Observer-Based Finite-Time Adaptive Reinforced Super-Twisting Sliding Mode Control for Robotic Manipulators

Introduction. Robotic manipulators operate in dynamic environments under uncertainties, external disturbances, and actuator faults, posing a critical challenge to their control design. While traditional control strategies, such as PID or computed torque control, offer simplicity, they often lack robustness to unmodeled dynamics. The development of robust and practically implementable control algorithms is becoming increasingly important with the growing use of manipulators in dangerous, precise and ultra-fast operations (industrial automation, medicine, space and service robots). Conventional PID controllers and torque calculation methods are simple but not robust enough to handle unmodeled effects. Sliding Mode Control (SMC), particularly the Super-Twisting variant (STA), provides strong robustness, but suffers from chattering and typically requires prior knowledge of system bounds. Recent advancements like Adaptive Global Integral Terminal Sliding Mode Control (AGITSMC) improve finite-time convergence but may result in overestimated control gains and residual switching effects. This research addresses a critical gap in current methods: the lack of a unified control approach that ensures finite-time convergence, suppresses chattering, and compensates for both unknown disturbances and actuator faults using observer feedback. The objective of this work is to design and analyze an Observer-Based Finite-Time Adaptive Reinforced Super-Twisting Sliding Mode Control (OFASTSMC) framework that adaptively adjusts its gains, estimates disturbances online, and guarantees smooth, robust performance even in the presence of severe nonlinearities and faults. The objective of this study is to develop and analyze an Observer-Based Finite-Time Adaptive Reinforced Super-Twisting Sliding Mode Control (OFASTSMC) framework that unifies finitetime observer feedback, adaptive gain tuning, and reinforced sliding surfaces to achieve robust trajectory tracking of robotic manipulators under disturbances and actuator faults, while effectively minimizing chattering and ensuring practical implementability.

Materials and Methods. This study considers the standard dynamic model of an 𝑛𝑛-DOF robotic manipulator derived using Lagrangian mechanics. The model accounts for nonlinear coupling effects, viscous friction, external disturbances, and additive actuator faults. To achieve robust finite-time control, a reinforced sliding surface is constructed using nonlinear error terms with adaptive power exponents, which accelerates error convergence. A finite-time extended state observer (ESO) is incorporated to estimate lumped disturbances and actuator fault torques in real time. Based on these estimates, the control law integrates a super-twisting sliding mode algorithm with adaptive gain tuning and boundarylayer smoothing to reduce chattering while ensuring strong robustness. The closed-loop system stability is formally analyzed within a Lyapunov framework, where rigorous proofs confirm finite-time convergence of the tracking error under the proposed controller. The proposed OFASTSMC algorithm is implemented in MATLAB/Simulink and validated on a 2-DOF planar robotic manipulator. The manipulator is subjected to time-varying disturbances and actuator degradation scenarios. For benchmarking, the method is directly compared with AGITSMC, using identical initial conditions, model parameters, and reference trajectories to ensure a fair and consistent performance evaluation.

Results. Simulation results demonstrate that the proposed OFASTSMC method significantly outperforms the benchmark AGITSMC in terms of tracking precision, robustness, and control smoothness. Specifically, the maximum joint position errors were reduced by over 40% compared to AGITSMC, and the settling time to reach the desired trajectory was shortened by approximately 25%. Additionally, the proposed method effectively mitigated chattering in the control signal due to the use of saturation functions and gain limits, resulting in smoother actuator commands. The adaptive observer accurately estimated the lumped disturbance and fault inputs in real time, providing effective fault compensation without prior knowledge. These improvements were validated across multiple scenarios including abrupt actuator failures, nonlinear load torques, and varying trajectory speeds. The sliding surface convergence was achieved in finite time, confirming the theoretical guarantees of the method.

Discussion. The results validate that OFASTSMC achieves robust, high-precision tracking for robotic manipulators operating under real-world uncertainties. Its novelty lies in the integration of adaptive exponent tuning, finite-time observer feedback, and gain-limited super-twisting control into a unified and practical framework. Unlike previous methods that rely on fixed gain structures or ignore observer feedback, OFASTSMC adapts in real-time and maintains finite-time convergence guarantees with minimal chattering.

Conclusion. The results obtained confirm that OFASTSMC is an efficient and robust solution to the trajectory tracking problem in the presence of uncertainties. The method is computationally efficient and easy to implement in digital control systems, making it suitable for practical deployment in industrial robots, service manipulators, or surgical arms. Future research will focus on extending this method to task-space control and real hardware implementation under sensor noise and model mismatches.

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