End-Trajectory Sliding Mode Control Algorithm Design of Hybrid Polishing Robot Based on Nonlinear Disturbance Observer

SUN, Bo ;LI, Xin ;GUO, Feng ;CHENG, Gang .
End-Trajectory Sliding Mode Control Algorithm Design  of Hybrid Polishing Robot Based  on Nonlinear Disturbance Observer. 
Strojniški vestnik - Journal of Mechanical Engineering, [S.l.], v. 72, n.1-2, p. 3-12, september 2025. 
ISSN 0039-2480.
Available at: <https://www.sv-jme.eu/sl/article/end-trajectory-sliding-mode-control-algorithm-design-of-hybrid-polishing-robot-based-on-nonlinear-disturbance-observer/>. Date accessed: 06 apr. 2026. 
doi:http://dx.doi.org/10.5545/sv-jme.2025.1393.

Sun, B., Li, X., Guo, F., & Cheng, G.
(2026).
End-Trajectory Sliding Mode Control Algorithm Design  of Hybrid Polishing Robot Based  on Nonlinear Disturbance Observer.
Strojniški vestnik - Journal of Mechanical Engineering, 72(1-2), 3-12.
doi:http://dx.doi.org/10.5545/sv-jme.2025.1393

@article{sv-jmesv-jme.2025.1393,
	author = {Bo  Sun and Xin  Li and Feng  Guo and Gang  Cheng},
	title = {End-Trajectory Sliding Mode Control Algorithm Design  of Hybrid Polishing Robot Based  on Nonlinear Disturbance Observer},
	journal = {Strojniški vestnik - Journal of Mechanical Engineering},
	volume = {72},
	number = {1-2},
	year = {2026},
	keywords = {hybrid polishing robot; dynamical model; sliding mode control; disturbance observer; trajectory tracking control; },
	abstract = {The five-degrees-of-freedom (5-DOF) hybrid polishing robot is utilized for machining large optical mirrors. Since the existing kinematics control strategy does not meet high-precision control requirements, it is necessary to develop a dynamics controller to improve the operational performance of the robot. To enhance the trajectory control accuracy of the polishing robot’s end-effector, a sliding mode control algorithm based on a nonlinear disturbance observer is proposed. First, the dynamic model, which accounts for joint friction effects, is derived using the Newton-Euler method, and a complete explicit dynamic model is established through parameter substitution. Subsequently, considering the influence of the coupling of inertia parameters of each component in the dynamic model on computational efficiency, the model is simplified while compensating for errors caused by neglected terms via the Whale Optimization Algorithm-Elman (WOA-Elman) algorithm to reconstruct the dynamic model with error compensation terms. Finally, based on an analysis of the reaching law and the design of the nonlinear disturbance observer, the end-effector trajectory sliding mode control algorithm is developed. Simulation and experimental results indicate that the inclusion of an improved reaching term effectively reduces system chattering. Furthermore, the nonlinear disturbance observer is employed to estimate system errors and external disturbances, significantly mitigating error fluctuations during the convergence process and thus validating the robustness and high precision of the trajectory tracking control system for the polishing robot.},
	issn = {0039-2480},	pages = {3-12},	doi = {10.5545/sv-jme.2025.1393},
	url = {https://www.sv-jme.eu/sl/article/end-trajectory-sliding-mode-control-algorithm-design-of-hybrid-polishing-robot-based-on-nonlinear-disturbance-observer/}
}

Sun, B.,Li, X.,Guo, F.,Cheng, G.
2026 September 72. End-Trajectory Sliding Mode Control Algorithm Design  of Hybrid Polishing Robot Based  on Nonlinear Disturbance Observer. Strojniški vestnik - Journal of Mechanical Engineering. [Online] 72:1-2

