Multi-link Flexible Robot Research Articles

Modal characterization with nonlinear behaviors of a two-link flexible manipulator

This present work has made a noteworthy attempt to demonstrate brief modeling of N-link manipulator and subsequent modal characterization along with the determination of static deflection of a two-link flexible manipulator with a payload. In addition, investigation of nonlinear phenomena of dynamic responses under 3:1 internal resonance has also been accomplished considering geometric nonlinearities. An appropriate and realistic dynamic modeling of the two-link manipulator taking into account of inertia coupling and geometry compatibility between equations of motion and boundary conditions has been derived using the extended Hamilton’s principle. The effect of parametric variation on system eigenfrequencies is well tabulated, and the corresponding eigenspectrums are illustrated graphically. Further, the nonlinear phenomena of dynamic solutions have been demonstrated by using MMS of second order for its statutory effect onto the system instability for the existence of S-N bifurcations. The effect of nonlinearities and various design parameters on the dynamic responses and subsequent bifurcations for 3:1 internal resonance has also been demonstrated. The outcome of the present work enables new understanding into the design criterion and performance limitation of multi-link flexible robots.

An efficient finite element formulation of dynamics for a flexible robot with different type of joints

If two adjacent links of a flexible robot are connected via a revolute joint or a fixed prismatic joint, the relative motion of the next link will depend on both the joint motion and the elastic displacement of the distal end of the previous link. However, if the two adjacent links are connected via a sliding prismatic joint, the relative motion of the next link will depend additionally on the elastic deformation distributed along the previous link. Therefore, formulation of the motion equations for a multi-link flexible robot consisting of the revolute joints, the fixed prismatic joints and the sliding prismatic joints is challenging. In this study, the finite element kinematic and dynamic formulation was successfully developed and validated for the flexible robot, in which a transformation matrix is proposed to describe the kinematics of both the joint motion and the link deformation. Additionally, a new recursive formulation of the dynamic equations is introduced. As compared with the previous methods, the time complexity of the formulation is reduced by O(2η), where η is the number of finite elements on all links. The numerical examples and experiments were implemented to validate the proposed kinematic and dynamic modelling method.

Evolutionary computation approaches to tip position controller design for a two-link flexible manipulator

Evolutionary computation approaches to tip position controller design for a two-link flexible manipulator Controlling multi-link flexible robots is very difficult compared rigid ones due to inter-link coupling, nonlinear dynamics, distributed link flexure and under-actuation. Hence, while designing controllers for such systems the controllers should be equipped with optimal gain parameters. Evolutionary Computing (EC) approaches such as Genetic Algorithm (GA), Bacteria Foraging Optimization (BFO) are popular in achieving global parameter optimizations. In this paper we exploit these EC techniques in achieving optimal PD controller for controlling the tip position of a two-link flexible robot. Performance analysis of the EC tuned PD controllers applied to a two-link flexible robot system has been discussed with number of simulation results.

Inverse Kinematics of Multilink Flexible Robots for High-Speed Applications

A straightforward inverse kinematic algorithm for multilink flexible robots is proposed to improve the control performance. The inclusion of a dynamic constraint maximizes the performance of feedback controllers in high-speed applications. To obtain a numerically feasible solution, the singular perturbation approach is employed, which decomposes the inverse kinematics into an averaged part (slow part) and a parasitic part (fast part). The solution of the averaged part is considered the desired inverse kinematics, while the parasitic part is intentionally removed. The parameter expansion is carried out to obtain the solution sequentially. The implicit expansion method, which is a refined version of the expansion method, reduces computing time considerably. The formula in discrete time offers efficiency in computer applications. In addition, a requirement on differentiability of the desired task trajectory is derived.

Joint tracking controller for multi‐link flexible robot using disturbance observer and parameter adaptation scheme

AbstractAn improved composite controller of singular perturbation approach is designed for controlling a multi‐link flexible robot with uncertainties. We adopt the standard form of a singular perturbation approach for modeling. To reduce the coupling effect from flexibility, the bandwidth of a slow subsystem is modulated by considering the fundamental frequency. The disturbance observer provides a means for defining the bandwidth of a slow subsystem as well as compensating disturbances. At the same time, uncertainties in the fast subsystem are updated to enhance the capability for vibration suppression in conjunction with PID (Proportional‐integrative derivative) modal feedback. We draw conditions for Lyapunov stability of the modal feedback and adaptive scheme. A numerical simulation will support the validity of our research results. © 2002 Wiley Periodicals, Inc.

