Flexible Joint Robot Research Articles

Joint torque control of flexible joint robots based on sliding mode technique

For robots with flexible joints, the joint torque dynamics makes it difficult to control. An effective solution is to carry out a joint torque controller with fast enough dynamic response. This article is dedicated to design such a torque controller based on sliding mode technique. Three joint torque control approaches are proposed: (1) The proportional-derivative (PD)-type controller has some degree of robustness by properly selecting the control gains. (2) The direct sliding mode control approach which fully utilizes the physical properties of electric motors. (3) The sliding mode estimator approach was proposed to compensate the parameter uncertainties and the external disturbances of the joint torque system. These three joint torque controllers are tested and verified by the simulation studies with different reference torque trajectories and under different joint stiffness.

Reconfigurable control of flexible joint robot with actuator fault and uncertainty

Abstract This paper presents the fault tolerant control (FTC) of a flexible joint robot using singular perturbation method in order to compensate for the lost performance due to the occurrence of actuator fault and the uncertainty. This FTC is based on Lyapunov redesign principle. The singular perturbation method is used to reduce the dynamic model of the flexible joint robot in a fast and slow subsystem. The time scale reduction of the flexible joint model is carried out when their joint stiffness is large enough and the singular perturbation parameter is set to zero. The fault-tolerant control structure in this paper is based on two parts. The first term described the composite control for the system without defect and without uncertainty which represents the sum between slow and fast controllers. While the second term of the fault tolerant command describes additive control designed to compensate for the fault effect of the actuator on the uncertain system. The additive approach is based on the Lyapunov theorem, which guarantees asymptotic stability despite the presence of actuator defects and the parametric uncertainty. The theoretical results are applied on a robot manipulator with a single flexible joint.

Feedback error learning-based type-2 fuzzy neural network predictive controller for a class of nonlinear input delay systems

In this paper, a type-2 fuzzy neural network predictive (T2FNNP) controller has been designed in the feedback error learning (FEL) framework for a class of input delay nonlinear systems considering of unknown disturbance and uncertainties. In this method, the predictor has been utilized to estimate the future state variables of the controlled system to compensate for the time-varying input delay. To establish the control objectives, the predicted states are fed to the controller which is in FEL framework and includes T2FNN parallel with classical feedback controller. Using the proposed T2FNNP controller, it is shown that the system output tracks the reference signal in presence of the measurement noise, time-varying delay, and bounded disturbance. An appropriate Lyapunov function has been exploited to study stability of the closed-loop system and to derive the adaptation laws for both the predictor and controller. A flexible joint robot system has been used to validate performance of the proposed T2FNNP controller and has been compared with a type-1 fuzzy sliding predictive controller through some simulations. The results indicate the efficiency of the proposed T2FNNP controller in dealing with time-varying delay as well as high level of measurement noise which exists in the sensor.

Passive Friction Compensation Using a Nonlinear Disturbance Observer for Flexible Joint Robots with Joint Torque Measurements

The friction and ripple effects from motor and drive cause a major problem for the robot position accuracy, especially for robots with high gear ratio and for high-speed applications. In this paper we introduce a simple, effective, and practical method to compensate for joint friction of flexible joint robots with joint torque sensing, which is based on a nonlinear disturbance observer. This friction observer can increase the performance of the controlled robot system both in terms of the position accuracy and the dynamic behavior. The friction observer needs no friction model and its output corresponds to the low-pass filtered friction torque. Due to the link torque feedback the friction observer can compensate for both friction moment and external moment effects acting on the link. So it can be used not only for position control but also for interaction control, e.g., torque control or impedance control which have low control bandwidth and therefore are sensitive to ripple effects from motor and drive. In addition, its parameter design and parameter optimization are independent of the controller design so that it can be used for friction compensation in conjunction with different controllers designed for flexible joint robots. Furthermore, a passivity analysis is done for this observer-based friction compensation in consideration of Coulomb, viscose and Stribeck friction effects, which is independent of the regulation controller. In combining this friction observer with the state feedback controller \cite{Albu-Schaeffer2}, global asymptotic stability of the controlled system can be shown by using Lyapunov based convergence analysis. Experimental results with robots of the German Aerospace Center (DLR) validate the practical efficiency of the approach.

