Flexible Robot Manipulator Research Articles

Adaptive Neural Command Filtered Tracking Control for Flexible Robotic Manipulator With Input Dead-Zone

In this paper, an adaptive neural network (NN) command filtered tracking control method is developed for a flexible robotic manipulator with dead-zone input. To deal with the input dead-zone nonlinearity, it is viewed as a combination of a linear part and bounded disturbance-like term. The Neural networks (NNs) are used to estimate the uncertain nonlinearities appeared in the control system. By using the command filter technique, the problem of `explosion of complexity' is overcome. The proposed controller guarantees that all the closed-loop signals are bounded and the system output can track the given reference signal. The simulation results are provided to demonstrate the effectiveness of the proposed controller.

Transient probabilistic design of flexible multibody system using a dynamic fuzzy neural network method with distributed collaborative strategy

To improve the efficiency and accuracy of transient probabilistic analysis of flexible multibody systems, a dynamic fuzzy neural network method-based distributed collaborative strategy is proposed by integrating extremum response surface method and fuzzy neural network. Distributed collaborative dynamic fuzzy neural network method is mathematically modeled and derived by considering the high nonlinearity, strong coupling, and multicomponent characteristics of a flexible multibody system. The proposed method is demonstrated to perform the transient probabilistic analysis of a two-link flexible robot manipulator. We obtain the distributional characteristics, reliability degree, and sensitivity degree of robot manipulator, which are useful for the effective design of robot manipulator. By comparing the full-scale method, extremum response surface method, dynamic fuzzy neural network method, and distributed collaborative dynamic fuzzy neural network method, we find that the distributed collaborative dynamic fuzzy neural network method can be used to perform the transient probabilistic analysis of the robot manipulator and improve the computational efficiency while maintaining a good accuracy. Moreover, this study offers a useful insight for the reliability-based design optimization of flexible multibody systems, and enriches the field of mechanical reliability theory as well.

Controlling the Non-parametric Modeling of Double Link Flexible Robotic Manipulator using Hybrid PID Tuned by PType ILA.

Utilization of robotic manipulator with multi-link structure encompasses a great influence in most of the present industries. However, controlling the motion of multi-link manipulator has become a troublesome errand particularly once the flexible structure is employed. As of now, the framework utilizes the complicated arithmetic to resolve desired hub angle with the coupling result and vibration within the framework. Hence, this research aims to develop a dynamic system and controller for double-link flexible robotics manipulator (DLFRM) with the enhancement on hub angle position and vibration concealment. The research utilised neural network because the model estimation supported NARX model structure. In the controllers’ development, this research focuses on self-tuning controller. P-Type iterative learning algorithm (ILA) control theme was enforced to adapt the controller parameters to fulfill the required performances once there is changes to the system. The hybrid of proportional-integral-derivate (PID) controller was developed for hub motion and end-point vibration suppression of every link respectively. The controllers were tested in MATLAB/Simulink simulation setting. The performance of the controller was compared with the fixed hybrid PID-PID controller in term of input tracking and vibration concealment. The results indicated that the proposed controller was effective to maneuver the double-link flexible robotic manipulator to the specified position with reduction of the vibration at the tip of the DLFRM structure.

A model-based velocity controller for chaotization of flexible joint robot manipulators

This article presents a model-based velocity controller able to induce a chaotic motion on n-degrees of freedom flexible joint robot manipulators. The proposed controller allows the velocity link vector of a robot manipulator to track an arbitrary, chaotic reference vector field. A rigorous theoretical analysis based on Lyapunov’s theory is used to prove the asymptotic stability of the tracking error signals when using the proposed controller, which implies that a chaotic motion is induced to the robotic system. Experimental results are provided using a flexible joint robot manipulator of two degrees of freedom. Finally, by using Poincaré maps and Lyapunov exponents, it is shown that the behavior exhibited by the robot joint positions is chaotic.

High resolution flexible 4-PPR U-base planar parallel microstage robotic manipulator

Numerous compliant manipulators, actuated by voice coil, have been developed and are widely used for micro/nano-manipulation. One of the greatest difficulties lies in optimizing the design with consideration of various parameters like high stiffness, large amplification, higher precise tracking, and highly accurate positioning. A modular and compact planar 3PPR+PPR parallel micro positioning platform is presented (3-degrees of freedom) and its symmetric design equips it with various advantages. The parallel-kinematic arrangement of the manipulator with optimum sizes results in high rigidity and greater load carrying capacities. The proposed planar parallel compliant manipulator possesses higher structural rigidity, better amplification, higher accuracy and precision trajectory tracking ability and positioning. The present work is on a flexure-based micro positioning stage with 3 degrees-of-freedom, incorporating compliant double parallelogram mechanism. An innovative idea of multistage compliant compound parallelogram mechanism is proposed here for the development of a three degrees-of-freedom (X-Y- θ) micro-positioning system, with the range of motion larger than 10 mm. The established models and the performance of the proposed stage are verified through finite-element analysis (FEA).

