Single-link Flexible 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.

Sliding Mode Robust Active Disturbance Rejection Control for Single-Link Flexible Arm with Large Payload Variations

This paper proposes a novel robust control scheme for tip trajectory tracking of a lightweight flexible single-link arm. The developed control scheme deals with the influence of tip payload changes and disturbances during the working process of the flexible arm, thus realizing the accurate tracking for the tip reference trajectory. The robust control scheme is composed of an inner loop and an outer loop. The inner loop adopts the traditional PD control, and an active disturbance rejection control (ADRC) with a sliding mode (SM) compensation is designed in the outer loop. Moreover, the sliding mode compensation is mainly used to cope with the disturbance estimation error from the extended state observer (ESO), by which the insensitivity to tip payload variations and strong disturbance resistance is achieved. Finally, some numerical simulations are performed to support the theoretical analysis. The results show that the system is more robust to the tip mass variations of the arm and more resistant to the external torque after adding the sliding mode robustness term to the ADRC.

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.

Adaptive Sliding Mode Impedance Control of Single-Link Flexible Manipulators interacting with the Environment at an Unknown Intermediate Point

SUMMARYThis paper proposes an adaptive robust impedance control for a single-link flexible arm when it encounters an environment at an unknown intermediate point. First, the intermediate collision point is estimated using a collision detection algorithm. The controller, then, switches from free to constrained motion mode. In the unconstrained motion mode, the exerted force to environment is nearly zero. Thus, the reference trajectory is a prescribed desired trajectory in position control. In the constrained motion mode, the reference trajectory is determined by the desired target dynamic impedance. The simulation results demonstrate the efficiency of proposed control scheme.

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.

Stability analysis of a single-link flexible arm driven by a motor of speed reference type

The stability analyses for motion and vibration control of a single-link flexible arm having a tip payload are investigated using a linear distributed parameter model. The controller design in this paper includes the joint angle proportional–integral–derivative (PID), the bending strain (S) and bending strain integration (SI) feedbacks, and their combinations. The paper presents a new method applying the properties of an irrational passive transfer function and root locus to study the effect of various feedbacks on the infinitely many open loop poles, necessary and sufficient conditions in terms of the dimensionless positive gain constants are reported such that the closed-loop is asymptotically stable. The exact solutions of the infinite-dimensional closed-loop system are obtained using the infinite product formulation. Since the controller design is based on the infinite-dimensional system and is independent of system parameters, the proposed system promises stability robustness to parameter uncertainties and is also free of spillover problems. The validity of the controllers is assessed and compared with the experimental results in the existing literature.

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.

Payload Mass Identification of a Single-Link Flexible Arm Moving under Gravity: An Algebraic Identification Approach

We deal with the online identification of the payload mass carried by a single-link flexible arm that moves on a vertical plane and therefore is affected by the gravity force. Specifically, we follow a frequency domain design methodology to develop an algebraic identifier. This identifier is capable of achieving robust and efficient mass estimates even in the presence of sensor noise. In order to highlight its performance, the proposed estimator is experimentally tested and compared with other classical methods in several situations that resemble the most typical operation of a manipulator.

Time-delay control with switching action using a frequency-shaped integral sliding surface

The Time Delay Control with switching Action (TDCSA) method was recently proposed as a promising technique in a robust control area, where a plant has unknown dynamics with parameter variations and substantial disturbances are present. When TDCSA is applied to a nonlinear system with frequency resonances, TDCSA reveals a chattering problem or an undesired vibration. This undesired vibration and chattering problem comes from the switching action and high gains. Fast sliding mode dynamics or fast desired error dynamics improve the control performance, but excite the un-modeled resonance modes and cause an undesired vibration or chattering. To solve this problem, we proposed an integral sliding surface design method using frequency-shaping features. This method incorporates frequency-shaping LQ design techniques into an integral sliding surface. In this paper, the stability analysis of TDCSA using a frequency-shaped integral sliding surface is analyzed. Based on the experimental results, the frequency-shaped integral sliding surface was shown to be practicable for a single-link flexible arm. Motion control of a single-link flexible arm with un-modeled flexible modes was taken into account. The desired trajectory was tracked while minimally exciting the un-modeled flexible modes.

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.

PASSIVITY-BASED INTEGRAL CONTROL AND STABILITY ANALYSIS OF A CONSTRAINED SINGLE-LINK FLEXIBLE ARM

The design of flexible manipulator is complicated due to inherently infinite dimension in nature. The sequential challenge is the problem such a non-minimum phase that is the cause of system instability. In this paper, a constrained single-link flexible arm is fully investigated using a linear distributed parameter model. In order to overcome the inherent limitations, a new input induced by the joint angular acceleration and an output generated using the contact force and root shear force are defined. A necessary and sufficient condition is thus derived so that all poles and zeros of the new transfer function lie on the imaginary axis. Also, the passive integral control is designed to accomplish the regulation of the contact force. The excellent performance of the passive integral controller is verified through numerical simulations.

