unavailable regressor and regression parameter. To estimate the unavailable regressor, an observer is constructed, such that the disturbance cancellation is converted to an adaptive control problem. An auxiliary dynamic system (ADS) is employed to mitigate the effect of the input saturation. Then, a robust adaptive tracking control law is proposed incorporating the above and a robustifying term into the adaptive vectorial backstepping design tool. It is proven theoretically that the asymptotic convergence of the output tracking errors of Euler–Lagrange systems is achieved, while the uniform ultimate boundedness of the remaining signals of the resulting closed-loop control system is guaranteed. Simulation and comparison results on a two-link rigid manipulator and a scale model ship are presented to illustrate the effectiveness and the superiority of the proposed control scheme.

Backstepping based adaptive finite-time tracking control of manipulator systems with uncertain parameters and unknown backlash

In this paper, the adaptive finite-time command filtered backstepping control is investigated for uncertain manipulator systems with unknown backlash. The finite-time command filters, virtual control signal, adaptive update law and error compensation mechanism are designed respectively, which can deal with the computation complexity problem of conventional backstepping, and guarantee that the joint position tracking error reaches to a sufficiently small region including the origin in finite time although the uncertain parameters and unknown backlash are existed. The dynamic models of a two-link robot manipulator and the PUMA 560 manipulator are applied in simulation to verify the effectiveness of the given control strategy.

Bipartite Consensus in Networked Euler–Lagrange Systems With Uncertain Parameters Under a Cooperation-Competition Network Topology

This letter studies the bipartite consensus control problem of networked Euler–Lagrange systems under directed network topology with the coexistence of positive and negative interaction weights. An adaptive bipartite consensus control law is proposed for solving bipartite consensus in networked Euler–Lagrange systems with uncertain parameters. By exploiting the specific structure of the Laplacian matrix associated with cooperation-competition networks, we introduce a novel coordinate transformation based on which the corresponding convergence analysis of closed-loop controlled systems is provided. Finally, simulations conducted on a network composed by seven two-link revolute joint manipulators are provided to illustrate the theoretical results.

Optimal Point-to-Point Path Planning of Manipulator by Using Vibration Damping Optimization Algorithm and Game Theory Method

Abstract In this article, designing an optimal path in two forms of point-to-point is investigated. In the first case, the optimal path planning and determination of the load-carrying capacity of a manipulator in a point-to-point and open-loop case is studied. In the second case, the path-planning problem and maximum load-carrying capacity of manipulators are investigated in a closed-loop point-to-point case. Designing an optimal path in a point-to-point and open-loop case is studied using a vibration damping optimization algorithm. In order to design the controller in the closed-loop case, the game theory approach, which is a generalized form of nonlinear optimum control, is used. In this method, in addition to considering the dynamics of the manipulator, the dynamics of the driving system are also considered. Moreover, the method is able to investigate the effects of the disturbances introduced by the driving system. In the proposed method, the voltage of engines and system disturbances are considered as the players. The optimum strategy of players is calculated based on the Nash equilibrium strategy, and the optimum value of control inputs is determined using an iterative algorithm based on solving Riccati equations. The problem of designing a controller is proposed in the form of a differential game problem with zero sum. The results indicate that for a fixed-base two-link manipulator, the design of the controller based on a differential game made it possible to control the effect of system disturbances so that the load-carrying capacity experienced small changes compared to the desired case and without system disturbances resulting from the data obtained from point-to-point and open-loop cases.

Robotic manipulator control based on an optimal fractional-order fuzzy PID approach: SiL real-time simulation

Robotic manipulator control is a challenging task due to its nonlinear, interacting multi-input–multi-output dynamics. In this paper, we proposed an optimal robust fractional-order fuzzy PID controller based on multi-objective particle swarm optimization (MOPSO) algorithm for a two-link robotic manipulator. In order to minimize position and trajectory-tracking error, MOPSO finds the optimal parameters of fuzzy membership functions and order of the fractional operators. To show the effectiveness of the proposed controller, the software-in-the-loop real-time simulation is executed, and the results are compared to conventional fuzzy PID, fractional-order PID, and linear PID controllers.

Identification of nonlinear state-space time-delay system

PurposeThis paper aims to investigate an identification strategy for the nonlinear state-space model (SSM) in the presence of an unknown output time-delay. The equations to estimate the unknown model parameters and output time-delay are derived simultaneously in the proposed strategy.Design/methodology/approachThe unknown integer-valued time-delay is processed as a latent variable which is uniformly distributed in a priori known range. The estimations of the unknown time-delay and model parameters are both realized using the Expectation-Maximization (EM) algorithm, which has a good performance in dealing with latent variable issues. Moreover, the particle filter (PF) with an unknown time-delay is introduced to calculated the Q-function of the EM algorithm.FindingsAlthough amounts of effective approaches for nonlinear SSM identification have been developed in the literature, the problem of time-delay is not considered in most of them. The time-delay is commonly existed in industrial scenario and it could cause extra difficulties for industrial process modeling. The problem of unknown output time-delay is considered in this paper, and the validity of the proposed approach is demonstrated through the numerical example and a two-link manipulator system.Originality/valueThe novel approach to identify the nonlinear SSM in the presence of an unknown output time-delay with EM algorithm is put forward in this work.

L-Stable Method for Differential-Algebraic Equations of Multibody System Dynamics

An L-stable method over time intervals for differential-algebraic equations (DAEs) of multibody system dynamics is presented in this paper. The solution format is established based on equidistant nodes and nonequidistant nodes such as Chebyshev nodes and Legendre nodes. Based on Ehle’s theorem and conjecture, the unknown matrix and vector in the L-stable solution formula are obtained by comparison with Pade approximation. Newton iteration method is used during the solution process. Taking the planar two-link manipulator system as an example, the results of L-stable method presented are compared for different number of nodes in the time interval and the step size in the simulation, and also compared with the classic Runge-Kutta method, A-stable method, Radau IA, Radau IIA, and Lobatto IIIC methods. The results show that the method has the advantages of good stability and high precision and is suitable for multibody system dynamics simulation under long-term conditions.