Flexible Link Manipulator Research Articles

Adaptive cerebellar model articulation controller–nonlinear control system for flexible link manipulator

This paper deals with the problem of controlling flexible link manipulators on the dynamic phase of the trajectory. A flexible beam/arm is an appealing option for civil and military applications, such as space-based robot manipulators. However, flexibility brings with it unwanted oscillations and severe chattering which may even lead to an unstable system. To tackle these challenges, a novel control architecture scheme is presented. First, a nonlinear controller based on the equation of motion of the robot is elaborated. Its aim is to produce a stable tracking control and dump the vibration of the links. Then, an adaptive cerebellar model articulation controller is implemented to compensate for structured and unstructured uncertainties. Efficiency of the new controller obtained is tested facing an important variation of the dynamic parameters of the manipulator. Simulation results on a dynamic trajectory with a high acceleration/deceleration ratio show the effectiveness of the proposed control strategy.

A nonlinear high gain observer based input–output control of flexible link manipulator

The input–output control strategy needs all of the states feedback. However, in flexible link robot manipulators, measuring the time rate of elastic degrees of freedom is practically impossible. In this paper, a new nonlinear high gain observer has been developed to estimate the elastic degrees of freedom and their time derivatives. The control strategy is based on an output redefinition approach which stabilizes the zero dynamics of the manipulator. Finally, the results are presented by implementing the proposed observer and controller on a single link flexible manipulator. Numerical simulations will support the validity of our research results.

Nonlinear output feedback control of a flexible link using adaptive neural network: controller design

This paper presents an adaptive output-feedback control method based on neural networks for a flexible link manipulator that is a nonlinear non-minimum phase system. The proposed controller comprises a linear, a neuro-adaptive, and an adaptive robustifying part. The neural network is designed to approximate the matched uncertainties of the system. The inputs of the neural network are the tapped delays of the system input-output signals.

Effective active vibration control of single link flexible manipulator with modified positive position feedback control in the presence of instrumentation phase lead/lag

Accurate trajectory regulation of flexible link manipulators is a challenging task. The presence of hardware filters with the cut-off frequency near the resonant frequency cause an additional closed loop instability problem in the control system. This problem can be solved using modified Kalman filters along with certain hardware circuits called compensators. A linear quadratic Gaussian controller has been used to control the hub position. A positive position feedback (PPF) controller has been used at the piezoelectric actuators at the flexible link in the present work to minimize the end-effector vibrations. Normally the design parameters (i.e. coefficients of the numerator and denominator polynomial) of the PPF controller are selected by hit and trial. Pattern search technique has been used as an efficient design method to design these controllers which otherwise have no systematic way to design.

VIBRATION REDUCTION ON SINGLE-LINK FLEXIBLE MANIPULATOR USING H∞ CONTROL

This paper is concerned with the vibration and position control of a single link flexible manipulator. Robot link manipulators are widely used in various industrial applications. It is desirable to build light weight flexible manipulators. Light flexible manipulators have a variety of applications, most significantly in space exploration,manufacturing automation, construction, mining, and hazardous operation. Timoshenko beam theory is used to derive mathematical model of a flexible manipulator. The dynamic equations of motion are obtained using the Lagrange's formulation of dynamics.The H∞ controller is designed for vibration and position control of the system. Simulations are presented and show that vibration and position control of a single flexible link can be controlled with the designed H∞ controller.DOI : http://dx.doi.org/10.22342/jims.14.2.52.73-82

Truncation errors of assumed shape modeling for flexible-link manipulators

The assumed mode shape method has been widely used to derive finite degree-of-freedom dynamic models for flexible-link manipulators, which theoretically have infinite degree-of-freedom dynamics. For a single flexible manipulator, this approximation changes locations of the zeros of transfer functions between base torque and end-effector displacement. The change in locations of zeros considerably affects accuracy of the model and therefore the performance of model-based controllers. This article presents a comprehensive study on the change in locations of zeros due to the truncation associated with assumed mode shape method. It is shown that the locations of approximate zeros depend on four non-dimensional parameters, whereas the locations of analytical zeros depend on only two non-dimensional parameters. Approximate zeros are obtained from assumed mode shape method models, whereas analytical zeros are derived from infinite order models. A thorough study of the differences between approximate zeros and analytical zeros versus the number of mode shapes as well as all the physical parameters is performed. Moreover, guidelines are provided to select the numbers of mode shapes such that the approximate zeros become close to the analytical zeros. These guidelines can easily be used by control and modeling engineers, making them valuable for modeling and control of flexible robot manipulators.

