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Journal ArticleDOI

Nonlinear control of electrical flexible-joint robots

01 Mar 2012-Nonlinear Dynamics (Springer Netherlands)-Vol. 67, Iss: 4, pp 2549-2559
TL;DR: In this article, a nonlinear tracking control of electrically driven flexible-joint manipulators using the voltage control strategy is proposed, which is based on a simple robust adaptive control under both structured and unstructured uncertainty.
Abstract: This paper is devoted to the nonlinear tracking control of electrically driven flexible-joint manipulators using the voltage control strategy. Despite the torque control laws that are involved in the complexity of manipulator dynamics, the proposed control law is free from manipulator dynamics. This novelty is for adopting the voltage control strategy to derive a simple robust adaptive control under both structured and unstructured uncertainty. The proposed control approach has a fast response with a good tracking performance under the well-behaved control efforts in the form of decentralized control. The control method is justified by the stability analysis and simulated on a flexible-joint electrically driven robot manipulator.
Citations
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Journal ArticleDOI
TL;DR: In this article, a nonlinear adaptive fuzzy estimation and compensation of uncertainty is proposed to model the uncertainty as a non-linear function of the joint position error and its time derivative, and a comparison between the proposed Nonlinear Adaptive Fuzzy Control and a Robust Nonlinear Control (NAFC) is presented.
Abstract: This paper presents a novel robust decentralized control of electrically driven robot manipulators by adaptive fuzzy estimation and compensation of uncertainty. The proposed control employs voltage control strategy, which is simpler and more efficient than the conventional strategy, the so-called torque control strategy, due to being free from manipulator dynamics. It is verified that the proposed adaptive fuzzy system can model the uncertainty as a nonlinear function of the joint position error and its time derivative. The adaptive fuzzy system has an advantage that does not employ all system states to estimate the uncertainty. The stability analysis, performance evaluation, and simulation results are presented to verify the effectiveness of the method. A comparison between the proposed Nonlinear Adaptive Fuzzy Control (NAFC) and a Robust Nonlinear Control (RNC) is presented. Both control approaches are robust with a very good tracking performance. The NAFC is superior to the RNC in the face of smooth uncertainty. In contrast, the RNC is superior to the NAFC in the face of sudden changes in uncertainty. The case study is an articulated manipulator driven by permanent magnet dc motors.

103 citations

Journal ArticleDOI
TL;DR: An optimal fuzzy sliding mode controller is used for tracking the position of robot manipulator and the mathematical proof shows the closed-loop system in the presence of this controller has the global asymptotic stability.
Abstract: In this paper, an optimal fuzzy sliding mode controller is used for tracking the position of robot manipulator, is presented. In the proposed control, initially by using inverse dynamic method, the known sections of a robot manipulator’s dynamic are eliminated. This elimination is done due to reduction over structured and unstructured uncertainties boundaries. In order to overcome against existing uncertainties for the tracking position of a robot manipulator, a classic sliding mode control is designed. The mathematical proof shows the closed-loop system in the presence of this controller has the global asymptotic stability. Then, by applying the rules that are obtained from the design of classic sliding mode control and TS fuzzy model, a fuzzy sliding mode control is designed that is free of undesirable phenomena of chattering. Eventually, by applying the PSO optimization algorithm, the existing membership functions are adjusted in the way that the error tracking robot manipulator position is converged toward zero. In order to illustrate the performance of the proposed controller, a two degree-of-freedom robot manipulator is used as the case study. The simulation results confirm desirable performance of optimal fuzzy sliding mode control.

97 citations

Journal ArticleDOI
TL;DR: In this article, an optimal adaptive fuzzy sliding mode controller is presented for a class of nonlinear systems, in which the boundaries of parametric uncertainties are defined by a Gaussian distribution.
Abstract: In this paper, an optimal adaptive fuzzy sliding mode controller is presented for a class of nonlinear systems. In the proposed control, in the beginning, the boundaries of parametric uncertainties...

68 citations


Cites background from "Nonlinear control of electrical fle..."

  • ...…control is one of the most important points in designing a controller for industrial systems, because if the computational burden of the controller is high, owing to delay in online control, the stability of the closed- loop system cannot be guaranteed (Soltanpour and Fateh, 2009; Fateh, 2012a)....

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Journal ArticleDOI
TL;DR: In this article, a robust Lyapunov-based controller for flexible-joint electrically driven robots considering voltage as control input is proposed, which is free from mechanical subsystem of the actuator dynamics, considered here as unmodeled dynamics.
Abstract: This paper addresses the design of a robust Lyapunov-based controller for flexible-joint electrically driven robots considering to voltage as control input. The proposed approach is related to the key role of electrical subsystem of the motors, thus is free from mechanical subsystem of the actuator dynamics, considered here as unmodeled dynamics. The main contribution of this paper is to prove that the closed-loop system composed by full nonlinear actuated robot dynamics and the proposed controller is BIBO stable, while actuator/link position errors are uniformly ultimately bounded stable in agreement with Lyapunov’s direct method in any finite region of the state space. It also forms a constructive and conservative algorithm for suitable choice of gains in PID controller. The analytical studies as well as experimental results produced using MATLAB/SIMULINK external mode control on a flexible-joint electrically driven robot demonstrate high performance of the proposed control schemes.

