In this paper, we present a broad learning control method for a two-link flexible manipulator with prescribed performance (PP) and actuator faults. The trajectory tracking errors are processed through two consecutive error transformations to achieve the constraints in terms of the overshoot, transient error, and steady-state error. And the barrier Lyapunov function is employed to implement constraints on the transition state variable. Then, the improved radial basis function neural networks combined with broad learning theory are constructed to approximate the unknown model dynamics of flexible robotic manipulator. The proposed fault-tolerant PP control cannot only ensure tracking errors converge into a small region near zero within the preset finite time but also address the problem caused by actuator faults. All the closed-loop error signals are uniformly ultimately bounded via the Lyapunov stability theory. Finally, the feasibility of the proposed control is verified by the simulation results.

A Pneumatic Muscle Actuator (PMA) is a new pneumatic component sharing similar characteristics with biological muscles, and the flexible manipulator actuated by PMAs can better reflect the flexibility of the mechanism. First and foremost, based on the study of the characteristics of human shoulder joints, the configuration design of the flexible manipulator is analyzed, and its kinematics and dynamics models are established. Furthermore, with regard to the nonlinearity, time-invariance and uncertainty of the control system, three aspects of improvement are proposed, which are based on the Radial Basis Function (RBF) network torque control algorithm. The Genetic Algorithm is used to optimize the initial values of RBF network parameters; RBF network parameters are adjusted dynamically by using the additional momentum method; the Levenberg--Marquardt (LM) algorithm, instead of the gradient descent method, is adopted to adjust Proportion Integration Differentiation (PID) parameters online in real time. At last, to test the effects that the improved algorithm exerts on the flexible manipulator control system, some physical platform experiments are carried out. It turns out that the control accuracy and robustness of the improved algorithm are well improved, and the mechanism can be controlled better to track the circular arc trajectory. It lays fundamental importance to the practical application for the working environment.

In this paper, based on the Youla-Kucera (Y-K) parameterization, the control of a flexible beam acting as a flexible robotic manipulator is investigated. The method of Youla parameterization is the simple solution and proper method for describing the collection of all controllers that stabilize the closed-loop system. This collection comprises function of the Youla parameter which can be any proper transfer function that is stable. The main challenge in this approach is to obtain a Youla parameter with infinite dimension. This parameter is approximated by a subspace with finite dimensions, which makes the problem tractable. It is required to be generated from a finite number of bases within that space and the considered system can be approximated by an expansion of the orthonormal bases such as FIR, Laguerre, Kautz and generalized bases. To calculate the coefficients for each basis, it is necessary to define the problem in the form of an optimization problem that is solved by optimization techniques. The Linear Quadratic Regulator (LQR) optimization tool is employed in order to optimize the controller gains. The main aim in controller design is to merge the closed-loop system and the second order system with the desirable time response characteristic. The results of the Youla stabilizing controller for a planar flexible manipulator with lumped tip mass indicate that the proposed method is very efficient and robust for the time-continuous instances.

Maximum load carrying capacity (MLCC) of flexible robot manipulators is computed based on closed-loop approach. In open-loop approach, controller is not considered, so the end effector deviation from the predefined path is significant and the accuracy constraint restrains the maximum payload before actuators go into saturation mode. In order to improve the MLCC, a method based on closed-loop strategy is presented. Since in this case the accuracy is improved the actuators constraint is not a major concern and full power of actuators can be used. Since controller can play an important role in improving the maximum payload, a sliding mode based partial feedback linearization controller is designed. Furthermore, a fuzzy variable layer is used in sliding mode design to boost the performance of the controller. However, the control strategy required measurements of elastic variables velocity that are not conveniently measurable. So a nonlinear observer is designed to estimate these variables. Stability analysis of the proposed controller and state observer are performed on the basis of Lyapunov's direct method. In order to verify the effectiveness of the presented method, simulation is done for a two-link flexible manipulator. The obtained maximum payload in open-loop and closed-loop cases is compared and the superiority of the method is illustrated and the results are discussed.

In the authors' previous paper,10 an input shaping method was presented to reduce motion-induced vibrations effectively for various classes of flexible systems. In this paper, the effectiveness of the shaping method is experimentally demonstrated with a two-link flexible manipulator system

The manipulator for experiments includes two revolute joints and two flexible links, and moves on a vertical plane under gravity. An analytic model is developed considering the flexibility of the system and its joint stiffness in order to derive an appropriate estimation of dynamic modal properties. The input shaping method used in this work utilizes time-varying modal properties obtained from the model instead of the conventional input shaping method which employs time-invariant modal properties. A point-to-point motion is tested in order to show the effectivess of the proposed shaping method in vibration reduction during and after a given motion. The given reference trajectories are shaped to suppress the motion induced vibration. The test results demonstrate that the link vibration can be greatly suppressed during and after a motion, and the residual vibration reduction was observed more than 90% by employing this time-varying impulse shaping technique.

The dynamics modeling and payload adaptability of a light-weight flexible one-link manipulator are studied. Using the FEM (Finite-Element Method) model of a flexible manipulator, a lower order Linear Quadratic Gaussian compensator can provide satisfactory performance without controller/observer spillover. Moreover, the payload can be separated from the beam model, therefore, it is expected that the identification algorithm should have better robustness than the other schemes. The simulation results have shown that the proposed payload-adaptation synthesizer, which synthesizes a payload identifier and a nominal regulator/estimator interpolator to obtain a near-optimal compensator, has good adaptability with varying payload. And the resulting synthesizer also provides a near-optimal damping for this sensor-actuator noncolocated system.