A New Method for Dynamic Modeling of Flexible-Link Flexible-Joint Manipulators

In this article, by combining the assumed mode shape method and the Lagrange’s equations, a new and efficient method is introduced to obtain a closed-form finite dimensional dynamic model for planar Flexible-link Flexible-joint Manipulators (FFs). To derive the dynamic model, this new method separates (disassembles) a FF into two subsystems. The first subsystem is the counterpart of the FF but without joints’ flexibilities and rotors’ mass moment of inertias; this subsystem is referred to as a Flexible-link Rigid-joint manipulator (FR). The second subsystem has the joints’ flexibilities and rotors’ mass moment of inertias, which are excluded from the FR; this subsystem is called Flexible-Inertia entities (FI). While the method proposed here employs the Lagrange’s equations, it neither requires the derivation of the lengthy Lagrangian function nor its complex derivative calculations. This new method only requires the Lagrangain function evaluation and its derivative calculations for a Single Flexible link manipulator on a Moving base (SFM). By using the dynamic model of a SFM and the Lagrange multipliers, the dynamic model of the FR is first obtained in terms of the dependent generalized coordinates. This dynamic model is then projected into the tangent space of the constraint manifold by the use of the natural orthogonal complement of the Jacobian constraint matrix. Therefore, the dynamic model of the FR is obtained in terms of the independent generalized coordinates and without the Lagrange multipliers. Finally, the joints’ flexibilities and rotors’ mass moment of inertias, which are included in the FI, are added to the dynamic model of the FR and a closed-form dynamic model for the FF is derived. To verify this new method, the results of simulation examples, which are obtained from the proposed method, are compared with those of a full-nonlinear finite element analysis, where the comparisons indicate sound agreement

End-effector trajectory tracking of a flexible link manipulator using integral manifold concept

A new controller for the end-effector trajectory tracking of a single flexible link manipulator is introduced. The linear dynamic model of the single flexible link manipulator is expressed in the singularly perturbed form. To reduce the end-effector trajectory tracking error, a corrective torque is added to the computed torque command of the rigid link counterpart of the single flexible link manipulator. The corrective torque is derived based on the concept of the integral manifold of the singularly perturbed differential equations. This corrective torque is of order ε 2 where , and f is the fundamental natural frequency of the single flexible link manipulator. The implementation of the introduced technique does not require the full-state measurements since by designing an observer, the time derivative of the link's lateral deflection is estimated. The stability proof of the new controller, which is based on the Lyapunov criterion, is presented. The results of the simulation and experimental studies are also included to, respectively, show the effectiveness and feasibility of the new controller.

Comparative Dynamic Response of a Optimized Single Link Flexible Manipulator

—In this work, comparative study for dynamic response is carried out for optimized single link flexible robotic manipulator under various types of excitations. Manipulator is considered as an Euler-Bernoulli beam and shape is optimized for circular area of cross-section. Finite element method is used to obtain fundamental frequency and sequential quadratic programming (SQP) is used for its maximization.

Robust trajectory modification for tip position tracking of flexible-link manipulators

This paper presents a composite controller for tip position tracking of flexible link manipulators. The main control challenge for flexible link manipulators is the non-minimum phase characteristics of the system. In this regard, an inner/outer control structure is proposed. As opposed to previous research in this area, the desired reference trajectory is robustly modified in an online scheme to minimize the tip tracking error utilizing the outer controller. The outer trajectory modifier is a [Formula: see text] synthesis based controller which modifies the reference trajectory of the inner loop in the uncertain situations. The inner loop controller is based on the Lyapunov redesign feedback linearization (LRFL) approach which is applied to alleviate the degrading effects of uncertainties and non-linearities presents in the dynamics of the flexible-link manipulator. In the inner loop, a conventional redefined output namely ‘close to the tip’ is considered to avoid the difficulties associated with the non-minimum phase behaviour of the main output (the tip). Conventional control strategies based on this choice of outputs lead to undesirable oscillations in the tip position. However, these oscillations are considerably minimized by applying the proposed outer loop trajectory modifier. Experimental and Simulation results are presented to illustrate the significant improvements in tip tracking performance over the conventional methods.

