Two-link Rigid-flexible Manipulator Research Articles

FEM and simscape modelling and LQG control of a two-link rigid-flexible manipulator

FEM and simscape modelling and LQG control of a two-link rigid-flexible manipulator

FEM and simscape modelling and LQG control of a two-link rigid-flexible manipulator

FEM and simscape modelling and LQG control of a two-link rigid-flexible manipulator

Motion Planning and Adaptive Neural Tracking Control of an Uncertain Two-Link Rigid–Flexible Manipulator With Vibration Amplitude Constraint

This article deals with an uncertain two-link rigid-flexible manipulator with vibration amplitude constraint, intending to achieve its position control via motion planning and adaptive tracking approach. In motion planning, the motion trajectories for the two links of the manipulator are planned based on virtual damping and online trajectories correction techniques. The planned trajectories can not only guarantee that the two links can reach their desired angles, but also have the ability to suppress vibration, which can be adjusted to meet the vibration amplitude constraint by limiting the parameters of the planned trajectories. Then, the adaptive tracking controller is designed using the radial basis function neural network and the sliding mode control technique. The developed controller makes the two links of the manipulator track the planned trajectories under the uncertainties including unmodeled dynamics, parameter perturbations, and persistent external disturbances acting on the joint motors. The simulation results verify the effectiveness of the proposed control strategy and also demonstrate the superior performance of the motion planning and the tracking controller.

Nonlinear Partial Differential Equation Model-Based Coordination Control for a Master–Slave Two-Link Rigid–Flexible Manipulator With Vibration Repression

AbstractIn this study, vibration control problem is considered for a coordinative master–slave two-link rigid–flexible manipulator. By the help of Hamilton's principle, the dynamic model of the master–slave two-link rigid–flexible manipulator is expressed using nonlinear partial differential equations (PDEs). Based on the nonlinear PDE model, we propose a novel coordination controller for the master–slave system. The proposed controller can achieve the following three objectives: (1) making the master manipulator track the given angles; (2) making the slave manipulator track the angles of the master manipulator; and (3) repressing the deflection and vibration of both the master and the slave flexible manipulators. Stability analysis of the closed-loop system is proven by LaSalle's invariance principle. Two simulation cases are given to validate the effectiveness of the coordination controller.

Uncalibrated Visual Servoing for a Planar Two Link Rigid-Flexible Manipulator Without Joint-Space-Velocity Measurement

In this article, to solve trajectory tracing problem and vibration suppression for a planar two-link rigid-flexible manipulator subject to joint-velocity measurement noise, a novel uncalibrated visual servoing control is proposed. To begin with, the manipulator’s dynamic model is established by the assumed mode method (AMM). On this basis, based on the singular perturbation theory, two subsystem controllers are designed, one is slow subsystem controller, and the other one is fast subsystem controller. In the slow subsystem, to cope with the complication of the camera calibration, an adaptive algorithm is formulated to evaluate the parameters of a fixed camera online. Aiming to overcome the challenge that exact joint-velocity measurement may be disturbed by external noise, a nonlinear sliding observer is developed to estimate the state of joint velocity accurately. The asymptotic convergence of image tracking error is proved by means of Lyapunov analysis. Additionally, for the purpose of restraining the flexible beam’s elastic vibration, a linear quadratic regulator (LQR) approach is adopted in the fast subsystem control design. The realistic comparing simulation experiments are presented to demonstrate the performance of the proposed controller.

Three-dimensional modeling and input saturation control for a two-link flexible manipulator based on infinite dimensional model

In this paper, the modeling and controlling problem is studied for a two-link rigid-flexible manipulator in three-dimensional (3D) space under input saturation. The dynamics of the 3D manipulator is first derived in infinite dimension model, which is represented by partial differential equations (PDEs). The controller can achieve joint angle control and vibration suppression control in the presence of input constraint. The stability analysis of the closed-loop system is given based on LaSalle’s Invariance Principle. Numerical simulations illustrate the effectiveness of the proposed controller.

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.

Boundary vibration control for a two-link rigid–flexible manipulator with quantized input

The aim of this paper is to investigate the control problem for a two-link rigid–flexible manipulator with input quantization. Abundant studies of the quantized control problem are based on the lumped parameter system, which is expressed using ordinary differential equations. In this paper, the dynamic model for a two-link rigid–flexible manipulator is represented using partial differential equations. The controller design and analysis with input quantization are based on the partial differential equation model. By means of an auxiliary system, tracking errors and boundary vibrations can be eliminated. Simulations are given to verify the effectiveness of the proposed controller with quantized input.