Workpiece Pose Optimization for Milling with Flexible-Joint Robots to Improve Quasi-Static Performance

Although industrial robots are widely used in production automation, their applications in machining have been limited because of the structural vibrations induced by periodic cutting forces. Since the dynamic characteristics of an industrial robot depends on its configuration, the responses of the robot structure to the cutting forces are affected by how the workpiece is placed within the workspace of the robot. This paper presents a method for workpiece pose optimization for a robotic milling system to improve the quasi-static performance during machining. Since the milling forces are time-varying due to the characteristics of the multi-tooth and discontinuity of milling, these forces can excite vibrations inside the robot structure. To address this issue, a structural dynamics model is established for industrial robots, considering their joint flexibility, and a milling force formulation is incorporated into the robot dynamics model to investigate the forced vibrations of the flexible joints. Then, the quasi-static performance of the robotic machining system is evaluated by the vibration-induced offset of the cutter tool that is mounted on the end-effector. Finally, an optimization approach is given for the workpiece pose to minimize the cutter tool offset under the periodic milling force. A numerical simulation demonstrates that the optimal workpiece pose can significantly reduce the overall tool offset during machining and can lower the variation of the tool offset along the milling path.

End-Effector Force Estimation for Flexible-Joint Robots With Global Friction Approximation Using Neural Networks

This paper proposes an improved disturbance observer to realize accurate contact force estimation using the joint torque sensor. The joint torque sensor separates the dynamics of the link side from the motor side of the robot manipulator. Therefore, only computing the partial dynamics on the link side can realize external force estimation. This can considerably reduce the modeling workload and error terms that may affect the estimation results. Furthermore, this paper presents that the observed residual value during free motion can be considered as the friction dynamics, which is approximated by the neural network (NN) due to its inherent capacity in approximating nonlinear functions. After that, the estimation accuracy of the observer is considerably improved. Compared to other local NN approximation method, we analyzes the properties of the friction force in detail to select appropriate excitation trajectory for accurate global approximation results using only limited training data. We have presented that the suitable excitation trajectory and the use of global basis function are the sufficient conditions for global friction approximation. The proof of this theorem is also given. The Kalman filter is also utilized to reduce the noise of the estimation results in real time. The experimental results also demonstrate the efficacy of the proposed method, which accurately estimates the contact force for flexible joint robots.

Hybrid approach to design Takagi–Sugeno observer‐based FTC for non‐linear systems affected by simultaneous time varying actuator and sensor faults

This study uses a novel approach, integrating fault estimation and fault decoupling methods, in designing a new Takagi–Sugeno multiple integral unknown input observer (TSMIUIO)-based fault tolerant control (FTC) system. The motivation is to tackle the challenges underlined in designing observer-based FTC for non-linear systems affected by simultaneous time-varying actuator and sensor faults, exogenous input, and sensor noise. In such systems, the FTC design challenges are the constraints imposed by the structure of input/output matrices, the need of extending the order of the observer to estimate simultaneous faults, the bi-directional interaction caused by the state and faults’ estimation errors, and the unpredictable time behaviour of fault signals. These challenges motivate the proposal of TSMIUIO to (i) ensure acceptable FTC performance, irrespective of the time behaviour of sensor fault; (ii) relax the complexity of TSMIUIO by avoiding the use of extended state approach for estimating simultaneous faults; and (iii) eliminate the BDI in the estimated signals that feed the controller. The effectiveness of the proposed method is illustrated using a single-link flexible joint robot and translational oscillator with an eccentric rotational proof mass actuator benchmark.