Hybrid Control Method for a Flexible Manipulator

This paper proposes an inverse adaptive network based fuzzy inference system (ANFIS) to control the nonlinearity, wide variations in loads, and uncertain disturbance of a single-link flexible robot manipulator. To reduce the end-point vibration of a single-link flexible manipulator without sacrificing its speed of response is a very important problem as the motion become faster. An inverse-ANFIS with feedback and feed-forward method is used to optimize parameters of the controller for flexible dynamic of the systems. The system performance with the controllers is presented and analyzed in the time and frequency domains. Moreover, it concentrates on the system from input torque to hub-angle, hub-velocity and end-point acceleration outputs. The results of the simulation test prove that the proposed are effective and suitable.

Dynamic Analysis of Flexible Robotic Manipulators Constructed of Functionally Graded Materials

In this paper, the motion equations of n-flexible-link robotic manipulators constructed of functionally graded materials, whose properties vary continuously along the axial direction and also along the thickness, are investigated. Gibbs–Appell formulation and Timoshenko beam theory based on the assumed mode method are used to derive the motion equations and to model the flexible characteristics of links, respectively. In mathematical modeling the effects of torsion, longitudinal deformation, bending in two directions and gravity effects are also considered. Subsequently, the effect of power law index on the vibration behavior of a two-link functionally graded robotic manipulator is studied for two cases in which the mechanical properties of links vary once along the axial direction and again along the thickness direction of each link. By introducing a parameter called signal energy, it is shown that the power law index has a significant influence on the vibrational behaviors of the mentioned system; and that by choosing an appropriate power law index, system vibrations can be reduced substantially in a passive way. Finally, to verify the accuracy of the numerical simulations, the results of this work are compared with the previous works and the reliability of the results of numerical simulations is investigated for the cases in which manipulators are constructed of materials with constant mechanical properties.

Boundary vibration control for a flexible Timoshenko robotic manipulator

The authors investigate the dynamic modelling problem and the active vibration control design problem for a flexible Timoshenko robotic manipulator in this study. For the practical robotic manipulator, the authors analyse the dynamic characteristic considering the shear deformation and elastic deflection of the flexible arm link and describe this flexible system with a coupled partial differential equation and ordinary differential equations (PDE–ODEs) model. Furthermore, the authors design the active vibration control and disturbance observers to solve the vibration problem of the flexible robotic manipulator under the external disturbances, namely, to reduce the shear deformation and the deflection of the flexible Timoshenko link. Besides, the manipulator is driven to track the given angular position with an active angular controller, simultaneously. The effectiveness of the designed vibration control laws is analysed by the theoretical analysis and verified by the numerical simulation.

Gain scheduling LQI controller design for LPV descriptor systems and motion control of two-link flexible joint robot manipulator

This paper proposes a gain scheduling linear quadratic integral (LQI) servo controller design, which is derived from linear quadratic regulator (LQR) optimal control, for non-singular linear parameter varying (LPV) descriptor systems. It is assumed that state space matrices are non-singular since many mechanical systems do not have any non-singular matrices such as the natural state space forms of robotic manipulator, pendulum and suspension systems. A controller design is difficult for the systems due to rational LPV case. Therefore, the proposed gain scheduling controller is designed without the difficulty. Accordingly, the motion control design is implemented for two-link flexible joint robotic manipulator. Finally, the control system simulation is performed to prove the applicability and performance.

Vibration avoidance method for flexible robotic arm manipulation

A new principle, run with flexible deformation, for avoiding vibration throughout trajectories of a flexible robot manipulator is proposed. It comprises the hysteretic and leading mechanisms to maintain a steady pace of flexible (neutral surface) evolution with rigid (joint axis) advance, with the surface staying on a single side of the axis for constant deformation. A simple proportional–derivative (PD) controller is presented to realize the mechanisms, capable of adapting deformation into an invariant set that the single-sided pace-keeping is dependable over a steady or transient period. Analytically this set is the dynamic equilibrium target, in which negativeness of the Lyapunov function’s derivative is uncertain, and is proven globally uniformly asymptotically stable via a generalized Lyapunov and LaSalle’s argument. Further, the desired deformation is same stable in the sense of Lyapunov theorem due to recursive slowdown by the controller. The theoretical work is validated by the numerical simulations, which shows that the desired performance is well achieved. Significant advantages such as vibration-free servo control of a flexible-axis-based trajectory are demonstrated.

