Single-link Flexible Robot Arm Research Articles

Research on Dynamic Modeling Method of Single Linkage Flexible Robotic Arm

In this paper, a dynamics modeling method is proposed for a single-link flexible robotic arm. Firstly, the dynamic equation of the flexible manipulator system is deduced by using the Lagrange equation, secondly, the nonlinear model of the single-link flexible robotic arm is obtained by separating the spatio-temporal variables using the assumed modes method, and the model is verified by the Quanser flexible robotic arm experimental platform. Finally, the model is modified for the dead zone of the actuator found in the experimental process, which improves the accuracy of the model.

Precise tip-positioning control of a single-link flexible arm using a fractional-order sliding mode controller

This article presents an efficient scheme based on fractional order sliding mode control approach for precision tip position control of a single link flexible robot arm. The proposed control strategy is robust against the system parameters variations such as payload and viscous friction variations in the presence of the sinusoidal disturbance and the unknown Coulomb friction disturbances. The aim of controller design is reduction of the deviation caused by the link flexibility and then the precision tip positioning control of the single-link flexible arm. In this regard, sliding mode control strategy is performed in two stages. In the first stage, the difference between the motor angle (load angle) and the tip angle of the flexible link is reduced by applying the proposed fractional order sliding mode controller and then, in the second step, the precision tracking of the tip position of the link is done by adding another sliding mode control scheme. The feasibility and effectiveness of the proposed control scheme is demonstrated via numerical simulation results.

Similar Fault Isolation of Discrete-Time Nonlinear Uncertain Systems: An Adaptive Threshold Based Approach

In this paper, a new concept of “similar fault” is introduced to the field of fault isolation (FI) of discrete-time nonlinear uncertain systems, which defines a new and important class of faults that have small mutual differences in fault magnitude and fault-induced system trajectories. Effective isolation of such similar faults is rather challenging as their small mutual differences could be easily concealed by other system uncertainties (e.g., modeling uncertainty/disturbances). To this end, a novel similar fault isolation (sFI) scheme is proposed based on an adaptive threshold mechanism. Specifically, an adaptive dynamics learning approach based on the deterministic learning theory is first introduced to locally accurately learn/identify the uncertain system dynamics under each faulty mode using radial basis function neural networks (RBF NNs). Based on this, a bank of sFI estimators are then developed using a novel mechanism of absolute measurement of fault dynamics differences. The resulting residual signals can be used to effectively capture the small mutual differences of similar faults and distinguish them from other system uncertainties. Finally, an adaptive threshold is designed for real-time sFI decision making. One important feature of the proposed sFI scheme is that: it is capable of not only isolating similar faults that belong to a pre-defined fault set (used in the training/learning process), but also identifying new faults that do not match any pre-defined faults. Rigorous analysis on isolatability conditions and isolation time is conducted to characterize the performance of the proposed sFI scheme. Simulation results on a practical application example of a single-link flexible joint robot arm are used to show the effectiveness and advantages of the proposed scheme over existing approaches.

Reinforcement Learning Control of a Single-Link Flexible Robot Arm based on Actor-Critic

Reinforcement Learning Control of a Single-Link Flexible Robot Arm based on Actor-Critic

Robust position-based impedance control of lightweight single-link flexible robots interacting with the unknown environment via a fractional-order sliding mode controller

SUMMARYThis paper presents a fractional-order sliding mode control scheme equipped with a disturbance observer for robust impedance control of a single-link flexible robot arm when it comes into contact with an unknown environment. In this research, the impedance control problem is studied for both unconstrained and constrained maneuvers. The proposed control strategy is robust with respect to the changes of the environment parameters (such as stiffness and damping coefficient), the unknown Coulomb friction disturbances, payload, and viscous friction variations. The proposed control scheme is also valid for both unconstrained and constrained motions. Our novel approach automatically switches from the free to the constrained motion mode using a simple algorithm of contact detection. In this regard, an impedance control scheme is proposed with the inner loop position control. This means that in the free motion, the applied force to the environment is zero and the reference trajectory for the inner loop position control is the desired trajectory. However, in the constrained motion the reference trajectory for the inner loop is determined by the desired impedance dynamics. Stability of the closed loop control system is proved by Lyapunov theory. Several numerical simulations are carried out to indicate the capability and the effectiveness of the proposed control scheme.

