Adaptive Backstepping Sliding Mode Control of Trajectory Tracking for Robotic Manipulators

Zhu, Dachang; Du, B. X.; Puchen, Zhu; Wu, Wenqiang

doi:10.1155/2020/3156787

Cited by 10 publications

(7 citation statements)

References 34 publications

(41 reference statements)

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“…Remark 4. Note that the SMC and BC have been combined to build a more efficient control named backstepping sliding mode control (BSMC) [42] that can be suggested to be applied later.…”

Section: Remarkmentioning

confidence: 99%

A Comparative Study of Nonsingular Terminal Sliding Mode and Backstepping Schemes for the Coupled Two‐Tank System

2021

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This paper presents an implementation of two radically different control schemes for a state-coupled two-tank liquid-level system. This is due to the purpose of transferring theoretical studies to industrial systems. The proposed schemes to be introduced and compared are the nonsingular terminal sliding mode control (NTSMC) and the backstepping control (BC). The performances of the developed methods are experimentally tested on a particular class of second-order nonlinear systems. The main purpose of the considered control schemes is to achieve a tracking trajectory for a coupled-tank system. It is proved that the designed robust controllers guarantee the stability of the corresponding closed loop systems. The obtained results are verified with the same setup test to ensure a suitable basis for their comparison. During the experiments, we resorted to adding an integrator to the backstepping control so that we improve the results, leading to the appearance of the integrator backstepping control (IBC). To focus on the adequacy and applicability of the suggested control layout, theoretical comparisons as well as experimental results are afforded and debated.

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“…Remark 4. Note that the SMC and BC have been combined to build a more efficient control named backstepping sliding mode control (BSMC) [42] that can be suggested to be applied later.…”

Section: Remarkmentioning

confidence: 99%

A Comparative Study of Nonsingular Terminal Sliding Mode and Backstepping Schemes for the Coupled Two‐Tank System

2021

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“…The sliding mode control produces a switching control law to force the system to converge to the sliding surface within a boundary layer near the sliding surface under the convergence of the Lyapunov stability theory. This approach solves unmodeled dynamics and external disturbances [4], while the adaptive controller allows the user to estimate the unknown dynamic system parameters. Moreover, the backstepping control is used to deal with nonlinear systems in which the states are used as virtual control signals in control law design, and the virtual signals and their derivatives are required at every step of the design process [4, 5].…”

Section: Introductionmentioning

confidence: 99%

“…This approach solves unmodeled dynamics and external disturbances [4], while the adaptive controller allows the user to estimate the unknown dynamic system parameters. Moreover, the backstepping control is used to deal with nonlinear systems in which the states are used as virtual control signals in control law design, and the virtual signals and their derivatives are required at every step of the design process [4, 5]. The main advantage of the backstepping scheme is its ability to handle systems with different relative degrees (the difference between the number of poles and zeros).…”

Section: Introductionmentioning

confidence: 99%

A robust control scheme for a 2PUS+RR parallel robot for ankle rehabilitation

Flores-Salazar¹,

Lugo-González²,

Arias-Montiel³

et al. 2023

Robotica

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This paper presents a robust adaptive controller based on the backstepping technique using an extended state observer (ESO), implemented on a 2PUS+RR parallel robot, to minimize the trajectory tracking error. The proposed backstepping-ESO controller scheme is designed to compensate for the robot’s structured (parametric) and unstructured (nonlinear friction, external disturbances, and dynamics) uncertainties. The overall stability of the controller is guaranteed by the Lyapunov theory. Cosimulation in MATLAB-Simulink and ADAMS View is presented to validate the results of the ESO and backstepping controller implemented in the virtual and physical prototype. For the virtual prototype, it was determined that the system is stable in 2 s and presents a maximum absolute error of 3.5 × $10^{-6}$ m for the actuator position and 2.8 × $10^{-5}$ rad for mobile platform orientation. Regarding the physical robot, a maximum absolute error of 5 × $10^{-4}$ m for the actuator position and 0.0575 rad for the orientation of the robot mobile platform values do not represent a problem for ankle rehabilitation movements. Experimental results were also presented and compared with ankle motion to demonstrate that the applied control system meets the motion requirements of the ankle rehabilitator.

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“…A Lyapunov-based method was utilized to guarantee the stability and control. Dachang et al [10] developed an adaptive backstepping sliding mode control to solve precise trajectory tracking in the presence of external disturbances in a complex environment. The dynamic response characteristics of a two-link robotic manipulator was analyzed using a back-stepping algorithm based on the Lyapunov theory to stabilize the sliding mode controller.…”

Section: Introductionmentioning

confidence: 99%

Identification and Machine Learning Prediction of Nonlinear Behavior in a Robotic Arm System

Wang

Zhu

2021

Symmetry

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In this study, the subject of investigation was the dynamic double pendulum crank mechanism used in a robotic arm. The arm is driven by a DC motor though the crank system and connected to a fixed side with a mount that includes a single spring and damping. Robotic arms are now widely used in industry, and the requirements for accuracy are stringent. There are many factors that can cause the induction of nonlinear or asymmetric behavior and even excite chaotic motion. In this study, bifurcation diagrams were used to analyze the dynamic response, including stable symmetric orbits and periodic and chaotic motions of the system under different damping and stiffness parameters. Behavior under different parameters was analyzed and verified by phase portraits, the maximum Lyapunov exponent, and Poincaré mapping. Firstly, to distinguish instability in the system, phase portraits and Poincaré maps were used for the identification of individual images, and the maximum Lyapunov exponents were used for prediction. GoogLeNet and ResNet-50 were used for image identification, and the results were compared using a convolutional neural network (CNN). This widens the convolutional layer and expands pooling to reduce network training time and thickening of the image; this deepens the network and strengthens performance. Secondly, the maximum Lyapunov exponent was used as the key index for the indication of chaos. Gaussian process regression (GPR) and the back propagation neural network (BPNN) were used with different amounts of data to quickly predict the maximum Lyapunov exponent under different parameters. The main finding of this study was that chaotic behavior occurs in the robotic arm system and can be more efficiently identified by ResNet-50 than by GoogLeNet; this was especially true for Poincaré map diagnosis. The results of GPR and BPNN model training on the three types of data show that GPR had a smaller error value, and the GPR-21 × 21 model was similar to the BPNN-51 × 51 model in terms of error and determination coefficient, showing that GPR prediction was better than that of BPNN. The results of this study allow the formation of a highly accurate prediction and identification model system for nonlinear and chaotic motion in robotic arms.

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Adaptive Backstepping Sliding Mode Control of Trajectory Tracking for Robotic Manipulators

Cited by 10 publications

References 34 publications

A Comparative Study of Nonsingular Terminal Sliding Mode and Backstepping Schemes for the Coupled Two‐Tank System

A Comparative Study of Nonsingular Terminal Sliding Mode and Backstepping Schemes for the Coupled Two‐Tank System

A robust control scheme for a 2PUS+RR parallel robot for ankle rehabilitation

Identification and Machine Learning Prediction of Nonlinear Behavior in a Robotic Arm System

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