Tip-contact force control of a single-link flexible arm using feedback and parallel compensation approach

SUMMARYIn this paper, the force control of a constrained one-link flexible arm is investigated using a feedback parallel compensation algorithm based on a linear distributed parameter model with internal damping of Kelvin–Voigt type. Generally, the non-collocation of the joint torque input and the tip contact force output comes along with the non-minimum phase in nature. To overcome this inherent limitation, a new input induced by the measurement of root-bending moment and its derivative, and a virtual contact force output generated by a parallel compensator are defined. Therefore, the transfer function from the new input to the virtual contact force output is proved not only strictly minimum phase but also in a stable condition. A PD controller then improves the performance of the overall closed-loop system. Furthermore, the perfect asymptotic tracking of a desired contact force trajectory with internal stability can be achieved accurately. The exact solutions of the infinite-dimensional system are obtained using the infinite product formulation. The proposed system promises stability robustness to parameter uncertainties, also free of spillover problems. Numerical simulations are provided to verify the effectiveness of the proposed approach.

Achieving Passive Integral Control Using Feedback and Output Redefinition

There exist an infinite number of right-half plane zeros in the transfer function relating the joint torque input to the tip contact force output for a constrained single-link flexible arm. Since the non-minimum phase nature is the cause of instability or stability but caused the smaller control bandwidth. In order to overcome the inherent limitations caused by the non-minimum phase nature, a new input induced by the measurement of joint angular acceleration and a output generated using the measurements of contact force and root shear force are defined. A necessary and sufficient condition is derived such that all poles and zeros of the new transfer function lie on the imaginary axis. The passive integral control is designed to accomplish the regulation of the contact force. The excellent performance of the passive integral controller is verified through numerical simulations.

Infinite Dimensional Stability Study of a Single-Link Flexible Arm with the Internal Damping

Infinite Dimensional Stability Study of a Single-Link Flexible Arm with the Internal Damping

Robust Filter Based Control of A Single-link Flexible Arm and Its Collision Detection Using Innovation Process

Robust Filter Based Control of A Single-link Flexible Arm and Its Collision Detection Using Innovation Process

Robust tip trajectory tracking of a very lightweight single-link flexible arm in presence of large payload changes

This article discusses a robust control scheme for the trajectory tracking of very lightweight single-link flexible arms. Since the payload is one of the most variable parameters in a manipulator, the control is designed to achieve stability during the robot manoeuvres for any value of tip mass, while accurately tracking the desired tip trajectory. The proposed controller additionally guarantees stability for small uncertainties in parameters such as stiffness or motor friction. The effect of spillover on the performance of the controlled system is also analysed, and it is proven that stability is preserved independently of the non-modelled high-order dynamics. The theoretical analysis is supported by an extensive set of numerical simulations which shows controlled system response when variations in the robot parameters, or dynamics neglected in the controller design, are considered. The proposed method is compared to some of the most efficient current robust control strategies for suppressing flexible structure vibrations: Integral Resonant Control, Wave-Based Control, H-infinity control and LQR control. Finally, some experiments have been carried out in order to test the performance of the tip trajectory tracking of the proposed control system.

Collision Detection and Control of Single-link Flexible Arm Using Optimal Disturbance Decoupling and Kalman Filters

Collision Detection and Control of Single-link Flexible Arm Using Optimal Disturbance Decoupling and Kalman Filters

Position control of very lightweight single-link flexible arms with large payload variations by using disturbance observers

In this article, a robust control scheme for trajectory tracking of very lightweight single-link flexible arms is discussed. Since the payload is one of the most variable parameters in a manipulator, the control is designed to achieve an accurate tracking of the desired tip trajectory for any value of the robot tip mass, or even for a tip mass changing during the maneuver. The proposed controller also guarantees stability for small uncertainties in parameters such as stiffness or motor friction. In addition, the effect of spillover on the performance of the controlled system is analyzed, and it is proven that stability and a good performance are preserved independently from the non-modeled high-order dynamics. The control scheme is based on a two nested loops structure. Each of these loops implements a Generalized Proportional Integral (GPI) controller. Moreover, the outer loop includes a disturbance compensation term based on a disturbance observer, which achieves the required insensitivity to payload changes. The theoretical analysis is supported by an extensive set of numerical simulations which shows controlled system response when variations in the robot payload, or dynamics neglected in the controller design, are considered. Finally, some experiments have been carried out in order to test the performance of the tip trajectory tracking of the proposed control system.