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Introduction <p>Trajectory tracking of robotic manipulators with multiple degrees of freedom is a challenging task due to highly nonlinear system dynamics, external disturbances, and measurement noise. Traditional control strategies often struggle to maintain accuracy and robustness under such uncertain operating conditions.</p> Materials and methods <p>In this study, an improved Noise-Tolerant Zeroing Neural Network (NTZNN) is an enhanced zeroing neural network framework designed to improve convergence accuracy and robustness in the presence of external disturbances, modeling uncertainties, and measurement noise during dynamic system tracking and control tasks.</p> <p>Simulation experiments are conducted on a three-degree-of-freedom manipulator with link masses of 2&#xa0;kg, 1.5&#xa0;kg, and 1&#xa0;kg, and link lengths of 1&#xa0;m, 0.8&#xa0;m, and 0.6&#xa0;m, respectively. A sampling rate of 0.01&#xa0;s is used. The controller employs a base convergence gain of 5 and an adaptive factor of 50 to enhance convergence speed. Disturbance and noise amplitudes are set to 0.05 and 0.01, respectively. Performance is evaluated using root mean square error (RMSE), convergence time, and tracking accuracy.</p> Results <p>The proposed NTZNN controller achieves RMSE values of 0.0781 radians, 0.2305 radians, and 0.2063 radians for joints one, two, and three, respectively. The system demonstrates rapid convergence within approximately 5–6&#xa0;s and maintains steady-state tracking errors within ± 0.1 to 0.2 radians.</p> Discussion <p>The results indicate that the proposed NTZNN-based control strategy significantly improves tracking accuracy, convergence speed, and robustness against disturbances and noise compared to classical ZNN controllers and other conventional methods. The adaptive mechanism contributes to enhanced performance under varying operating conditions.</p> Conclusion <p>The improved NTZNN controller provides an effective and robust solution for trajectory tracking in multi-degree-of-freedom robotic manipulators. Its superior performance over classical approaches highlights its potential for advanced robotic manipulation applications under uncertain and noisy environments.</p>

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Robust trajectory tracking control of robotic manipulators based on an improved NTZNN algorithm

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月8日

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  • Peilei Zhang

摘要

Introduction

Trajectory tracking of robotic manipulators with multiple degrees of freedom is a challenging task due to highly nonlinear system dynamics, external disturbances, and measurement noise. Traditional control strategies often struggle to maintain accuracy and robustness under such uncertain operating conditions.

Materials and methods

In this study, an improved Noise-Tolerant Zeroing Neural Network (NTZNN) is an enhanced zeroing neural network framework designed to improve convergence accuracy and robustness in the presence of external disturbances, modeling uncertainties, and measurement noise during dynamic system tracking and control tasks.

Simulation experiments are conducted on a three-degree-of-freedom manipulator with link masses of 2 kg, 1.5 kg, and 1 kg, and link lengths of 1 m, 0.8 m, and 0.6 m, respectively. A sampling rate of 0.01 s is used. The controller employs a base convergence gain of 5 and an adaptive factor of 50 to enhance convergence speed. Disturbance and noise amplitudes are set to 0.05 and 0.01, respectively. Performance is evaluated using root mean square error (RMSE), convergence time, and tracking accuracy.

Results

The proposed NTZNN controller achieves RMSE values of 0.0781 radians, 0.2305 radians, and 0.2063 radians for joints one, two, and three, respectively. The system demonstrates rapid convergence within approximately 5–6 s and maintains steady-state tracking errors within ± 0.1 to 0.2 radians.

Discussion

The results indicate that the proposed NTZNN-based control strategy significantly improves tracking accuracy, convergence speed, and robustness against disturbances and noise compared to classical ZNN controllers and other conventional methods. The adaptive mechanism contributes to enhanced performance under varying operating conditions.

Conclusion

The improved NTZNN controller provides an effective and robust solution for trajectory tracking in multi-degree-of-freedom robotic manipulators. Its superior performance over classical approaches highlights its potential for advanced robotic manipulation applications under uncertain and noisy environments.