Input-state feedback linearization control of a single-link flexible robot arm moving under gravity and joint friction

In this paper we address the trajectory tracking problem of the end-effector of a single link flexible arm in which the gravity forces and the joint friction forces are taken into account. As an overall approach, a double loop cascade control is used to deal with the joint friction: in its inner loop a two-degree-of-freedom controller is responsible for the joint position in the presence of Coulomb friction disturbances, while in its outer loop an input-state feedback linearization-based controller is implemented to suppress the vibrations and track an end-effector trajectory. To highlight the benefits of the proposed controller in presence of joint friction, the controller was compared with other approaches based on feedback linearization reported in the literature, which considered only a single loop. The results of this comparison showed that our approach provides superior performance in terms of settling time, maximum overshoot and residual vibrations.The design of the controller presented relies on a non-linear single-lumped mass dynamic model that describes the dynamics of a single link arm with only one significant vibrational mode. The hypothesis of a single lumped mass model could be considered inaccurate given the distributed nature of the link mass, especially in situations in which the link mass is comparable to the payload mass held by the robot. However, for the parameters of our physical platform two studies are presented to demonstrate that the single lumped mass model is a proper description of the system even in situations in which the link mass is up twice bigger than the payload mass. The results of the paper are demonstrated with co-simulations with Matlab/Simulink and MSC ADAMS, and experimental validation.

Control of Flexible Beam with Unmodelled Dynamics Using Second-Order Pole Placement and LQR Techniques

Control of a flexible beam such as that in flexible-link robot manipulators in many mechanical devices is very challenging, due in part to its intrinsic nature of unmodelled dynamics in a system. Such a system is said to be subjected to nonholonomic constraints, hence its feedback control is difficult to realize. This paper presents the application of control design based on second-order pole placement and LQR approaches to a single-link flexible robotic arm. In this case, a controller considering the flexibility of highly-flexible arm is employed to suppress the tip vibration of the manipulator. The effectiveness of the method is verified through computer simulations and consequently, the adequateness of the control performance and the feasibility of the system with a super-light link are shown.

Sliding mode tracking control of a very lightweight single-link flexible robot robust to payload changes and motor friction

A sliding mode control design methodology is applied to solve the position tracking problem of an uncertain very lightweight single-link flexible robot arm. Throughout this work we seek a control scheme robust with regards to payload and actuator friction changes, without the establishment of any bounding limits on these parameter variations. Based on the decomposition of the robot dynamics into the motor and flexible link submodels, two nested control loops are proposed, each one of these controlled by an independent sliding mode controller. By carrying on this model decomposition, both motor friction and payload changes become matched uncertainties in their respective models, allowing for their effective rejection using these sliding controllers. Simulations and experimental results are shown to demonstrate the performance of the control system proposed.

Optimal Tuning of a PD Controller for a Single-Link Flexible Robot Arm Using Adaptive Genetic Algorithm

Flexible manipulators have received wide attention because they are more realistic than their rigid counterparts in many practical conditions. The control of the motion and vibration of an elastic model has inspired many studies in the past decades. In this paper, a finite element model is developed and used for the modeling of the single-link flexible arm. A new adaptive genetic algorithm (AGA) is proposed to optimize the feedback gains of a proportional derivative (PD) controller for the control of the motion and vibration of the flexible arm. The proposed technique is based on a new adaptive mutation operator to adjust the probability of mutation of each chromosome based on the average fitness value at each generation. The results are compared with those obtained by applying simple GA and a direct evaluation of the objective function in the domain. It has been shown that the new developed adaptive mechanism is faster in convergence and the obtained solutions are of higher fitness values. Compared analysis shows the effectiveness of the proposed adaptive GA over traditional genetic algorithms that have the defects of premature convergence and stagnation when applied in optimization problems. Three different objective functions based on minimizing the error function are tested and compared. Multi-objective error fitness function combined with AGA has given the best system response. Simulation results demonstrate the effectiveness of the proposed technique which encourages for further research into the application of the technique in controlling multiple link flexible robots for further applications.

Experimental control of a single-link flexible robot arm using energy shaping

Flexible-link robotic manipulators are mechanical devices whose control can be rather challenging, among other reasons because of their intrinsic under-actuated nature. This paper presents the application of an energy-based control design methodology (the so-called IDA-PBC, interconnection and damping assignment passivity-based control) to a single-link flexible robotic arm. It is shown that the method is well suited to handle this kind of under-actuated device not only from a theoretical viewpoint but also in practice. A Lyapunov analysis of the closed-loop system stability is given and the design performance is illustrated by means of a set of simulations and laboratory control experiments, comparing the results with those obtained using conventional control schemes for mechanical manipulators.

Mathematical Modeling and Simulation of a Flexible Shaft-Flexible Link System With End Mass

In this study, the equation of motion of a single link flexible robotic arm with end mass, which is driven by a flexible shaft, is obtained by using Hamilton's principle. The physical system is considered as a continuous system. As a first step, the kinetic energy and the potential energy terms and the term for work done by the nonconservative forces are established. Applying Hamilton's principle the variations are calculated and the time integral is constructed. After a series of mathematical manipulations the coupled equations of motion of the physical system and the related boundary conditions are obtained. Numerical solutions of equations of motion are obtained and discussed for verification of the model used.

