Single-link Flexible Arm Research Articles

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.

Trajectory tracking and active vibration suppression of a smart Single-Link flexible arm using a composite control design

This paper is concerned with the trajectory tracking and vibration suppression of a single-link flexible arm by using piezoelectric materials. The dynamics of a single flexible arm with PZT patches as sensor and actuator is derived using extended Hamilton's principle. Resulting equations show that the coupled beam dynamics including beam vibration and its rigid in-plane rotation takes place in two different time scales. By using singular perturbation theory, the system dynamics is divided into two subsystems. Then, a composite control scheme is elaborated that makes the orientation of the arm track a desired trajectory while suppressing its vibration. The proposed controller has two parts: one is a tracking controller designed for the slow (rigid) subsystem, and the other one is a stabilizing controller for the fast (flexible) subsystem. The outputs considered for the system are angular position of the hub and voltage of the sensor mounted on the structure. To avoid requiring further measurements of beam vibration and also angular velocity of the hub for the fast and slow control laws, respectively, two sliding mode observers for estimating the unknown states are also designed.

A Trajectory Planning Method for Output Tracking of Linear Flexible Systems Using Exact Equilibrium Manifolds

This paper describes a new trajectory planning method for the output tracking control of linear flexible systems; this method computes the exact solution of the equilibrium manifold. We establish a system of differential equations by combining kinematic and dynamic constraints and reformulate them in a singularly perturbed dynamics to obtain the equilibrium manifold in the form of an infinite series, which is our planned trajectory. We show that for the desired output defined by exponential functions, the equilibrium manifold becomes a converging geometric series that has a succinct form of summation. In addition, the inverse torque, which is the feedforward command, is easily produced by using the computed exact equilibrium manifold. We validate the effectiveness of the proposed method through simulations and experimental studies using a single-link flexible arm.

Generalised proportional integral torque control for single-link flexible manipulators

In this study, a generalised proportional integral (GPI) output feedback control scheme is proposed to control the torque of a single-link flexible arm for free and constrained motion. The control is based on the properties of differential flat systems. The control is also found to be robust with respect to the motor static friction. The only variable to measure is the torque in the hub by means of only one sensor, which in this case, is constituted by a pair of strain gauges. An hybrid control law is presented to control the manipulator in collision with an object (constrained motion) and when it can freely move (free motion) commanded by an on-line impact detection algorithm. Experiments are presented to verify the goodness of the proposed control law.

Stabilization of a Parallel Structured Single-link Flexible Arm Mounted on Moving Base Using Kalman Filter Based LEQG Control

Stabilization of a Parallel Structured Single-link Flexible Arm Mounted on Moving Base Using Kalman Filter Based LEQG Control

Force control of a very lightweight single-link flexible arm based on coupling torque feedback

In this paper, a feedback control law is proposed for regulating the contact force exerted by a very lightweight single-link flexible manipulator when it comes into contact with a motionless object. This control law is based on a lumped-parameter model. The tracking of the desired contact force is obtained by using a feedback loop control of the coupling torque between the motor and the flexible arm. To achieve a good performance on the force control it is only necessary to measure the coupling torque at the root of the arm. Neither the contact force sensor nor the angular position sensor of the motor are used in the control method. A modified PID controller is proposed for this control law. In this work the force control problem is studied for both free and constrained motions of the flexible manipulator, and a collision detection algorithm is also described.

Design of Trajectories with Physical Constraints for very Lightweight Single Link Flexible Arms

This article deals with feedforward control of very lightweight, flexible robotic arms. In particular, we develop a new, objective method of designing a trajectory that can be used as a modified input, to cancel tip vibrations during robot manoeuvres. This method takes into account the constraints found in real actuators (DC-motors), such as the maximum torque the motor can supply, and also those due to the mechanical limits of the link, like the maximum deflection before reaching the elastic limit of the link. The parameters of the internal control of the actuators are also derived from the design process, achieving the fastest performance possible without saturating the motor. Lastly, we show some experimental results which clearly demonstrate the benefits of the new trajectories by comparing them to a ramp one.

Modified PID Control of a Single-Link Flexible Robot

The use of flexible links in robots has become very common in different engineering fields. The issue of position control for flexible link manipulators has gained a lot of attention. Using the vibration signal originating from the motion of the flexible-link robot is one of the important methods used in controlling the tip position of the single-link arms. Compared with the common methods for controlling the base of the flexible arm, vibration feedback can improve the use of the flexible-link robot systems. In this paper a modified PID control (MPID) is proposed which depends only on vibration feedback to improve the response of the flexible arm without the massive need for measurements. The arm moves horizontally by a DC motor on its base while a tip payload is attached to the other end. A simulation for the system with both PD controller and the proposed MPID controller is performed. An experimental validation for the control of the single-link flexible arm is shown. The robustness of the proposed controller is examined by changing the loading condition at the tip of the flexible arm. The response results for the single-link flexible arm are presented with both the PI and MPID controller used. A study of the stability of the proposed MPID is carried out.

Comprehensive mathematical modelling of a lightweight flexible link robot manipulator

This paper deals with a comprehensive study of the application of the Timoshenko Beam Theory (TBT) concepts to the mathematical modelling of a planar lightweight single link flexible robot manipulator arm pinned at its actuated base and carrying a payload at its free end-point. The emphasis being essentially set on obtaining accurate and complete equations of the transversely vibrating motion that display the most relevant aspects of structural properties inherent to the modelled lightweight flexible link, two important damping mechanisms, internal structural viscoelasticity (Kelvin-Voigt damping) and external viscous air damping, have been included in addition to the TBT classical effects of cross section shear deformation and rotational inertia. Torsional, gravitational and longitudinal elongation effects have been neglected. Digital simulations are performed to show the free vibrational behaviour of the modelled robotic system.