59 citations

Journal ArticleDOI
01 Feb 2017-Robotica
TL;DR: This paper intuitively shows that in order to perform repetitive tasks; the least common multiple (LCM) of fundamental period durations of the desired trajectories of the joints is a proper value for the fundamental period duration of the Fourier series expansion.
Abstract: This paper presents a novel control algorithm for electrically driven robot manipulators. The proposed control law is simple and model-free based on the voltage control strategy with the decentralized structure and only joint position feedback. It works for both repetitive and non-repetitive tasks. Recently, some control approaches based on the uncertainty estimation using the Fourier series have been presented. However, the proper value for the fundamental period duration has been left as an open problem. This paper addresses this issue and intuitively shows that in order to perform repetitive tasks; the least common multiple (LCM) of fundamental period durations of the desired trajectories of the joints is a proper value for the fundamental period duration of the Fourier series expansion. Selecting the LCM results in the least tracking error. Moreover, the truncation error is compensated by the proposed control law to make the tracking error as small as possible. Adaptation laws for determining the Fourier series coefficients are derived according to the stability analysis. The case study is an SCARA robot manipulator driven by permanent magnet DC motors. Simulation results and comparisons with a voltage-based controller using adaptive neuro-fuzzy systems show the effectiveness of the proposed control approach in tracking various periodic trajectories. Moreover, the experimental results on a real SCARA robot manipulator verify the successful practical implementation of the proposed controller.

58 citations


Cites background from "Nonlinear control of electrical fle..."

  • ...According to (30), we have Ia = K−1m ( Jmr−1q̈ + Bmr−1q̇ + r (Dq̈ + Cq̇ + G) ) (52) Using (52) and its time derivative, the lumped uncertainty F(t) in (18) can be rewritten as F(t) = F1(q)̇q̈ + F2(q, q̇)q̈ + F3(q, q̇)q̇ + F4(q, q̇) (53) where F1(q) = LK−1m rD(q) and F2(q, q̇) = RK−1m ( Jmr−1 + rD ) + LK−1m (Bmr−1 + rḊ + rC) + Kbr−1 − In (54) F3(q, q̇) = RK−1m ( Bmr−1 + rC(q, q̇) ) + LK−1m rĊ(q, q̇) (55) F4(q, q̇) = RK−1m rG(q) + LK−1m rĠ(q, q̇) (56) According to the stability analysis, in the sinusoidal steady state, the joint position q and its time derivatives converge to their desired trajectories....

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  • ...Substituting (37) into (36) and some simple manipulations yields V̇ ≤ −q̃T Kpq̃ + ∥∥q̃T E∥∥ λe−δt ‖y‖ + λe−δt (38) Using the inequality ab a+b < a ∀a, b > 0, (38) can be rewritten as V̇ ≤ −q̃T Kpq̃ + λe−δt (39) According to Qu et al.,1 (39) implies that q̃ asymptotically converges to zero and P̃ is bounded....

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  • ...V (t) = q̃ T q̃ 2 + P̃ T P̃ 2γ (32) The time derivative of (32) given by V̇ (t) = q̃T ˙̃q − P̃ T ˙̂P γ (33) Substituting ˙̃q from (29) into (33) yields V̇ = q̃T (−Kpq̃ + ξ P̃ + ε − Fr) − P̃ T ˙̂P γ (34) Using (31), we can simplify (34) as V̇ = q̃T (−Kpq̃ + ε − Fr) (35) It follows from (35) and Assumption 3 that V̇ ≤ −q̃T Kpq̃ + ∥∥q̃T E∥∥ − q̃T Fr (36) According to Qu et al.,1 we can propose the robustifying control term Fr as Fr = yE‖y‖ + λe−δt (37) in which λ and δ are positive scalars and y = Eq̃....

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  • ...Using (9)–(13), the state-space model is obtained ẋ = F(x)+bv (14) in which x = [q q̇ Ia ]T , b = [0 0 L−1 ]T (15) F(x) = ⎡ ⎣ x2(Jr−1 + rD(x1))−1(−(Br−1 + rC(x1, x2))x2 − rG(x1) + Kmx3) −L−1(Kbr−1x2 + Rx3) ⎤ ⎦ (16)...

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  • ...Using Assumption 1, bounded-ness of the control law (27) is obtained....