RECURSIVE IDENTIFICATION OF PHYSICAL PARAMETERS IN A FLEXIBLE ROBOT ARM

ABSTRACTRecursive identification of a physically parameterized model of a single link flexible robot arm is considered. The parameters are estimated using a recursive prediction error method applied to a linear continuous time model structure and discrete time data. The algorithm is applied to real data from an industrial robot, and three important parameters are identified using only measurements of the motor angle. The experiments show that the particular parameter that is estimated will have big influence on the algorithm behavior.

Sliding Mode Tracking Control for a Single-Link Flexible Robot Arm

In this paper two different sliding mode tracking approaches for controlling single link-flexible manipulators are presented. On the basis of an approximated finite-dimensional nonlinear flexible model, the first robust controller is derived using classical sliding mode techniques and the second control strategy using continuous sliding mode approach. The performances of the proposed control law are demonstrated by simulations and experiments carried out with the single-link flexible robot arm of our Institute. Another new aspect of this article consists of the extension of the continuous sliding mode approach to tracking problems and the practical implementation of the developed control concepts.

Shear force feedback control of a single-link flexible robot with a revolute joint

In this paper we present a shear force feedback control method for a single-link flexible robot arm with a revolute joint for which it has been shown that direct bending strain feedback can suppress its vibration. Our primary concern is the stability analysis of the closed-loop equation which has not appeared in the literature. We show the existence of a unique solution and the exponential stability of this solution by doing spectral analysis and estimating the norm of the resolvent operator associated with this equation. Some experiments are also conducted to verify these theoretical developments.

Optimal Design and Sensitivity Analysis of Flexible Robotic Manipulators Fabricated from Advanced Composite Materials

The strategy for optimization design of flexible robotic manipulators fabricated from fibrous polymeric composite materials is presented. The formulation of the optimization design problem is accomplished by integrating design variables such as lamina thickness, fiber orientations, and fiber volume fractions, which characterize the mass, damping, and stiffness properties of the robotic manipulators. The formulation of the optimal problem is also accomplished by defining the objective function and the domains corresponding to the constraints. The optimal numerical simulation is based on the viscoelastodynamic finite element analysis. The generalized reduced gradient method is adopted for optimal algorithm. A sensitivity analysis of the dynamic response of robotic manipulators is discussed herein as post-optimal analysis to determine which design variables of the analysis model are the most sensitive parameters in determining the solutions. This strategy is illustrated by considering the design of a single-link flexible robotic arm fabricated from laminated composites. Tip deflection of the link of the robot arm was selected as the objective function, whereby the mass, damping, and stiffness characteristics of the structures are automatically introduced into the design procedures. It is shown in an example that the optimal solutions have significant improvement in performance relative to an arbitrary initial design. The sensitivity analysis also identified the most important design parameters to be considered when redesigning the robot manipulator.

Robust regulation and trajectory tracking for flexible robots by using piezoelectric actuators

We show how thin planar piezoelectric actuators can be used for the robust regulation and trajectory tracking of flexible robots. The analysis is restricted to single-link flexible robot arms, having a planar 'sandwich' structure, constituted by two piezoelectric films, mounted on a thin elastic support. The motion of the structure can be approximately described by finite dimensional, linear, time-invariant equations. The proposed controller provides the regulation of the generalized coordinates, which describe the structure shape, to zero or to constant reference signals with zero steady-state error, and the tracking of ramp reference signals with a finite, arbitrarily bounded, steady-state error, even when variations of the structure parameters occur. Some simulation results are reported.

129 Harmonic response measurements of single-link flexible robot arms

129 Harmonic response measurements of single-link flexible robot arms

Comparison of models for a single-link flexible robot ARM

The paper deals with the approximate dynamic modelling of a single-link flexible robot arm by using two different approaches (the Ritz method and the finite-element method), the effectiveness of which is studied. The link has been modelled as a Bemoulli-beam with constant cross section and density. Some experimental tests have been carried out to validate the dynamic models in the frequency domain.

Robust regulation and trajectory tracking for flexible robots by using piezoelectric actuators

Thin planar piezoelectric actuators are used for the robust regulation and trajectory tracking of flexible robots. The analysis is restricted to single-link flexible robot arms, having a planar “sandwich” structure, constituted by two piezoelectric films, mounted on a thin elastic support. The motion of the structure can be approximately described by finite dimensional, linear, time invariant equations. The proposed controller provides the regulation of the generalized coordinates, that describe the structure shape, to zero or to constant reference signals with zero steady-state error, and the tracking of constant velocity reference signals with a finite, arbitrarily bounded, steady-state error, even when variations of the structure parameters occur. Some simulation results are reported.

On Trajectory Planning for Flexible Robots

A computational technique, based on radial basis functions, for deriving trajectories for a single link flexible robot arm, is presented in this paper. Using an approximation based on radial basis functions and point collocation method, the trajectory planning problem is transformed into a linear least-squares problem. This technique is easy to implement and is computationally efficient. Furthermore, the trajectories obtained do not produce any residual vibration at the end of the move. A computer simulation based on a finite-element model indicates the effectiveness of the proposed technique.