Linear and Nonlinear Active Disturbance Rejection Controllers for Single - Link Flexible Joint Robot Manipulator based on PSO Tuner

Linear and Nonlinear Active Disturbance Rejection Controllers for Single - Link Flexible Joint Robot Manipulator based on PSO Tuner

Intelligent modeling of double link flexible robotic manipulator using artificial neural network

The paper investigates the application of the Artificial Neural Network (ANN) in modeling of double-link flexible robotic manipulator (DLFRM). The system was categorized under multi-input multi-output. In this research, the dynamic models of DLFRM were separated into single-input single-output in the modeling stage. Thus, the characteristics of DLFRM were defined separately in each model and the coupling effect was assumed to be minimized. There are four discrete SISO model of double link flexible manipulator were developed from torque input to the hub angle and from torque input to the end point accelerations of each link. An experimental work was established to collect the input-output data pairs and used in developing the system model. Since the system is highly nonlinear, NARX model was chosen as the model structure because of its simplicity. The nonlinear characteristic of the system was estimated using the ANN whereby multi-layer perceptron (MLP) and ELMAN neural network (ENN) structure were utilized. The implementation of the ANN and its’ effectiveness in developing the model of DLFRM was emphasized. The performance of the MLP was compared to ENN based on the validation of the mean-squared error (MSE) and correlation tests of the developed models. The results indicated that the identification of the DLFRM system using the MLP outperformed the ENN with lower mean squared prediction error and unbiased results for all the models. Thus, the MLP provides a good approximation of the DLFRM dynamic model compared to the ENN.

Dynamic modeling and adaptive robust boundary control of a flexible robotic arm with 2‐dimensional rigid body rotation

SummaryThis paper investigates the control of a single‐link flexible robot manipulator with a tip payload appointed to rotate about 2 perpendicular axes in space. The control objective is to regulate the rigid body rotation of the manipulator with guaranteeing the stability of its vibration in the presence of exogenous disturbances. To achieve this, a Lyapunov‐based control design procedure is used and accomplished in some steps. First, the partial differential equation (PDE) dynamic model governing the rigid‐flexible hybrid motion of the arm is derived by applying Hamilton's principle. Next, based on the developed PDE model, an adaptive robust boundary control is established using the Lyapunov redesign approach. To this end, an adaptation mechanism is proposed so that the robust boundary control gains are dynamically updated online and there is no need for prior knowledge of disturbance upper bounds. The actuators and sensors are fully implemented at the arm boundary without using distributed actuators or sensors. Furthermore, in order to avoid control errors resulting from the spillover, control design is directly based on infinite‐dimensional PDE model without resorting to model truncation. Simulation results illustrate the efficacy of the considered method.

Nonlinear Control of a Flexible Joint Robotic Manipulator with Experimental Validation

This article addresses the design and implementation of robust nonlinear control approaches to obtain the desired trajectory tracking of a flexible joint manipulator driven with a direct-current (DC) geared motor. The nonlinear control schemes have been designed and implemented such that they locally stabilize the closed loop system considering all the states as bounded. The system model has been derived using Euler-Lagrange approach. Two different approaches based on sliding mode control (SMC), i.e. the traditional SMC and integral SMC, have been considered in the present study. To experimentally validate the proposed control laws, an electrically-driven single-link flexible manipulator has been designed and fabricated. The designed control algorithms have been developed and experimentally validated on the custom-developed platform. The results obtained both from MATLAB/Simulink and the experimental platform verify the performance of the proposed control algorithms.

Dynamic Characteristics and Restraint Mechanism of Elastically Restrained Connecting Joints on the Flexible Robotic Manipulator

