Control Of Flexible Robot Manipulators Research Articles

Nonlinear Observer-Based Visual Servoing and Vibration Control of Flexible Robotic Manipulators With a Fixed Camera.

This article studies the visual servoing and vibration suppression control for flexible manipulators when the system states are unmeasurable and only the image feedback is available. The dynamic equations of flexible manipulators are decomposed into the slow and fast subsystems based on the singular perturbation theory. The nonlinear observers based on the state transformation using the Lie derivatives are proposed to estimate the unmeasurable system states and unknown camera intrinsic parameters at the same time. Then, the image-based controllers utilizing the estimated states are, respectively, designed in the slow and fast subsystems to regulate the image positions of feature points and suppress the vibration of flexible manipulators simultaneously. In the proposed approach, only the visual feedback is required to generate the control input for flexible manipulators, which simplifies the controller implementation. The stability of the proposed control scheme is proved based on the Lyapunov theory. Finally, experimental results on a flexible single-link manipulator are provided to demonstrate the effectiveness of the proposed control approach.

End-Effector Position Estimation and Control of a Flexible Interconnected Industrial Manipulator Using Machine Learning

The control of flexible robot manipulators is a challenging task, especially when one considers parallel and interconnected manipulators under flexibility considerations. This paper proposes a method to estimate the position of the end-effector of a flexible interconnected manipulator based on a virtual sensor principle and function approximation schemes. By using SolidWorks/MSC ADAMS software, we developed a virtual prototype of a flexible interconnected manipulator, and rigorously evaluated the feasibility of using function approximation schemes such as Neural Networks (NN), Support Vector Machines (SVM), and Gaussian Process (GP) in estimating the deflection error arising due to the flexibility of the robot structure. Our rigorous computational experiments have shown that: (1) the NN, SVM, and GP models were are able to attain the promising and reasonable prediction accuracy, (2) a feedforward NN with 535 neurons and an Ascending distribution of its nodes achieves the best prediction and generalization to unseen environments (the upper bound of the error was <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.15\times 10^{-3}$ </tex-math></inline-formula> m); implying the robust estimation of the position of the end-effector under flexibility considerations, and (3) the control based on the inverse Jacobian and a NN-based estimator was able to follow a sinusoidal trajectory with reasonable tracking and error performance in MSC ADAMS & MATLAB/Simulink co-simulation. Our results show the feasibility and effectiveness of the nonlinear relationships learned by NN, SVM, and GP in aiding estimation and control of the position of the end-effector of the flexible manipulator with a promising/desirable capability.

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.

Vibration Control of a Space Flexible Robot Manipulator Using PZT Actuators

The dynamic analysis and control of flexible robot manipulators have been the main concerns of many recent studies in aeronautics and robotics. Moreover, the complexity of this problem increases when a flexible manipulator carries a payload. In this paper, we proposed a space two-link flexible manipulator with tip payload featuring surface-bonded piezoelectric torsional actuator and shear actuator. The equations of motion for the system are obtained using Hamilton’s principle. A Lyapunov-based controller is proposed to suppress the vibration of the system. Stability of the system is also investigated. The simulation results demonstrate the proposed control strategy is well suited for active control of vibration suppression on flexible manipulators.

Identification of nonlinear systems by nonparametric approach with application to control of flexible robot manipulator

We apply nonparametric techniques to identify nonlinear dynamic block-oriented systems of Hammerstein type. Hammerstein system consists of a memoryless nonlinear system followed by a dynamic, linear system. We introduce identification algorithms based on input-output observations for both systems and study their convergence and the rates. The performance of identification algorithms is validated in simulation studies. We apply Hammerstein system identification algorithms to identification of nonlinearities in a flexible robot manipulator.

Motion control of flexible-link manipulators

A new method is proposed for the end-effector trajectory tracking control of flexible robot manipulators. The equations of motion are separated into two parts that represent the pseudostatic equilibrium and the deviations from it. The part of the control input for the pseudostatic equilibrium is determined algebraically, and the other part of the control input for the stabilization of the deviations is obtained by a state variable feedback law, by using strain, joint variable, and end-effector position measurements. The feedback gain matrix is determined online by continuously updated pole placement. The pseudostatic equilibrium is defined here as a hypothetical state, in which the velocity and acceleration of the end-effector have their desired values whereas the elastic deformations are instantaneously constant. In order to demonstrate the method, a planar two-link robot with a flexible forearm is taken into consideration. The elasticity of the forearm is approximately described by the first two modes, and a controller is designed by using this two-mode model. Furthermore, in order to investigate the effects of modelling discrepancies, a ‘submodel controller’ is designed by using a model with only the first mode and it is applied to the same system with the two-mode model. The performances of these two controllers are compared by means of simulations. The behaviour of the flexible robot is also simulated by using the computed torque method as if the robot is rigid in order to illustrate the importance of including the flexibility effects in the formation of an appropriate control law. The spillover effect that causes the dominant poles to approach towards the imaginary axis is inspected by monitoring the real parts of the dominant poles of the closed-loop system under the effect of the ‘submodel’ and ‘computed torque’ controllers.