Dynamic Model and Robust Control of Flexible Link Robot Manipulator

The problems of a flexible link manipulator are uncertainties and parametric nonlinearities. This paper presents design and development of a robust control based on linear quadratic regulator (LQR) for a flexible link manipulator. System performances were evaluated in terms of input tracking capability of hub angular position response, end-point displacement, end-point residual and hub velocity. For the controller of the system, LQR was developed to solve flexible link robustness and input tracking capability of hub angular position. The results achieved by the proposed controller are compared with conventional PID, to substantiate and verify the advantages of the proposed scheme and its promising potential in control of a flexible link manipulator. The robust control presented faster settling time and smaller overshoot responses and tracking performances of the proposed controller compared with PID controllers.

An existence condition for the inverse dynamics solution of a slewing Euler–Bernoulli beam

Causal inverse dynamics problem of a slewing flexible beam has been identified as being ill-posed because it violates the stability of solution. Such problem has been studied intensively for the past three decades due to its application to the tip tracking control of flexible-link manipulators. A well known remedy has been to modify the location of the boundary point, or the output function in tracking control. This paper re-examines the problem by analyzing a closed form solution. Such a solution is made possible by truncating the assumed modes beam deflection model after the first mode. An existence condition for the solution is established, which links to the deflection mode shape, payload inertia, and the location of boundary point. This condition indicates that for certain system parameters, causal solutions may exist. Existing remedies as suggested by many published results can be explained by the condition. Extension to a multi-mode model is discussed and examined through numerical simulations.

Wrist Camera-Based Vibration Suppression Control for a Flexible Manipulator

This paper addresses a vision-based method for estimating vibration excited in the tip of a flexible-link manipulator. In this method, estimation of vibration is achieved by observing the variation of image features projected on a wrist camera. It mimics the situation of utilizing a wrist camera in tip vibration control of a space manipulator. In space, a vision sensor can be expected to be a feasible means for measuring the elastic vibration of the space manipulators, since they are more reliable compared with sensors like strain gauges. The method proposed in this paper takes advantage of the frequential characteristics of visual information that are reflected as a blurred background scene. With the high-frequency component of the projected image features, a Kalman filter-based observer is implemented as the estimator for the vibration. This implementation is characterized by the considerations of incorporating the slow sensor of the camera in the fast servo loop and compensation of the time delay due to image processing. With the vibration estimator, vibration suppression control relying solely on a wrist camera becomes possible. This scheme is successfully verified by experiments.

Use of inverse dynamics for trajectory tracking of flexible-link manipulator with account of link shortening effect

In this paper, the deflection of a two-link flexible manipulator has been modeled with each point on the flexible link being described by both axial and lateral displacement variables instead of lateral displacement variable only. This has been possible by including the shortening of the projection effect on the deformed link. A control law based on computed-torque formulation has been utilized to expose the difference between the responses of the two models, and thus the impact of the shortening of projection effect due to the flexible link deformation on following the desired trajectory is presented.

Trajectory Tracking for the End-effector of a Class of Flexible Link Manipulators

A new controller for the end-effector trajectory tracking (EETT) of a class of flexible link manipulators which consists of a chain of rigid links with a flexible end-link (CRFE) is introduced. To design this new controller, a dynamic model of the CRFE is expressed in the singularly perturbed form; that is, decomposed into slow and fast subsystems. The states of the slow subsystem are the joints’ rotations and their time derivative, while the states of the fast subsystem are the flexible variables, which model the lateral deflection of the end-link, and their time derivative. For the slow subsystem, the new controller requires only ‘‘one’’ corrective torque in addition to the computed torque command of the rigid link counterpart of the CRFE for the reduction of the EETT error. This corrective torque is derived based on the concept of the integral manifold of the singularly perturbed differential equations. The need for only one corrective torque and its derivation are among the contributions of the new controller. To stabilize the fast subsystem, an observer-based controller is designed according to the gain-scheduling technique. Due to the application of the observer-based controller there is no need for the measurement of the time derivative of the flexible link’s lateral deflection, in which its measurement is difficult if not impossible in practice. This feature of the new controller is an advantage for it. To facilitate the derivation and implementation of this controller, several properties of the matrices in the dynamic model of the CRFE are introduced and used which are other contributions of this research. The effectiveness and feasibility of the new controller are shown by simulation and experimental studies.