Parameter Identification of a Substitution Model for a Flexible Link

Using robots for very wide operating ranges or for heavy loads requires taking the elastic deformations of the links into account. A recent model independent approach for damping the vibrations of a multilink flexible robot is the control concept of the virtual spring-damper, in which the actuators are controlled to act like spring-damper-systems. To improve performance requirements, an independent substitution model for the arm is introduced, because obtaining an accurate analytical model for multilink flexible robots involves considerable problems. This paper deals with a substitution model which describes the essential dynamic and vibration behavior of the flexible link. To avoid obtaining an analytical model, the substitution parameters have to be identified by system measurements. Therefore the position of the end effector, however, cannot be measured.

Active Vibration Control of Flexible Robots Using Virtual Spring-damper Systems

When using robots for heavy loads and huge operating ranges, elastic deformations of the links have to be taken into account during modeling and controller design. Whereas for conventional rigid multilink industrial robots modeling can schematically be done by standard techniques, it is a massive problem to obtain an accurate analytic model for multilink flexible robots. But an accurate analytic model is essential for most modern controller design techniques, and modeling errors can lead to instability of the controlled system due to spillover since the eigenvalues of the system are only slightly damped. A new approach to active damping control for flexible robots is presented in this paper where the actuators act like virtual spring-damper-systems. As the spring-damper-element is a passive energy dissipative device, it will never destabilize the system and thus the control concept will be very insensitive to modeling errors. Basically, the two parameters, spring stiffness and damping constant of this system, are arbitrary and model independent. To satisfy performance requirements they are adjusted using knowledge of the system model. The more it is known about the system model, the better these parameters may be adjusted. The new input of the controlled system is a virtual variation of the spring base. The paper illustrates this technique with the help of a simple and easy to model one link flexible robot which is also available as a real laboratory testbed.

Modelling and Model Fitting of Flexible Robots – a Multibody System Toolkit Approach

During the last decade robots with flexible links became a popular research object for control engineers. This is because of their sophisticated properties referring to feedback control, e.g., non-minimum phase behaviour in end-effector control. Massive problems already occur trying to obtain an accurate analytic model for multilink flexible robots. This paper presents an effective way for numerical modelling of multilink flexible robots using the multibody system toolkit M{\mobilelogo}BILE. The experimental model fitting to a laboratory test bed of a two-link flexible robot is documented.

Redundant robot manipulators with joint and link flexibility—II. Residual vibration decreasing

For a robot manipulator with link and joint flexibility in the meantime, the end effector vibration will continue even though nominal motion is stopped. This kind of residual vibration can be decreased effectively by using redundancy of the multi-link flexible joint and link robot manipulators. With the help of redundancy, an optimal self-motion which yields minimum end effector vibration can be found. The significant advantage of this method is the nominal end effector position/posture can be maintained fixed while the links move in an optimal way. Simulation results show the method is effective.

Dynamic Analysis of Flexible Manipulator Arms With Distributed Viscoelastic Damping

The main objective of this work is to predict the effect of distributed viscoelastic damping on the dynamic response of multilink flexible robot manipulators. A general approach, based on the principle of virtual work, is presented for the modeling of flexible robot arms with distributed viscoelastic damping. The finite element equations are developed, and a recurrence formulation for numerical integration of these equations is obtained. It is demonstrated, by a numerical example, that the viscoelastic damping treatments have a significant effect on the dynamic response of flexible robot manipulators.

NON-MODEL-BASED POSITION CONTROL OF A PLANAR MULTI-LINK FLEXIBLE ROBOT

This paper presents a class of non-model-based position controllers for a planar multi-link flexible robot. One can achieve not only the closed-loop stability of the original distributed parameter system, but also the asymptotic stability of the truncated system, which is obtained through representing the deflection of each link by an arbitrary finite number of flexible modes. The system dynamics (which are very complicated in the case of a multi-link flexible robot) are not explicitly involved in the controller design and stability proof. Instead, only a very basic system energy relationship and the dynamic equations of a single-link flexible robot are utilised. The controllers possess several remarkable advantages over traditional model-based ones. Numerical simulations are carried out on a two-link flexible robot and satisfactory results are obtained.

Energy-based robust controller design for multi-link flexible robots

A class of robust stable controllers to control the tip position of a multi-link flexible robot is presented. In contrast to traditional model-based methods, the controllers are derived by using a basic relationship of system energy and are independent of the system dynamics. The approach allows controller design in the absence of a system model (which is very complicated in the case of the multi-link flexible robot) and provides great freedom in feedback control design. Further, the controllers are easy to implement in practice because, depending on actual instrumentation, all the signals can be chosen to be measurable. Simulation results of a two-link flexible robot are provided to show the effectiveness of the presented approach.