Constrained Motion Control of Flexible Robot Manipulators Based on Recurrent Neural Networks

In this paper, a neural network approach is presented for the motion control of constrained flexible manipulators, where both the contact force everted by the flexible manipulator and the position of the end-effector contacting with a surface are controlled. The dynamic equations for vibration of flexible link and constrained force are derived. The developed control, scheme can adaptively estimate the underlying dynamics of the manipulator using recurrent neural networks (RNNs). Based on the error dynamics of a feedback controller, a learning rule for updating the connection weights of the adaptive RNN model is obtained. Local stability properties of the control system are discussed. Simulation results are elaborated on for both position and force trajectory tracking tasks in the presence of varying parameters and unknown dynamics, which show that the designed controller performs remarkably well.

DESIGN AND ANALYSIS OF A FACILITY FOR FREE – FLOATING FLEXIBLE ROBOTIC MANIPULATORS

The development of the Waterloo Flexible Link Experimental (WATFLEX) facility was initiated at the University of Waterloo to provide resources for conducting experiments involving the dynamics and control of flexible robotic manipulators – specifically, two dimensional dynamic mass capture, impact dynamics and vibration suppression. The system consists of a number of different subsystems including the robotic manipulator, motion and deflection sensors, the digital controller, the data acquisition system, and the pneumatic system that floats the manipulator on a support structure. In this paper, the design and current status of each of these subsystems is described. Experimental analysis results of the support table, the data acquisition system, and some analog sensors are presented and analyzed.

Tracking control of flexible robot manipulators with active inertia links

SUMMARYThe flexible structure of a robot multi-links manipulator can be either a side effect or, on the contrary, an essential feature. We present a fairly general model to derive the corresponding dynamic equations in quite a systematic and simple way. To this end, we use the Lagrange formulation with strain energy potential and Raleigh (dissipation) functions. The approach can incorporate torsional deformation and aerodynamic friction, and it applies easily to robots working in the sea. The trajectory control appears to be one in the presence of model imprecision, and a slightly modified version of the classical sliding control technique is utilized to design the tracking control of the manipulator. Then we introduce the time-varying inertia link device (carried out by means of sliding masses) which we suggested in earlier work, and we show how it can be used to improve the tracking control scheme above. This paper contributes new ideas concerning flexible multi-links arms and active inertia links.

Application of optimal control theory to flexible robotic manipulations

The dynamic equatios of a single link flexible robotic manipulator and the measurements are formulated. The observer and the control law are derived based on optimal control theory. The numerical results of several cases obtained through computer simulation are presented here. The issues of nonlinearity and sampling rate, and the effects of gravity, white noises, and damping are investigated. The feasibility of real-time control of flexible robotic manipulators is discussed.

Issues in the dynamics and control of flexible robot manipulators

Issues associated with modeling and control of robots with elastic arms are considered. An approach similar to substructure synthesis is used to model the system, where each link is first modeled independently of the others. The joint displacements are then used as constraints to synthesize the equations of motion. It is shown that the centrifugal stiffening effect is the dominating factor for the overall system behavior. Different approaches are discussed for the control design. The effects of flexibility on the response and on the closed-loop control are examined within the context of an example. N important issue of concern in the control of robots is the difference between the total mass of the manipulator and the mass of the payload. If a robot is compared with the human body, it is easily concluded that the manipulator is very inefficient. An inefficient robot implies low productivity and higher costs. A robot can be made more efficient by reducing the thickness of its arms. The resulting increased flexibility, unless considered properly, reduces pointing accuracies and affects the stability of the payload. Another source of inaccuracy is flexibility of the joints. There is considerable debate in the literature as to which source causes more inaccuracies. This paper is concerned with the modeling and control of manipulators with substantial flexibility in the arms. An approach similar to substructure synthesis is used to model the manipulator, and different control strategies are discussed. The mathematical formulation is applicable to robots with revolute or spherical joints. Several methods of modeling manipulators with elastic joints or with flexible arms exist in the literature.111 Each of the approaches uses a variety of assumptions. For example, Refs. 1-4 consider only the static deflections of the links; Ref. 1 treats the connecting links as massless, and Ref. 4 considers only one flexible bending mode for each link. Refer