A Novel Model-Free Nonsingular Fixed-Time Sliding Mode Control Method for Robotic Arm Systems

Thanh Nguyen Truong, Anh Tuan Vo, Hee-Jun Kang () and Ic-Pyo Hong
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Thanh Nguyen Truong: Department of Electrical, Electronic and Computer Engineering, University of Ulsan, 93 Daehak-ro, Nam-gu, Ulsan 44610, Republic of Korea
Anh Tuan Vo: Department of Smart Information and Technology Engineering, Kongju National University, Cheonan 31080, Republic of Korea
Hee-Jun Kang: Department of Electrical, Electronic and Computer Engineering, University of Ulsan, 93 Daehak-ro, Nam-gu, Ulsan 44610, Republic of Korea
Ic-Pyo Hong: Department of Smart Information and Technology Engineering, Kongju National University, Cheonan 31080, Republic of Korea

Mathematics, 2025, vol. 13, issue 10, 1-27

Abstract: This paper introduces a novel model-free nonsingular fixed-time sliding mode control (MF-NFxTSMC) strategy for precise trajectory tracking in robot arm systems. Unlike conventional sliding mode control (SMC) approaches that require accurate dynamic models, the proposed method leverages the time delay estimation (TDE) approach to effectively estimate system dynamics and external disturbances in real-time, enabling a fully model-free control solution. This significantly enhances its practicality in real-world scenarios where obtaining precise models is challenging or infeasible. A significant innovation of this work lies in designing a novel fixed-time control framework that achieves faster convergence than traditional fixed-time methods. Building on this, a novel MF-NFxTSMC law is developed, featuring a novel singularity-free fixed-time sliding surface (SF-FxTSS) and a novel fixed-time reaching law (FxTRL). The proposed SF-FxTSS incorporates a dynamic proportional term and an adaptive exponent, ensuring rapid convergence and robust tracking. Notably, its smooth transition between nonlinear and linear dynamics eliminates the singularities often encountered in terminal and fixed-time sliding mode surfaces. Additionally, the designed FxTRL effectively suppresses chattering while guaranteeing fixed-time convergence, leading to smoother control actions and reduced mechanical stress on the robotic hardware. The fixed-time stability of the proposed method is rigorously proven using the Lyapunov theory. Numerical simulations on the SAMSUNG FARA AT2 robotic platform demonstrate the superior performance of the proposed method in terms of tracking accuracy, convergence speed, and control smoothness compared to existing strategies, including conventional SMC, finite-time SMC, approximate fixed-time SMC, and global fixed-time nonsingular terminal SMC (NTSMC). Overall, this approach offers compelling advantages, i.e., model-free implementation, fixed-time convergence, singularity avoidance, and reduced chattering, making it a practical and scalable solution for high-performance control in uncertain robotic systems.

Keywords: fixed-time stability; Lyapunov theory; model-free control method; sliding mode control; robotic arms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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