Nonlinear modeling and control of flexible-link manipulators subjected to parametric excitation

This paper presents nonlinear dynamic modeling and control of flexible-link manipulators subjected to parametric excitation. The equations of motion are obtained using the Lagrangian-assumed modes method. Singular perturbation methodology is developed for the nonlinear time varying equations of motion to obtain a reduced-order set of equations. Control strategies, computed torque control and a composite control, based on the singular perturbation formulation developed, are utilized to reduce mechanical vibrations of the flexible-link and enable better tip positioning. Under the composite control technique, the effect of the value of perturbation parameter on the control signal is investigated. Numerical simulations supported by real-time experiments show that the singular-perturbation control methodology developed for the nonlinear time-varying system offers better system response over the computed torque control as the manipulator is commanded to follow a certain trajectory.

Motion planning for flat systems using positive B-splines: An LMI approach

In this paper, the motion planning problem is studied for nonlinear differentially flat systems using B-spline parameterization of the flat output history. In order to satisfy the constraints continuously in time, the motion planning problem is transformed into a B-spline positivity problem. The latter problem is formulated as a convex semidefinite programming problem by means of a non-negative piecewise polynomial function description based on sum of squares decomposition. The contribution of the paper is thus a one-step design procedure for motion planning that satisfies constraints continuously in time where usual B-spline and collocation techniques need post-analysis. Finally, an example of flexible link manipulator motion is presented to illustrate the overall approach.

Effect of the joint inertia on selection of under-actuated control algorithm for flexible-link manipulators

Abstract In this paper, two control techniques, namely computed torque law and composite control based on the singular perturbation approach, are used to control the motion of a flexible-link manipulator. The effect of manipulator joint inertia on the selection of the control technique used has been investigated. It is found that, unlike composite control, the joint inertia increases the oscillations of the flexible arm when the arm is commanded to follow a certain trajectory under the computed torque control law alone. On the other hand, when we exclude the joint inertias, while modeling the flexible arm, there is no significant difference between the system response based on singular perturbation approach and that based on the computed torque method.

On the Zeros of the Transfer Function of Flexible Link Manipulators and Their Non-Minimum Phase Behaviour

In this article, a study of the zeros of the transfer function, between the base torque and the end-effector displacement, for flexible link manipulators is performed. The analysis is carried out on a single flexible link manipulator with the initial part of the link being rigid. This type of manipulator is referred to as a slewing single rigid—flexible link manipulator (SRFLM). A new method for finding the zeros of the transfer function of an SRFLM without using the corresponding transfer function is introduced. The changes of the locations of the zeros of an SRFLM owing to the changes in all the physical parameters (PPs) are investigated. It is shown that there are PPs where the increase in their values moves the zeros further from the imaginary axis; while by increasing the values of some other PPs the zeros become closer to the imaginary axis. Finally, there are PPs where the locations of the zeros are independent of their values. These findings will be beneficial in the design as well as control of flexible link manipulators and are among the main contributions of this work.

Vision-Based Task-Level Control of a Flexible-Link Manipulator

This paper discusses a vision-based approach to implement task-level control in flexible-link manipulators. The proposed approach emphasizes the advantage of using vision in the control of flexible manipulators. It is pointed out that taking advantage of the inherent robustness, implementation of an image-based visual servo can be regarded as a synthetic solution to precise task-level control of flexible manipulators. This approach is implemented in a three-dimensional flexible-link manipulator. The implementation makes good use of filters in decoupling task-level control and vibration suppression control. Moreover, we point out that although the robustness of the approach can help to overcome the difficulty in control resulting from the complex measurement of the link's elastic deformation, it lacks in capability of tip trajectory specification. This problem is analyzed in this research and it leads to the proposal for the integration of the image interpolation technique. This technique makes the proposed approach adequate for tasks involved with complex tip trajectories. For flexible-link manipulators, the proposed approach with the remedy is the first vision-based synthetic solution that attempts to make a flexible manipulator usable for a practical task.