This paper presents theoretical and experimental investigations into modelling a single-link flexible manipulator system. An analytical model of the manipulator, characterised by an infinite number of modes, is developed using the Lagrange's equation and modal expansion method. This is used to develop equivalent time-domain and frequency-domain working models of the system in state-space and transfer function forms respectively. The model parameters are then estimated experimentally using system's measured input/output data. The model thus obtained is validated through experimentation and results including the effect of payload on system characteristics presented and discussed.

Flexible manipulators have received wide attention because they surpass their rigid counterparts in many criteria. Unfortunately, traditional controller design methods for flexible arms implemented by human experts are usually tedious and intractable. In order to improve system behaviour, this paper proposes schemes based on genetic algorithms (GAs) which optimise the parameters of a fuzzy logic controller for a robotic manipulator with two-link flexibility and two-joint elasticity. Two alternative GA-optimised schemes are simulated and their control behaviour is compared with that of human-expert-designed controller.

This paper presents investigations into the applications and performance of positive and negative input shapers in command shaping techniques for the vibration control of a flexible robot manipulator. A constrained planar single-link flexible manipulator is considered and the dynamic model of the system is derived using the finite element method. An unshaped bang-bang torque input is used to determine the characteristic parameters of the system for design and evaluation of the input shaping control techniques. The positive and specified amplitude negative input shapers are designed based on the properties of the system. Simulation results of the response of the manipulator to the shaped inputs are presented in the time and frequency domains. Performances of the shapers are examined in terms of level of vibration reduction, time response specifications and robustness to parameters uncertainty. The effects of derivative order of the input shaper on the performance of the system are investigated. Finally, a comparative assessment of the impact amplitude polarities of the input shapers on the system performance is presented and discussed.

The passivity property of a noncollocated single-link flexible manipulator with a parameterized output is studied. The system can be characterized by either the irrational transfer function of an infinite-dimensional model or its truncated rational transfer functions. Necessary and sufficient conditions for these transfer functions to be passive are found. It is also shown that a non-passive, marginal minimum-phase, truncated transfer function can be rendered passive by using either the root strain feedback or the joint angular acceleration feedback. For the noncollocated truncated passive transfer function, a PD controller suffices to stabilize the overall system. Numerical results are given to show the efficacy of the proposed approaches.

This paper focuses on using a singularly perturbed approach to derive a vibration damping control law in which a pole assignment feedback method is utilized. The composite control system is characterized by two components which can be computed separately. The one is Cartesian-based PI control which drives the end-effector of a flexible manipulator to track the desired time-based trajectory. The other is pole assignment feedback control which damps out vibrations during and at the end of trajectory tracking. An advantage of this composite control method in real implementation is that it does not require a derivative of the end-effector's position, and the derivatives of signals from the strain gauges. From the characteristics and implementation points of view, it appears to be simple to use. Laboratory experiments were conducted to evaluate the performance of the proposed control method.

This paper presents an investigation into the development of parametric and non-parametric approaches for dynamic modelling of a flexible manipulator system. The least mean squares, recursive least squares and genetic algorithms are used to obtain linear parametric models of the system. Moreover, non-parametric models of the system are developed using a non-linear AutoRegressive process with eXogeneous input model structure with multi-layered perceptron and radial basis function neural networks. The system is in each case modelled from the input torque to hub-angle, hub-velocity and end-point acceleration outputs. The models are validated using several validation tests. Finally, a comparative assessment of the approaches used is presented and discussed in terms of accuracy, efficiency and estimation of the vibration modes of the system.

This paper rechecks the relative degree of the end-point tracking control system of a flexible manipulator. New added insights into the ill-defined behavior of the relative degree are presented by constructing a perturbed truncation model. The implications for the inverse dynamics motivate us to reformulate the inverse dynamics based on the perturbed truncation model in the extreme case of truncating all of the flexible modes. New potential advantages arising from this novel formulation are investigated for the inverse dynamics control design as well.

The question of control and stabilization of flexible space robots is considered. Although, this approach is applicable to space robots of other configurations, for simplicity, a flexible planar two-link robot, mounted on a rigid floating platform, is considered. The robotic arm has two revolute joints and its links undergo elastic deformation in the plane of rotation. Based on nonlinear inversion technique, a control law is derived for controlling output variables describing the position and orientation of the platform and the joint angles of the robot. Although, the inverse controller accomplishes reference trajectory tracking, it excites the elastic modes of the arm. For the vibration suppression, three different stabilizers are designed. Using linear quadratic optimal control theory, a composite stabilizer for stabilization of the rigid and flexible modes and a decoupled flexible mode stabilizer are designed for regulating the end point of the robot to the target point and vibration suppression. Stabilization using only elastic mode velocity feedback is also considered. For large maneuvers, first the inverse controller is active, and the stabilizer is switched for regulation when the motion of the robot lies in the neighborhood of the terminal equilibrium state. Simulation results are presented to show that in the closed-loop system including the inverse controller and each of the stabilizers, trajectory tracking and stabilization of elastic modes are accomplished.