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.

Adaptive actuator fault compensation control for a rigid-flexible manipulator with ODEs-PDEs model

ABSTRACTIn this paper, the actuator fault problem is studied for a two-link rigid-flexible manipulator system in the presence of boundary disturbance and state constraint. The system consists of a rigid beam, a flexible beam and a payload at the end, which are described by hybrid ordinary differential equations–partial differential equations. The novel controller includes a proportional-derivative feedback structure, a disturbance observer and a fault-tolerant algorithm, which can regulate the joint positions and eliminate vibration of flexible beam, on circumstance of boundary disturbance and actuator fault. With the help of Barrier Lyapunov Function, the states will not be violated. It is proved that the closed-loop system has asymptotic stability by LaSalle Invariance Principle. Simulations are provided to demonstrate the effectiveness of the proposed controller.

Vibration control for a rigid-flexible manipulator with full state constraints via Barrier Lyapunov Function

Considering full state constraints, this paper designs a boundary controller for a two-link rigid-flexible manipulator via Barrier Lyapunov Function. The dynamic model of the two-link rigid-flexible manipulator is described by coupled ordinary differential equations- partial differential equations (ODEs-PDEs). Based on the original model without neglecting the high-frequency modes, boundary controller is proposed to regulate the joint positions and eliminate the elastic vibration simultaneously. To ensure that the full state constraints which include position, speed and vibration constraints are not transgressed, a Barrier Lyapunov Function is employed in the proposed controller. The asymptotic stability of the closed-loop system is rigorously proved by the LaSalle's Invariance Principle. Simulations are given to verify the effectiveness of the proposed controller with state constraints.

Boundary control for a constrained two-link rigid–flexible manipulator with prescribed performance

ABSTRACTIn this paper, we consider a boundary control problem for a constrained two-link rigid–flexible manipulator. The nonlinear system is described by hybrid ordinary differential equation–partial differential equation (ODE–PDE) dynamic model. Based on the coupled ODE–PDE model, boundary control is proposed to regulate the joint positions and eliminate the elastic vibration simultaneously. With the help of prescribed performance functions, the tracking error can converge to an arbitrarily small residual set and the convergence rate is no less than a certain pre-specified value. Asymptotic stability of the closed-loop system is rigorously proved by the LaSalle's Invariance Principle extended to infinite-dimensional system. Numerical simulations are provided to demonstrate the effectiveness of the proposed controller.

An adaptive iterative learning algorithm for boundary control of a coupled ODE–PDE two-link rigid–flexible manipulator

To perform repetitive tasks, this paper proposes an adaptive boundary iterative learning control (ILC) scheme for a two-link rigid–flexible manipulator with parametric uncertainties. Using Hamilton׳s principle, the coupled ordinary differential equation and partial differential equation (ODE–PDE) dynamic model of the system is established. In order to drive the joints to follow desired trajectory and eliminate deformation of flexible beam simultaneously, boundary control strategy is added based on the conventional joints torque control. The adaptive iterative learning algorithm for boundary control scheme includes a proportional-derivative (PD) feedback structure and an iterative term. This novel controller is designed to deal with the unmodeled dynamics and other unknown external disturbances. Numerical simulations are provided to verify the performance of proposed controller in MATLAB.

A Direct Method of Adaptive FIR Input Shaping for Motion Control With Zero Residual Vibration

In this paper, we describe a method of adaptive feedforward control that can achieve zero residual vibration in rest-to-rest motion of a vibratory system. When a finite impulse response filter is used to preshape a command input, zero residual vibration is achieved for any input signal if the impulse response of the filter satisfies a condition of orthogonality with respect to the impulse response of the system under control. An equivalent condition involving sets of measured I/O data is derived that forms the basis of a direct method of adaptively tuning filter coefficients during motion. The approach requires no prior model of the system and can be applied to multimode and multiinput systems under arbitrary and nonrepetitive motions. Versions of the algorithm employing recursive least-squares techniques are developed and analyzed. As a special case of the general adaptation problem, tuning of impulse-based shapers with fixed impulse timings can also be achieved. An experimental implementation on a two-link rigid-flexible manipulator is presented. The method is thereby shown to be realizable and effective for real-world motion control problems.