%A Sun, Bo 
%A Li, Xin 
%A Guo, Feng 
%A Cheng, Gang 
%D 2026
%T End-Trajectory Sliding Mode Control Algorithm Design  of Hybrid Polishing Robot Based  on Nonlinear Disturbance Observer
%B 2026
%9 hybrid polishing robot; dynamical model; sliding mode control; disturbance observer; trajectory tracking control; 
%! End-Trajectory Sliding Mode Control Algorithm Design  of Hybrid Polishing Robot Based  on Nonlinear Disturbance Observer
%K hybrid polishing robot; dynamical model; sliding mode control; disturbance observer; trajectory tracking control; 
%X The five-degrees-of-freedom (5-DOF) hybrid polishing robot is utilized for machining large optical mirrors. Since the existing kinematics control strategy does not meet high-precision control requirements, it is necessary to develop a dynamics controller to improve the operational performance of the robot. To enhance the trajectory control accuracy of the polishing robot’s end-effector, a sliding mode control algorithm based on a nonlinear disturbance observer is proposed. First, the dynamic model, which accounts for joint friction effects, is derived using the Newton-Euler method, and a complete explicit dynamic model is established through parameter substitution. Subsequently, considering the influence of the coupling of inertia parameters of each component in the dynamic model on computational efficiency, the model is simplified while compensating for errors caused by neglected terms via the Whale Optimization Algorithm-Elman (WOA-Elman) algorithm to reconstruct the dynamic model with error compensation terms. Finally, based on an analysis of the reaching law and the design of the nonlinear disturbance observer, the end-effector trajectory sliding mode control algorithm is developed. Simulation and experimental results indicate that the inclusion of an improved reaching term effectively reduces system chattering. Furthermore, the nonlinear disturbance observer is employed to estimate system errors and external disturbances, significantly mitigating error fluctuations during the convergence process and thus validating the robustness and high precision of the trajectory tracking control system for the polishing robot.
%U https://www.sv-jme.eu/sl/article/end-trajectory-sliding-mode-control-algorithm-design-of-hybrid-polishing-robot-based-on-nonlinear-disturbance-observer/
%0 Journal Article
%R 10.5545/sv-jme.2025.1393
%& 3
%P 10
%J Strojniški vestnik - Journal of Mechanical Engineering
%V 72
%N 1-2
%@ 0039-2480
%8 2025-09-29
%7 2025-09-29

Sun, Bo, Xin  Li, Feng  Guo, & Gang  Cheng.
"End-Trajectory Sliding Mode Control Algorithm Design  of Hybrid Polishing Robot Based  on Nonlinear Disturbance Observer." Strojniški vestnik - Journal of Mechanical Engineering [Online], 72.1-2 (2026): 3-12. Web.  06 Apr. 2026

TY  - JOUR
AU  - Sun, Bo 
AU  - Li, Xin 
AU  - Guo, Feng 
AU  - Cheng, Gang 
PY  - 2026
TI  - End-Trajectory Sliding Mode Control Algorithm Design  of Hybrid Polishing Robot Based  on Nonlinear Disturbance Observer
JF  - Strojniški vestnik - Journal of Mechanical Engineering
DO  - 10.5545/sv-jme.2025.1393
KW  - hybrid polishing robot; dynamical model; sliding mode control; disturbance observer; trajectory tracking control; 
N2  - The five-degrees-of-freedom (5-DOF) hybrid polishing robot is utilized for machining large optical mirrors. Since the existing kinematics control strategy does not meet high-precision control requirements, it is necessary to develop a dynamics controller to improve the operational performance of the robot. To enhance the trajectory control accuracy of the polishing robot’s end-effector, a sliding mode control algorithm based on a nonlinear disturbance observer is proposed. First, the dynamic model, which accounts for joint friction effects, is derived using the Newton-Euler method, and a complete explicit dynamic model is established through parameter substitution. Subsequently, considering the influence of the coupling of inertia parameters of each component in the dynamic model on computational efficiency, the model is simplified while compensating for errors caused by neglected terms via the Whale Optimization Algorithm-Elman (WOA-Elman) algorithm to reconstruct the dynamic model with error compensation terms. Finally, based on an analysis of the reaching law and the design of the nonlinear disturbance observer, the end-effector trajectory sliding mode control algorithm is developed. Simulation and experimental results indicate that the inclusion of an improved reaching term effectively reduces system chattering. Furthermore, the nonlinear disturbance observer is employed to estimate system errors and external disturbances, significantly mitigating error fluctuations during the convergence process and thus validating the robustness and high precision of the trajectory tracking control system for the polishing robot.
UR  - https://www.sv-jme.eu/sl/article/end-trajectory-sliding-mode-control-algorithm-design-of-hybrid-polishing-robot-based-on-nonlinear-disturbance-observer/