Adaptive fuzzy dynamic surface control of flexible-joint robot systems with input saturation

In this paper, we propose an adaptive fuzzy dynamic surface control &#x0028 DSC &#x0029 scheme for single-link flexible-joint robotic systems with input saturation. A smooth function is utilized with the mean-value theorem to deal with the difficulties associated with input saturation. An adaptive DSC design with an auxiliary first-order filter is used to solve the &#x201C explosion of complexity &#x201D problem. It is proved that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood around zero. The main advantage of the proposed method is that only one adaptation parameter needs to be updated, which reduces the computational burden significantly. Simulation results demonstrate the feasibility of the proposed scheme and the comparison results show that the improved DSC method can reduce the computational burden by almost two thirds in comparison with the standard DSC method.

Adaptive fractional-order control of electrical flexible-joint robots: Theory and experiment

Real-time fractional-order control of electrically driven flexible-joint robots has been addressed in this article. An important contribution of this article is that the control law is designed based on the Fourier series that eliminates the need for computation of regressor matrix. Moreover, the nonlinear effects of actuator saturation are considered in the control law. The lumped uncertainty can be approximated using Fourier series with unknown coefficients. Then, the unknown coefficients are estimated using the adaptation law obtained in the stability analysis. The overall closed-loop system is proven to be robust and bounded-input bounded-output stable. In addition, it has been shown that the joint-position errors are uniformly bounded based on Lyapunov’s stability concept. The satisfactory performance of the proposed control scheme is verified by experimental results. To highlight the superiority of the proposed method, experimental results of two voltage-based controllers are also presented.

Robust Passivity and Passivity Relaxation for Impedance Control of Flexible-Joint Robots with Inner-Loop Torque Control

Passivity is a canonical condition for the safety of interactive systems, but practical limitations restrict its utility as a design tool. A system with a passive model can be unstable in high-stiffness environments, passivity is difficult to show with inner-loop controllers, and as it is a binary condition it provides limited design comparison insight; as a result, it is rarely used for inner-loop design. As passivity safety claims are limited by model accuracy, conditions for the passivity of a system with bounded-magnitude model uncertainty (robust passivity) are developed in this paper. Additionally, a condition for coupled environment-robot stability is developed using mixed passivity and small-gain condition, allowing rigorous relaxation of passivity at high frequencies for typical impedance-controlled systems. These approaches are used in the analysis of an impedance-controlled series-elastic actuated system with inner-loop torque control and also compared with traditional design tools (bandwidth ratio, sensitivity function, etc.). The approach is then validated experimentally, identifying model uncertainty bounds under various load conditions, and then using the measured uncertainty for controller synthesis. Robust passivity is then compared with nominal passivity in a validation experiment under manual excitation and impact.

Vibration Suppression of a Flexible-Joint Robot Based on Parameter Identification and Fuzzy PID Control

In order to eliminate the influence of the joint torsional vibration on the system operation accuracy, the parameter identification and the elastic torsional vibration control of a flexible-joint robot are studied. Firstly, the flexible-joint robot system is equivalent to a rotor dynamic system, in which the mass block and the torsion spring are used to simulate the system inertia link and elasticity link, for establishing the system dynamic model, and the experimental prototype is constructed. Then, based on the mechanism method, the global electromechanical-coupling dynamic model of the flexible-joint robot system is constructed to clear and define the mapping relationship between the driving voltage of the DC motor and the rotational speed of joint I and joint II. Furthermore, in view of the contradiction between the system response speed and the system overshoot in the vibration suppression effect of the conventional PID controller, a fuzzy PID controller, whose parameters are determined by the different requirements in the vibration control process, is designed to adjust the driving voltage of the DC motor for attenuating the system torsional vibration. Finally, simulation and control experiments are carried out and the results show that the designed fuzzy PID controller can effectively suppress the elastic torsional vibration of the flexible-joint robot system with synchronization optimization of control accuracy and dynamic quality.