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References
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Journal ArticleDOI

1,542 citations


"Nonlinear control of electrical fle..." refers background or methods in this paper

  • ...To simplify (42), we use a property of robot dynamics [ 7 ] that...

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  • ...However, a simplified model was provided that under some assumptions is being feedback linearized [ 7 ]....

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  • ...The vector of the gravitational torques g(θ ) is assumed to be a function of only the joint positions as used in the simplified model [ 7 ]....

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  • ...In a simplified model of flexible-joint robot [ 7 ], the links of manipulator are assumed rigid and the motors are elastically coupled to the links....

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  • ...For instance, PD control [3], robust control using voltage control strategy [4], integral manifold approach [5], singular perturbation theory [6], robust control [ 7 ], sliding mode control [8], adaptive control [9], adaptive neural network control [10], fuzzy control [11], learning control [12], neural network approach [13], passivity-based impedance control [14], and state observer based control [15] have been devoted to dealing with the ......

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01 Jan 1985

715 citations

Journal ArticleDOI
TL;DR: In this paper, the point-to-point control of a manipulator with three revolute elastic joints is considered and it is shown that a simple PD controller, similar to that used for rigid robots, suffices to globally stabilize the elastic joint robots about a reference position.
Abstract: The point-to-point control of manipulators having elastic joints is considered. It is shown that a simple PD (proportional plus derivative) controller, similar to that used for rigid robots, suffices to globally stabilize the elastic joint robots about a reference position. A robustness analysis is also given with respect to uncertainties on the robot parameters. The results of numerical simulation tests of a manipulator with three revolute elastic joints are presented. >

539 citations


"Nonlinear control of electrical fle..." refers background in this paper

  • ...For instance, PD control [ 3 ], robust control using voltage control strategy [4], integral manifold approach [5], singular perturbation theory [6], robust control [7], sliding mode control [8], adaptive control [9], adaptive neural network control [10], fuzzy control [11], learning control [12], neural network approach [13], passivity-based impedance control [14], and state observer based control [15] have been devoted to dealing with the ......

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  • ...Generally, a flexible-joint robot cannot be feedback linearized by static feedback [ 3 ]....

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Journal ArticleDOI
01 Aug 1987
TL;DR: The control problem for robot manipulators with flexible joints is considered and it is shown how to approximate the feedback linearizing control to any order in µ, an approximate feedback linearization which linearizes the system for all practical purposes.
Abstract: The control problem for robot manipulators with flexible joints is considered. The results are based on a recently developed singular perturbation formulation of the manipulator equations of motion where the singular perturbation parameter µ is the inverse of the joint stiffness. For this class of systems it is known that the reduced-order model corresponding to the mechanical system under the assumption of perfect rigidity is globally linearizable via nonlinear static-state feedback, but that the full-order flexible system is not, in general, linearizable in this manner. The concept of integral manifold is utilized to represent the dynamics of the slow subsystem. The slow subsystem reduces to the rigid model as the perturbation parameter µ tends to zero. It is shown that linearizability of the rigid model implies linearizability of the flexible system restricted to the integral manifold. Based on a power series expansion of the integral manifold around µ = 0, it is shown how to approximate the feedback linearizing control to any order in µ. The result is then an approximate feedback linearization which, assuming stability of the fast variables, linearizes the system for all practical purposes.

444 citations


"Nonlinear control of electrical fle..." refers methods in this paper

  • ...For instance, PD control [3], robust control using voltage control strategy [4], integral manifold approach [ 5 ], singular perturbation theory [6], robust control [7], sliding mode control [8], adaptive control [9], adaptive neural network control [10], fuzzy control [11], learning control [12], neural network approach [13], passivity-based impedance control [14], and state observer based control [15] have been devoted to dealing with the ......

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Journal ArticleDOI
TL;DR: A feedback linearization (FL)-based control law made implementable using an extended state observer (ESO) is proposed for the trajectory tracking control of a flexible-joint robotic system and the closed-loop stability of the system under the proposed observer-controller structure is established.
Abstract: In this paper, a feedback linearization (FL)-based control law made implementable using an extended state observer (ESO) is proposed for the trajectory tracking control of a flexible-joint robotic system. The FL-based controller cannot be implemented unless the full transformed state vector is available. The design also requires exact knowledge of the system model making the controller performance sensitive to uncertainties. To address these issues, an ESO is designed, which estimates the state vector, as well as the uncertainties in an integrated manner. The FL controller uses the states estimated by ESO, and the effect of uncertainties is compensated by augmenting the FL controller with the ESO-estimated uncertainties. The closed-loop stability of the system under the proposed observer-controller structure is established. The effectiveness of the ESO in the estimation of the states and uncertainties and the effectiveness of the FL + ESO controller in tracking are demonstrated through simulations. Lastly, the efficacy of the proposed approach is validated through experimentation on Quanser's flexible-joint module.

424 citations