@article{{sv-jme}{sv-jme.2025.1393},
	author = {Sun, B., Li, X., Guo, F., Cheng, G.},
	title = {End-Trajectory Sliding Mode Control Algorithm Design  of Hybrid Polishing Robot Based  on Nonlinear Disturbance Observer},
	journal = {Strojniški vestnik - Journal of Mechanical Engineering},
	volume = {72},
	number = {1-2},
	year = {2026},
	doi = {10.5545/sv-jme.2025.1393},
	url = {https://www.sv-jme.eu/sl/article/end-trajectory-sliding-mode-control-algorithm-design-of-hybrid-polishing-robot-based-on-nonlinear-disturbance-observer/}
}

TY  - JOUR
AU  - Sun, Bo 
AU  - Li, Xin 
AU  - Guo, Feng 
AU  - Cheng, Gang 
PY  - 2025/09/29
TI  - End-Trajectory Sliding Mode Control Algorithm Design  of Hybrid Polishing Robot Based  on Nonlinear Disturbance Observer
JF  - Strojniški vestnik - Journal of Mechanical Engineering; Vol 72, No 1-2 (2026): Strojniški vestnik - Journal of Mechanical Engineering
DO  - 10.5545/sv-jme.2025.1393
KW  - hybrid polishing robot, dynamical model, sliding mode control, disturbance observer, trajectory tracking control, 
N2  - The five-degrees-of-freedom (5-DOF) hybrid polishing robot is utilized for machining large optical mirrors. Since the existing kinematics control strategy does not meet high-precision control requirements, it is necessary to develop a dynamics controller to improve the operational performance of the robot. To enhance the trajectory control accuracy of the polishing robot’s end-effector, a sliding mode control algorithm based on a nonlinear disturbance observer is proposed. First, the dynamic model, which accounts for joint friction effects, is derived using the Newton-Euler method, and a complete explicit dynamic model is established through parameter substitution. Subsequently, considering the influence of the coupling of inertia parameters of each component in the dynamic model on computational efficiency, the model is simplified while compensating for errors caused by neglected terms via the Whale Optimization Algorithm-Elman (WOA-Elman) algorithm to reconstruct the dynamic model with error compensation terms. Finally, based on an analysis of the reaching law and the design of the nonlinear disturbance observer, the end-effector trajectory sliding mode control algorithm is developed. Simulation and experimental results indicate that the inclusion of an improved reaching term effectively reduces system chattering. Furthermore, the nonlinear disturbance observer is employed to estimate system errors and external disturbances, significantly mitigating error fluctuations during the convergence process and thus validating the robustness and high precision of the trajectory tracking control system for the polishing robot.
UR  - https://www.sv-jme.eu/sl/article/end-trajectory-sliding-mode-control-algorithm-design-of-hybrid-polishing-robot-based-on-nonlinear-disturbance-observer/

Sun, Bo, Li, Xin, Guo, Feng, AND Cheng, Gang.
"End-Trajectory Sliding Mode Control Algorithm Design  of Hybrid Polishing Robot Based  on Nonlinear Disturbance Observer" Strojniški vestnik - Journal of Mechanical Engineering [Online], Volume 72 Number 1-2 (29 September 2025)