Connecting joints are significant components in mechanical systems as well as the Cartesian flexible robotic manipulator (FRM) which consists of a flexible arm and a moving base through connecting joints. Uncertain factors, such as unqualified assembly, accidental collision, and longtime service, will reduce the restraint stiffness of the connecting joints and enhance the dynamic nonlinearity of the system subsequently. In this case, the traditional perfectly fixed restrained model cannot reflect the real property of the connecting joints. This paper focuses on the elasticity property of the connecting joints with uncertain restraint stiffness, which is defined as the elastically restrained connecting joints (ERCJ), and investigates the dynamic characteristics and restraint mechanism of the ERCJ. An elastic restrained model is proposed to describe the elasticity property of the connecting joints and determine the elastic restrained region of the ERCJ, and the frequency relationship equation in the elastic restrained region is simultaneously determined and verified. Based on the proposed elastic restrained model and Hamilton’s variational principle, the dynamic model and vibration displacement equation of the FRM with elastically restrained connecting joints (FRMERCJ) are established. The virtual prototype experiment of the FRMERCJ is conducted to verify the dynamic model and reveal the restraint mechanism of the ERCJ. The proposed elastic restrained model in this paper can accurately describe the elasticity property of the connecting joints, and the ERCJ is sensitive to motion velocities especially under higher velocities for higher‐order vibrations in the initial stage. The results are meaningful for the dynamic analysis and vibration control of robotic manipulators.

Separation of motion techniques for trajectory optimization in flexible redundant robot manipulators

This paper presents a computational method for optimization of trajectory in redundant robot manipulators. For this purpose, all possible answers are acquired based on rigid conditions and redundancy of the robot. Using open loop optimal control method, the trajectory which minimizes the objective function will be obtained. The objective function is considered as an integral index that will be minimized in the entire trajectory. The objective function and constraints of optimization problem will be selected based on conditions of motion. Dynamic equations of the system are constraints of optimization problem in point-to-point motion. For motion conditions in the specified path, kinematic equations will be added. Also, unequal constraints are applied for limiting the velocity and torque. By selecting the state and control signal vectors which are obtained by assuming rigid motion of the robot, the objective function and constraints will be changed to standard form of an optimization problem. Pontryagin’s maximum principle is used to solve equations. So, the equations of classical form will be changed into two-point boundary value problem. Suggested method is applied to point-to-point motion and movement in the specified path. Results demonstrate accuracy and efficiency of suggested method.

Coexistence of single- and multi-scroll chaotic orbits in a single-link flexible joint robot manipulator with stable spiral and index-4 spiral repellor types of equilibria

This paper reports various chaotic phenomena that occur in a single-link flexible joint (SLFJ) robot manipulator. Four different cases along with subcases are considered here to show different types of chaotic behaviour in a flexible manipulator dynamics. In the first three cases, a partial state feedback as joint velocity and motor rotor velocity feedback is considered, and the resultant autonomous dynamics is considered for analyses. In the fourth case, the manipulator dynamics is considered as a non-autonomous system. The system has (1) one stable spiral and one saddle-node foci, (2) two saddle-node foci and (3) one marginally stable nature of equilibrium points. We found single- and multi-scroll chaotic orbits in these cases. However, with the motor rotor velocity feedback, the system has two unstable equilibria. One of them has an index-4 spiral repellor. In the non-autonomous case, the SLFJ robot manipulator system has an inverse crisis route to chaos and exhibits (1) transient chaos with a stable limit cycle and (2) chaotic behaviour. In all the four cases, the SLFJ manipulator dynamics exhibits coexistence of chaotic orbits, i.e. multi-stability. The various dynamical behaviours of the system are analysed using available methods like phase portrait, Lyapunov spectrum, instantaneous phase plot, Poincare map, parameter space, bifurcation diagram, 0–1 test and frequency spectrum plot. The MATLAB simulation results support various claims made about the system. These claims are further confirmed and validated by circuit implementation using NI Multisim.

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.

Robust adaptive vibration control for an uncertain flexible Timoshenko robotic manipulator with input and output constraints

ABSTRACTThe problems of the constraints and the vibration suppression are investigated for the flexible Timoshenko robotic manipulator in this paper. Robust adaptive boundary control laws with the disturbance observes are designed to guarantee the convergence of the feedback flexible Timoshenko robotic manipulator system with the uncertain parameters and the states are proven to be uniform bounded. In addition, the proposed boundary controls are verified to be effectiveness by the numeral experiments.

Neural Network Control of a Flexible Robotic Manipulator Using the Lumped Spring-Mass Model

Adaptive neural networks (NNs) are employed for control design to suppress vibrations of a flexible robotic manipulator. To improve the accuracy in describing the elastic deflection of the flexible manipulator, the system is modeled via the lumped spring-mass approach. Full-state feedback control as well as output feedback control are proposed separately. Aiming at achieving the control objective, uniform ultimate boundedness of the closed-loop system is ensured. Numerical simulations for the lumped model of the flexible robotic system are carried out to verify the performance of the NN control. Finally, the experiments are given to further validate the feasibility of the proposed NN controllers on the Quanser platform.