Flexible Link Robot Research Articles

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.

Adaptive nonlinear boundary control of a flexible link robot arm

We consider the problem of designing a boundary controller for a flexible link robot arm with a payload mass at the link's free-end. Specifically, we utilize a nonlinear, hybrid dynamic system model (the model is hybrid in the sense that it comprises a distributed parameter, dynamic field equation coupled to discrete, dynamic boundary equations) to design a model-based control law which asymptotically stabilizes the link displacement while driving the actuator hub's position to a desired setpoint. We then illustrate how the control law can be redesigned as an adaptive controller which achieves the same control objective while compensating for parametric uncertainty including unknown payload mass. The control strategy is composed of a boundary control torque applied to the actuator hub and a boundary control force at the link's free-end. Experimental results are presented to illustrate the performance of the proposed control laws.

Vibration Control of Flexible Robots--Theoretical and Experimental Results

Using robots for heavy loads and huge operating ranges causes that elastic deformations of the links lead to vibration problems. A new, basically model independent approach to active damping control is presented in this paper where the actuators are controlled to act like virtual spring-damper-systems. The paper illustrates this technique with the help of a simple and easy to model one link flexible robot and shows experimental results from two laboratory testbeds.

Control of a Flexible Manipulator With Artificial Muscle-Type Pneumatic Actuators, Using μ-Synthesis

In this work, position and vibration control of a flexible one-link manipulator, with an unknown but bounded payload mass and a pair of artificial muscle-type pneumatic actuators, are investigated both analytically and experimentally. A robot with flexible links originally drew attention for its capability to generate fast motion with small-powered actuators. A flexible-link robot also has advantages over a rigid-link robot in the sense that it is much safer when it comes into contact with its environment, including humans. Furthermore, for the sake of safety, it would be more desirable if an actuator could deliver required force while maintaining proper compliance. An artificial muscle-type pneumatic actuator is adequate for such cases. However, it is difficult to make an effective control scheme for this type of robot due to the nonlinearity and uncertainties on the dynamics of the actuator and the vibration of the flexible link. In this study, a controller based on μ-synthesis is developed. Robust performances on the accurate positioning of the arm and vibration suppression of the flexible link are achieved against various model uncertainties on these actuators, the flexible link, the payload, and sensor noise. The effectiveness of the proposed control scheme is confirmed through simulations and experiments.

Experimental Modeling of a Two-Link Flexible Manipulator

Modeling of flexible link robot manipulators can be achieved by using tne Euler-Lagrange equations of motion, resulting in a closed-form model which strongly depends on the knowlegde of the used mode shapes. In addition, computing the natural frequencies of the manipulator represents a drawback of a pure analytical modeling. In this contribution, a very flexible two-link robot is modeled by using the Euler-Lagrange equations of motion. Once the closed-form model is obtained, all the unknown parameters are determined experimentally.

Backstepping boundary control of flexible-link electrically driven gantry robots

Gantry robots are used for precision manufacturing and material handling in the electronics, nuclear, and automotive industries. Light, flexible links require less power, but may vibrate excessively. An implementable boundary controller is developed to damp out undesirable vibrations in a flexible-link gantry robot driven by a brushed DC motor. Hamilton's principle produces the governing equations of motion and boundary conditions for the flexible link. The electrical subsystem dynamics for a permanent magnet brushed DC motor couple with the link dynamics to form a hybrid system of partial and ordinary differential equations. A boundary voltage control law is developed based on Lyapunov theory for distributed parameter systems. Through an embedded desired-current control law, the integrator backstepping controller generates the desired control force on the mechanical subsystem. A velocity observer estimates the gantry velocity, eliminating one feedback sensor. Modal analysis and Galerkin's method generate the closed-loop modal dynamics. Numerical simulations demonstrate the improved vibration damping characteristics provided by the backstepping boundary control law. Experimental results confirm the theoretical predictions, showing the high performance of backstepping boundary control.

Mathematical modeling and fuzzy control of a flexible-link robot arm

In this paper, the Timoshenko theory is applied to investigate a new mathematical model for the “shoulder-elbow-like” single flexible-link robot arm with dampings. Detailed analysis and derivation are given to support the mathematical modeling of this particular flexible mechanism. A new design of a fuzzy-logic-based ( PI + D) 2 control scheme is developed for both vibration suppression and set-point tracking. Computer simulation results for the modeling are performed to observe the significant vibration modes, and simulation results for the control scheme demonstrate that the controllers perform very well for the tracking based on this flexible-link model. A newly developed method for stability analysis using the “two-straight-lines” criterion is also presented.