Linear robust trajectory control of flexible joint manipulators

SUMMARYThis paper presents a practical approach for the point-to-point control of elastic-jointed robot manipulators. With the proposed approach only position and velocity feedback are referenced, as opposed to most of the existing control schemes of elastic-jointed manipulators which require additional acceleration and/or jerk feedback. To guarantee the robustness of the controller, it is designed on extreme parameter uncertainties due to highly elastic joints of manipulators and energy motivated Lyapunov functions are used to derive the control law. Four pertinent controller gains are chosen in light of the on-line position and velocity feedback of the links and joint sensors. Through a simulated experimental verification, it is demonstrated that the designed simple position and velocity feedback controller, similar to that used for rigid-jointed robots, can globally stabilize the elastic-jointed robot for a bounded reference position. In addition, the tracking performance of the controller reveals that this simple control algorithm is robust in terms of joint flexibility. And the simplicity of the presented control algorithm, as compared to other model-based techniques for flexiblejoint robots, is particularly advantageous. Even though the simulated experiments are conducted on a single-link flexible joint robot, control law derived in this paper has general meaning for multi-link flexible joint robots.

Lyapunov functions and the control of the Euler-Bernoulli beam

A controller for the Euler-Bernoulli beam is derived using the complete distributed model along with a Lyapunov function approach. Model structure is therefore preserved in the control law whose parameters can be used to balance two different types of behaviour: the gross motion of the beam and the vibration superimposed on it. In the limiting case of a rigid beam, these two types of behaviour become indistinguishable and so the controller reduces to a proportional feedback law. This approach also guarantees that the controller provides asymptotic trajectory tracking for smooth initial conditions. Also, since it is not constrained to linear systems it could, in principle, be used for multi-link flexible robot systems.

Control of flexible joint robots via external linearization approach

AbstractBased on the feedback linearization structure algorithm of differential geometric nonlinear control theory, an external linearization approach to the control of multilink flexible joint robots is considered in this article. The resulting externally linearized and input‐output decoupled closed‐loop system contains a linear subsystem and a nonlinear subsystem. The linear part describing the rigid motor motions is suitable for the design of nominal trajectory following control. However, the nonlinear joint deformation subsystem will cause perturbations in the nominal trajectory. To actively damp out the elastic vibrations and to render the complete closed‐loop system robust to uncertainty in system parameters, a combined LQR stabilizer and servocompensator is used as the internal stabilization and error correcting control. The tracking errors of the end effector caused by the quasi‐static joint deflections due to gravity can be compensated for by taking into account the nominal deflections in the trajectory planning and LQ regulation. A three‐link PUMA type arm is tested via simulation.

Inverse Dynamics and Kinematics of Multi- Link Elastic Robots: An Iterative Frequency Domain Approach

A technique is presented and experimentally validated for solving the inverse dynamics and kinematics of multi-link flexible robots. The proposed method finds the joint torques necessary to produce a specified end-effector motion. Since the inverse dynamic problem in elastic manipulators is closely coupled to the inverse kinematic problem, the solution of the first also renders the displacements and rotations at any point of the manipulator, including the joints. Further more the formulation is complete in the sense that it includes all the nonlinear terms due to the large rotation of the links. The Timoshenko beam theory is used to model the elastic characteristics, and the resulting equations of motion are discretized using the finite element method. An iterative solu tion scheme is proposed that relies on local linearization of the problem. The solution of each linearization is carried out in the frequency domain. The performance and capabilities of this technique are tested, first through simulation analysis, and second through experimental validation using feed-forward control. Results show the potential use of this method not only for open-loop control, but also for incorporation in feedback control strate gies. 1. This section contains a revised and corrected formulation of open-chain case. A previous method reported by the first author in: Computed Torque for the Fosition Control of Open-Chain Flexible Robots. Proc. 1988 IEEE International Conference in Robotics and Automation contained an error.

3-Dimensional vibration analysis of multi-link flexible robot arms.

This paper is concerned with a study of the 3-dimensional vibration analysis of multi-link flexible robot arms. The diformation of the arm is discussed on the basis of the Bernoulli-Euler beam theory. The 3-dimensional matrix equations are obtained for the beam element, the supported edge with elastic constraints, the free tip with payload, and the elbow composed of two joints connected together by a spring and a dashpot. The matrices are constructed by taking into acceunt the equilibriums of the displacements, the rotation angles, the bending and torsional moments, and the axial and lateral shear forces in the x^-, y^- and z^- directions. Numerical results are given for a two-Link flexible arm. It is shown that the vibration modes are separated into two groups, i.e., the in-plane modes and the out-of-plane vibration modes. In the in-plane mode both the in-plane bending deformation and the axial elongation are coupled, while in the out-of-plane mode the out-of-plane bending and the torsional deformations are coupled. This leads to the conclusion that the control of the out-of-plane vibration of two-link flexible arms can be discussed without referring to the effect of the in-plane vibration and vice versa.