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.

Feedforward control of multimode single-link flexible manipulators based on an optimal mechanical design

This paper proposes a method to modify the dynamics of single-link flexible arms in order to allow the design of a control system which is more robust to changes in the payload value. This is achieved by attaching some small lumped masses at some points of the link. Therefore, connections between the dynamics and the feedforward control of single-link flexible manipulators are considered to simplify the control and make the system faster and more robust. The feedforward controller design is based on the so-called dynamic model inversion technique derived from a discretization of the system dynamic model. A comparative assessment between the discrete model inversion based on feedforward control and the command preshaping technique is presented. Numerical examples and experimental results thus changing the payload values are carried out.

Robust vibration control of a flexible arm subjected to torque disturbance

This paper presents a perturbation estimator in sliding mode control system and applies it to vibration control of a flexible arm subjected to torque disturbance. The proposed estimator is featured by an integrated average value of the imposed perturbation over a certain sampling period. By implementing this type of estimator, undesirable chattering phenomenon can be effectively alleviated in the estimation process. In addition, the proposed method offers a flexibility for tuning the ratio of the estimation sampling time to the control input sampling time. In order to demonstrate the effectiveness of the proposed methodology, a single-link flexible arm is constructed. After formulating the governing equation of motion, a sliding mode controller which is integrated with the proposed estimator is designed. Vibration control performances of the flexible arm subjected to sinusoidal torque disturbances are evaluated through both computer simulation and experimental realization.

イノベーション過程に基づく１リンク柔軟アームの衝突発生の検知と停止制御

Damage avoidance of the flexible manipulators in collision with unlooked-for obstacle is a significant problem in industry and space programs. This paper presents a method of control for reducing damage and/or undesirable vibration of the single-link flexible arm due to collision. The detection of the collision is carried out using the detection function which was proposed recently by the author. The controller is designed to have twofold manner : i) to control the position and vibration of the flexible arm; and ii) to suspend the position control and to minimize the deformation and vibration of the arm whenever any collision has been detected. Numerical simulations and experiments are provided.

A new modeling approach to single-link flexible manipulator using singular perturbation method

This paper presents a new methodology for modeling a single-link flexible manipulator with an arbitrarily large (infinite) number of deflection modes based on the singular perturbation method. It is shown that a part of the fast dynamics of the singularly perturbed system representing flexibility is treated as a norm-bounded uncertainty. In other words, the proposed approach to modeling actually characterizes, in some sense, a reduced-order model of the system. Output feedback control of the tip position is controlled by utilizing the ɛ-dependent H∞ technique on the rest of the certain dynamics of the manipulator. Robust regulation is obtained by minimizing the influence of the uncertainty on the tip position. The proposed strategy is applied to a single-link flexible arm and the simulation results verify the effectiveness of the analysis and design.

시간 지연 추정을 이용한 강인 Backstepping 제어

A controller is proposed for the robust backstepping control of a class of nonlinear multiple-input multiple-output (MIMO) systems which can be converted to a strict feedback form. The proposed robust backstepping control scheme follows a systematic procedure for the design of control laws and uses time delay estimation (TDE) to estimate the uncertainties such as parameter variations, unknown disturbances, and unmodeled dynamics, etc. The proposed controller can be also applied to nonlinear MIMO systems with unmatched uncertainties. Stability analysis of the closed-loop system which contains the plant and the proposed controller is also studied and hereby a sufficient stability condition for the closed-loop system is proposed. The simulation results show that the control scheme works well with uncertainties and the proposed stability condition is valid. The controller is experimentally verified on a single-link flexible arm to show the effectiveness of the proposed scheme in the complicated systems with uncertainties.

Vibration control of a single-link flexible arm subjected to disturbances

Vibration control of a single-link flexible arm subjected to disturbances

2A1-3F-F7 トルクユニットを用いた 1 リンク柔軟アームの制御

2A1-3F-F7 トルクユニットを用いた 1 リンク柔軟アームの制御

Trajectory planning for the tracking control of systems with unstable zeros

In this paper, a trajectory control strategy for a nonminimum phase system is proposed. A continuous-time version of the zero-phase error-tracking controller (ZPETC), a well-known discrete-time feedforward controller for tracking control of a nonminimum phase system, is derived. The performance of the continuous ZPETC is further enhanced by adopting a specially designed sinusoidal trajectory to compensate gain error. The sinusoidal trajectory has a synergic effect on tracking performance when combined with the continuous ZPETC. The effectiveness of continuous ZPETC with sinusoidal trajectory is confirmed through simulation and experiment of a nonminimum phase plant, a single link flexible arm.

ADJOINT-TYPE ITERATIVE LEARNING CONTROL FOR A SINGLE-LINK FLEXIBLE ARM

Iterative learning control (ILC) obtains a desired input that exactly generates the desired output through repetitions of the similar tasks. In this paper, an experiment of the adjoint-type ILC based on the gradient method is carried out by using a single-link flexible arm. Experimental results showed that, even if the single-link flexible arm is modeled by a simple method and has some uncertainties, exact output tracking is achieved. Moreover, pre-actuation, which is remarkable aspect of the adjoint-type ILC, is observed.