On the Properties of a Dynamic Model of Flexible Robot Manipulators

Control design of flexible robot manipulators can take advantage of the structural properties of the model used to describe the robot dynamics. Many of these properties are physical characteristics of mechanical systems whereas others arise from the method employed to model the flexible manipulator. In this paper, the modeling of flexible-link robot manipulators on the basis of the Lagrange’s equations of motion combined with the assumed modes method is briefly discussed. Several notable properties of the dynamic model are presented and their impact on control design is underlined.

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.

Joint motion dynamics and reaction forces in flexible-link robotic mechanisms

In this paper the dynamics of joint motion and the systems of joint reaction forces are investigated in flexible-link robots with rotational and translational joints. Some new concepts are introduced concerning the kinematic and dynamic modeling of flexible links. The dynamic equations for the joint motions and for the systems of reaction forces are derived by using the Newton-Euler laws. The effects of joint friction are discussed. The formulation is applicable for large flexible displacements as well. The determination of bearing reaction forces is studied.

On Vibration Damping of Hydraulically Driven Flexible Robots

Abstract Using robots for heavy loads andlor huge operating ranges causes on the one hand that elastic deformations of the links have to be taken into account. On the other hand, they demand actuators with a significant power density able to produce high forces which can profitably be reached by the use of hydraulic differential cylinders. This paper considers aspects on vibration damping of a hydraulically driven one link flexible robot by intelligent control of the actuator. The modeling of a simple one flexible link system is shown in addition to possible considerations of the hydraulic cylinder. Some ideas of vibration detection using measured values from a laboratory testbed are treated.

Stable Sampled-data Adaptive Control of Robot Arms Using Neural Networks

Stable neural network-based sampled-data indirect and direct adaptive control approaches, which are the integration of a neural network (NN) approach and the adaptive implementation of the discrete variable structure control, are developed in this paper for the trajectory tracking control of a robot arm with unknown nonlinear dynamics. The robot arm is assumed to have an upper and lower bound of its inertia matrix norm and its states are available for measurement. The discrete variable structure control serves two purposes, i.e., one is to force the system states to be within the state region in which neural networks are used when the system goes out of neural control; and the other is to improve the tracking performance within the NN approximation region. Main theory results for designing stable neural network-based sampled data indirect and direct adaptive controllers are given, and the extension of the proposed control approaches to the composite adaptive control of a flexible-link robot is discussed. Finally, the effectiveness of the proposed control approaches is illustrated through simulation studies.

A neural network controller for flexible-link robots

The object of this paper is to achieve tracking control of a partially known flexible-link robot arm. We show how to stabilize the internal dynamics by selecting a physically meaningful modified performance output for tracking. The controller is composed of a singular-perturbation-based fast control and an outer-loop slow control. The slow subsystem is controlled by a neural network (NN) for feedback linearization, plus a PD outer-loop for tracking, and a robustifying term to assure the closed-loop stability. No off-line training or learning is needed for the NN. Tracking and stability are proven using Lyapunov techniques that yield a novel modified NN weight tuning algorithm. >

Decentralized sliding mode control for flexible link robots

A technique using augmented sliding mode control for robust, real-time control of flexible multiple link robots is presented. For the purpose of controller design, the n-link, n-joint robot is subdivided into n single joint, single link subsystems. A sliding surface for each subsystem is specified so as to be globally, asymptotically stable. Each sliding surface contains rigid-body angular velocity, angular displacement and flexible body generalized velocities. The flexible body generalized accelerations are treated as disturbances during the controller design. This has the advantage of not requiring explicit equations for the flexible body motion. The result is n single input, single output controllers acting at the n joints of the robot, controlling rigid body angular displacement and providing damping for flexible body modes. Furthermore, the n controllers can be operated in parallel so that compute speed is independent of the number of links, affording real-time, robust, control.

