Trajectory tracking of a mobile robot manipulator using fractional backstepping sliding mode and neural network control methods

In this paper, a fractional adaptive backstepping sliding mode control system based on the Caputo-Fabrizio derivative for a 2-DoF mobile robot manipulator is designed and described. The fractional dynamics of the system are obtained using the Atangana-Baleanu derivative and the Euler-LaGrange formalism, which include external disturbances, parametric uncertainties, and nonholonomic constraints. A fractional sliding mode control strategy is designed for trajectory tracking tasks. In order to compensate for the chattering phenomenon, the proposed controller is combined with a fractional backstepping strategy. Additionally, the Caputo-Fabrizio derivative is introduced to further reduce the chattering effects and improve the driver performance. A fractional adaptive control law is used to cope with the parametric uncertainties, while adding robustness to external disturbances. To further improve system performance, a tracking control strategy based on a fractional neural network is added. For a comparative analysis, the conventional adaptive neural network backstepping sliding mode control is implemented. Numerical simulations are described and discussed to validate the effectiveness of our control system for trajectory tracking tasks under different operating conditions such as trajectory changes and external disturbances. Our proposed control system and its traditional counterpart were tuned using the Cuckoo optimization approach.

本文针对二自由度（2-DoF）移动机器人机械手，设计并阐述了一种基于卡普托-法布里齐奥（Caputo-Fabrizio）导数的分数阶自适应反演滑模控制系统。本文借助阿坦加纳-巴莱亚努（Atangana-Baleanu）导数与欧拉-拉格朗日（Euler-LaGrange）形式化方法，推导得到系统的分数阶动力学模型，该模型涵盖外部扰动、参数不确定性与非完整约束。针对轨迹跟踪任务，本文设计了分数阶滑模控制策略；为抑制抖振现象，将所提控制器与分数阶反演策略相结合。此外，引入卡普托-法布里齐奥导数以进一步削弱抖振效应、提升驱动性能。采用分数阶自适应控制律应对参数不确定性，并增强系统对外部扰动的鲁棒性。为进一步优化系统性能，本文还加入了基于分数阶神经网络的跟踪控制策略。为开展对比分析，本文同时实现了传统自适应神经网络反演滑模控制方案。通过数值仿真对所提控制系统在轨迹变更、外部扰动等不同工况下的轨迹跟踪有效性进行了验证与讨论。本文所提控制系统及其传统对照方案，均采用布谷鸟（Cuckoo）优化方法进行参数整定。