Cooperative Fault Diagnosis for Uncertain Nonlinear Multiagent Systems Based on Adaptive Distributed Fuzzy Estimators

This paper presents a cooperative fault diagnosis scheme for a class of uncertain nonlinear multiagent systems component and sensor faults in individual agents. Since the faulty system affects the healthy systems through interconnections, for each agent an estimator is designed to collect neighboring output estimations errors to consider its faulty effects on others, when computing its estimations for local state and faulty parameters. A new structure of distributed estimators is proposed by filtering regressor signals and sharing them among agents. Then, the sharings of signals are planned by properly constructing auxiliary graphs for undirected and directed networks. Two conditions are given to preselect estimators parameters for the convergences of the estimation errors. Unlike the existing results dealing with one common parameter with full state measurement and only for undirected graphs, this paper presents an output measurement-based approach for multiple parameters in undirected/directed networks. It shows that for the faults not providing persistent excitation in a signal agent, it is possible to estimate the faults exactly if the they excite all agents persistently. A simulation example of a group of single-link flexible-joint robots is given to verify the effectiveness of the proposed method.

Combination of integral sliding mode control design with optimal feedback control for nonlinear uncertain systems

The purpose of this study is to present a new robust sliding mode control design for nonlinear systems where both matched and unmatched uncertainties are considered. The proposed controller strategy is composed of two components: the integral sliding mode control and the optimal feedback control law. Moreover, an integral sliding mode surface in integral type is developed to construct the reachability of sliding mode using the Lyapunov functions method. The main advantages of the proposed approach are ensuring the robustness throughout the whole system response against the uncertainties, decrease the chattering effect and eliminate the reaching phase. Finally, the validity of the proposed design strategy is demonstrated through the simulation of a flexible joint robot.

Force-free control for the flexible-joint robot in human-robot interaction

The force-free control means that the robot arm does not seem to be affected by gravity, frictions, and inertial force during the interaction with human. An advanced force-free control method can greatly improve work efficiency. In this paper, a novel force-free control method of the flexible-joint robot is proposed. First, the mathematical models of flexible joint and flexible-joint robot are established, and the force-free controller which can realize the gravity-free situation and reduce the frictions and inertial torques is designed based on the models. Then, the dynamic parameters of the robot arm are obtained by means of a self-measuring way. Finally, a flexible-joint robot experimental system is assembled, and the verification of force-free control method is carried out. Moreover, the method converts external force into joint velocities in the joint servo controllers to improve the stability of the movement.

Robust Adaptive Tracking Control Based on State Feedback Controller With Integrator Terms for Elastic Joint Robots With Uncertain Parameters

This brief addresses a robust adaptive control scheme based on a cascaded structure with a full state feedback controller with integrator terms as inner control loop and computed torque as outer control loop for flexible joint robots. Together with integrator effect, the adaptive control law can enhance position accuracy under uncertainties of the robot model, especially, the high friction caused by harmonic drive with high gear ratio. In this brief, the adaptive friction compensation is designed based on the LuGre friction model, which exhibits some advantages compared with the static friction model (e.g., no chattering effect at zero motor velocity). Furthermore, structural oscillations of the link side can be effectively damped by using joint torque feedback in the state feedback controller. Therefore, the proposed adaptive control approach can simultaneously provide high control performance both in terms of the dynamic behavior and the position accuracy. Global asymptotic tracking is achieved for the complete controlled system. The system stability is derived using Lyapunov approaches and Barbalat’s lemma. Experimental results validate the practical efficiency of the approach.