Inclusion of shear deformation term to improve accuracy in flexible-link robot modelling

The problem of developing a static and dynamic model of a single flexible manipulator link which is of sufficient accuracy for use in a multiflexible-link system is considered. Although flexible link modelling has received much attention in the past, none of the models developed have adequate accuracy for application in a multi-link system. Very high modelling accuracy is necessary because there is significant inter-link coupling in a flexible manipulator and any modelling errors are therefore cumulative. Previous work based on an assumed mode model has made some progress towards improving accuracy by including a correction factor derived from finite element analysis, and the work reported here extends this by including a shear deformation term in the equations. The significant improvements in modelling accuracy thereby achieved are demonstrated by simulations of link motion.

Fuzzy learning control for a flexible-link robot

There are two main drawbacks in fuzzy control: 1) the design of fuzzy controllers is usually performed in an ad hoc manner where it is often difficult to choose some of the controller parameters; and 2) the fuzzy controller constructed for the nominal plant may later perform inadequately if significant and unpredictable plant parameter variations occur. In this paper we illustrate these two problems on a two-link flexible robot testbed by: 1) developing, implementing, and evaluating a fuzzy controller for the robotic mechanism, and 2) illustrating that payload variations can have negative effects on the performance of a well designed fuzzy control system. Next, we show how to develop and implement a fuzzy model reference learning controller for the flexible robot and illustrate that it can automatically synthesize a rule-base for a fuzzy controller that will achieve comparable performance to the case where it was manually constructed, and automatically tune the fuzzy controller so that it can adapt to variations in the payload. >

The swing up control problem for the Acrobot

Underactuated mechanical systems are those possessing fewer actuators than degrees of freedom. Examples of such systems abound, including flexible joint and flexible link robots, space robots, mobile robots, and robot models that include actuator dynamics and rigid body dynamics together. Complex internal dynamics, nonholonomic behavior, and lack of feedback linearizability are often exhibited by such systems, making the class a rich one from a control standpoint. In this article the author studies a particular underactuated system known as the Acrobot: a two-degree-of-freedom planar robot with a single actuator. The author considers the so-called swing up control problem using the method of partial feedback linearization. The author gives conditions under which the response of either degree of freedom may be globally decoupled from the response of the other and linearized. This result can be used as a starting point to design swing up control algorithms. Analysis of the resulting zero dynamics as well as analysis of the energy of the system provides an understanding of the swing up algorithms. Simulation results are presented showing the swing up motion resulting from partial feedback linearization designs.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Experiments in Control of a Flexible-Link Robotic Manipulator With Unknown Payload Dynamics: An Adaptive Approach

This article presents technology that extends the concept of end-point control of a flexible-link robot arm to handle payloads with unknown internal dynamics. The approach is based on merging high-performance control with an innovative identification algorithm in a self-tuning regulator framework. Payload dynamics are identified in real time using recently de veloped subspace fitting techniques. Sufficient excitation issues are addressed. End-point feedback controllers are formulated using frequency-weighted linear quadratic gaussian design methods. Experimental results demonstrating precision control of a very flexible single-link robot arm with unknown dynamic payloads are presented.

Grasping with flexible link fingers: An initial study

Grasping with flexible fingers presents an attractive approach for certain robotic tasks. Its implementation requires simultaneous position and force control of flexible manipulators, an area about which there is little information in the literature. This paper presents an initial effort at designing controllers for flexible link robots to control both position and force. The analysis is done on a two degree-of-freedom two- link manipulator with the last link flexible. A control strategy is proposed and asymptotic stability is proved. Results from using this control law in simulations and on an experimental setup are presented.

A hybrid frequency?time domain adaptive fuzzy control scheme for flexible link manipulators

This paper addresses the implementation of an adaptive fuzzy controller for flexible link robot arms. The design technique is a hybrid scheme involving both frequency and time domain techniques. The eigenvalues of the open loop plant can be estimated through application of a frequency domain based identification algorithm. The region of the eigenvalue space, within which the system operates, is partitioned into fuzzy cells. Membership function are assigned to the fuzzy sets of the eigenvalue universe of discourse. The degree of uncertainty on the estimated eigenvalues is encountered through these membership functions. The knowledge data base consists of feedback gains required to place the closed loop poles at predefined locations. A rule based controller infers the control input variable weighting each with the value of the membership functions at the identified eigenvalue. The afore-mentioned controller is compared through simulation with conventional techniques, namely pole placement and gain scheduling.