Model Reduction of a Two-Link Rigid-Flexible Manipulator Based on Spectral Approximation Method

In this paper, the dynamic model of a two-link rigid-flexible manipulator was established by using the theory of Lagrange equation. Due to the model is a distributed-parameter system, we present a simple, efficient method for model reduction based on spectral approximation method such that a model-based scheme can be implemented. The method was illustrated by comparing with the simulation results of the reduced-order model and the virtual reduced model based on finite element method.

QFT control of a two-link rigid-flexible manipulator

This paper presents a new and simple controller design method based on QFT (quantitative feedback theory) for a two-link manipulator whose first link is rigid and the second is flexible. A piezoelectric patch is attached to the surface of the flexible link for vibration suppression of it. This system is modeled as a nonlinear multi-input multi-output (MIMO) control systems whose inputs are two motor torques which are applied on joints and a voltage which is applied on piezoelectric patch. To control the manipulator's end point position, motion of the manipulator is divided to two rigid and flexible parts. To control both parts, nonlinear equations of the motion is replaced by a family of uncertain linear time-invariant equivalent systems using Rafeeyan's method which results in three decoupled transfer functions established in the Laplace domains. Then the QFT method is used to design compensators and prefilters and a diagonal matrix is developed as the system controller. Results demonstrate the remarkable performance of the proposed controllers in reduction of residual vibration of elastic link and tracking a circular trajectory by the manipulator end point.

Hybrid bacterial foraging and particle swarm optimisation for fuzzy precompensated control of flexible manipulator

This paper presents hybrid approach combining the social foraging behaviour of Escherichia coli bacteria and particle swarm optimisation for optimising hybrid fuzzy precompensated proportional-derivative (PD) controller in trajectory control of two-link rigid-flexible manipulator. Numerical simulation using the dynamic model of the two-link rigid-flexible manipulator shows the effectiveness of the approach in trajectory tracking problems. The use of fuzzy precompensation has superior performance in terms of improvement in transient and steady state response, robustness to variations in loading conditions and ease to use in practice. Comparative evaluation with respect to genetic algorithm, particle swarm and bacterial foraging-based optimisation is presented to validate the controller design. The proposed algorithm performs local search through the chemotactic movement operation of bacterial foraging whereas the global search over the entire search space is accomplished by a particle swarm operator and so satisfactory tracking precision could be achieved using the approach.

Trajectory planning for residual vibration suppression of a two-link rigid-flexible manipulator considering large deformation

In this paper an optimal trajectory planning technique for suppressing residual vibrations in two-link rigid-flexible manipulators is proposed. In order to obtain an accurate mathematical model, the flexible link is modeled by taking the axial displacement and nonlinear curvature arising from large bending deformation into consideration. The equations of motion of the manipulator are derived using the Lagrangian approach and the assumed modes method. For the trajectory planning, the joint angle of the flexible link is expressed as a cubic spline function, and then the particle swarm optimization algorithm is used to determine the optimal trajectory. The optimal trajectory thus obtained satisfies the minimum vibration condition. By performing numerical simulations, the effectiveness of the proposed trajectory planning technique is verified.

128 大変形を考慮した2リンク剛体-フレキシブルマニピュレータのモデリングと残留振動抑制

This paper proposes a new method for the trajectory planning of a two-link rigid-flexible manipulator in a point-to-point motion. In order to obtain a mathematical model properly, the flexible link is modeled by considering the axial displacement and the nonlinear curvature due to large bending deformation. The Lagrangian approach in conjunction with the assumed modes method is applied to derive the equations of motion of the manipulator. In the trajectory planning, we express the desired joint angle of the flexible link by a cubic spline function, and then use a particle swarm optimization to minimize the joint driving torque. We show that the residual vibrations of the flexible link can be suppressed as a result of the minimum driving torque requirement. In the numerical calculation, we verify the effectiveness of the proposed trajectory planning.

514 2リンク剛体-フレキシブルマニピュレータの残留振動抑制のための軌道生成法

514 2リンク剛体-フレキシブルマニピュレータの残留振動抑制のための軌道生成法