An alternative stability proof for “Adaptive type-2 fuzzy estimation of uncertainties in the control of electrically flexible-joint robots”

This short note points out an improvement on the robust stability analysis for electrically driven flexible joint robots (EDFJR) given in the 2017 paper by Zirkohi and Fateh, entitled “Adaptive type-2 fuzzy estimation of uncertainties in the control of electrically flexible-joint robots.” In their paper, the authors present an interval Type-2 Adaptive fuzzy control scheme for EDFJR. The nonlinearities associated with actuator input constraints have been also considered in their paper. They discussed the saturated and unsaturated region of the control input separately and neglected the transition state between these regions. Moreover, they did not guarantee the stability of the closed-loop system in the saturated area. In this note, an alternative stability proof is presented that does not require this separation, and which guarantees the stability in a more general framework. The overall closed-loop system is proven to be robust, and bounded-input, bounded-output stable, while the motor/joint position errors are uniformly-ultimately bounded based on the Lyapunov's stability concept.

Dynamic learning from adaptive neural control for flexible joint robot with tracking error constraints using high-gain observer

ABSTRACTThis paper presents dynamic learning from adaptive neural control with prescribed tracking error performance for flexible joint robot (FJR) included unknown dynamics. Firstly, a system transformation method is introduced to convert the original FJR system into a normal system. As a result, only one neural network (NN) approximator is used to identify the uncertain system nonlinear dynamics and the verification on the convergence of neural weights is simplified extremely. To further solve the predefined performance issue, a performance function is introduced to describe a tracking error constraint and a error transformation technique is used to convert the constrained tracking control problem into the unconstrained stabilization of error system. By combining a high-gain observer and the backsteppig method, the adaptive neural controller is presented to stabilize the unconstrained error system. Under the satisfaction of the partial persistent excitation condition, the adaptive neural controller is shown to be capable of achieving unknown dynamics acquisition, expression and storage. Furthermore, a neural learning control with using the stored NN weights is proposed for the same or similar control task so that a time-consuming NN online adjustment process can be avoided and a better control performance can be obtained. Simulation results demonstrate the effectiveness of the proposed control method.

A Novel Discrete-time Nonlinear Model Predictive Control Based on State Space Model

This paper proposes a novel finite dimensional discrete-time Nonlinear Model Predictive Control. This technique is based on discrete-time state-space models, Taylor series expansion for prediction and performance index optimization. Furthermore, the technique extends the concept of the Lie derivative for the discrete time case using Euler backwards method. The performance validation for the discrete-time Nonlinear Model Predictive Control uses the simulation of a single-link flexible joint robot and the inverted pendulum. Comparison of the proposed finite dimensional discrete-time Nonlinear Model Predictive Control technique with Feedback Linearization Control is also discussed. Analytical and numerical results show excellent performances for both, the single-link flexible joint and inverted pendulum controllers using the proposed discrete-time Nonlinear Model Predictive Control technique.

A model-based velocity controller for chaotization of flexible joint robot manipulators

This article presents a model-based velocity controller able to induce a chaotic motion on n-degrees of freedom flexible joint robot manipulators. The proposed controller allows the velocity link vector of a robot manipulator to track an arbitrary, chaotic reference vector field. A rigorous theoretical analysis based on Lyapunov’s theory is used to prove the asymptotic stability of the tracking error signals when using the proposed controller, which implies that a chaotic motion is induced to the robotic system. Experimental results are provided using a flexible joint robot manipulator of two degrees of freedom. Finally, by using Poincaré maps and Lyapunov exponents, it is shown that the behavior exhibited by the robot joint positions is chaotic.

CONTROL OF FLEXIBLE JOINT ROBOT MANIPULATORS BY COMPENSATING FLEXIBILITY

A flexible-joint robot manipulator is a complex system because it is nonlinear, multivariable, highly coupled along with joint flexibility and uncertainty. To overcome flexibility, several methods have been proposed based on flexible model. This paper presents a novel method for controlling flexible-joint robot manipulators. A novel control law is presented by compensating flexibility to form a rigid robot and then control methods for rigid robots are applied. Feedback linearization and direct adaptive fuzzy control, based on rigid model, are designed with torque control strategy. A decentralized adaptive fuzzy controller is designed because of simplicity and ease of implementation. Effectiveness of the proposed control approach is demonstrated by simulations, using a three-joint articulated flexible-joint robot, driven by permanent magnet dc motors.