Predefined time adaptive sliding mode control for flexible space robot

doi:10.3785/j.issn.1008-973X.2025.02.013

Journal of ZheJiang University (Engineering Science)

2025, Vol. 59

Issue (2): 351-361 DOI: 10.3785/j.issn.1008-973X.2025.02.013

Predefined time adaptive sliding mode control for flexible space robot

Yicheng LIU(

),Jialing YANG,Rui TANG,Jing CHENG

College of Electrical Engineering, Sichuan University, Chengdu 610065, China

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Abstract

An adaptive sliding mode control method based on predefined time was proposed for the trajectory tracking control problem of a flexible space robot with typical nonlinear characteristics. The dynamic model of the multi-stage cable-driven flexible space robot was established by using the constant curvature method and Lagrangian formulation. A sliding mode controller based on predefined time theory was designed. A radial basis function (RBF) neural network was employed to compensate for modeling errors and external disturbances in the multi-stage cable-driven flexible space robot system. The convergence of trajectory tracking error within predefined time was proven using Lyapunov theory. The effectiveness of the model and controller was verified through numerical simulations. Comparative analysis against fixed-time controllers and uncompensated controllers showed that the proposed controller facilitated faster convergence of system trajectory error.

Key words： flexible space robot predefined time stability radial basis function neural network trajectory tracking sliding mode control

Received: 26 December 2023 Published: 11 February 2025

CLC:

TP 241

Fund: 清华大学横向协作项目（HG2020153）.

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Cite this article:

Yicheng LIU,Jialing YANG,Rui TANG,Jing CHENG. Predefined time adaptive sliding mode control for flexible space robot. Journal of ZheJiang University (Engineering Science), 2025, 59(2): 351-361.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2025.02.013 OR https://www.zjujournals.com/eng/Y2025/V59/I2/351

柔性空间机器人预定义时间自适应滑模控制

针对具有典型非线性特性的多段线驱动柔性空间机器人的轨迹跟踪控制问题，提出基于预定义时间的自适应滑模控制方法. 基于常曲率方法和拉格朗日法，建立多段线驱动柔性空间机器人的动力学模型. 设计基于预定义时间理论的滑模控制器，利用径向基函数（RBF）神经网络补偿多段线驱动柔性空间机器人系统的建模误差和外界干扰. 利用Lyapunov理论，证明轨迹跟踪误差可以在预定义时间内收敛. 通过数值仿真验证了模型和控制器的有效性，与固定时间控制器和无补偿的控制器相比，所提出的控制器使系统轨迹误差具有更快的收敛速度.

关键词： 柔性空间机器人, 预定义时间稳定性, 径向基函数神经网络, 轨迹跟踪, 滑模控制

Fig.1 Three-dimensional model of flexible space robot

Fig.2 Flexible manipulator

Fig.3 On-orbit service task scenario

Fig.4 Diagram of flexible arm bending

Fig.5 Bending plane angle

$ \mathit{\varphi } $

Fig.6 Coordinate transformation when bending plane angle is 0

Fig.7 Structure of RBF neural network

Tab.1 Model parameter of flexible space robot

Fig.8 Angle tracking when

$ {\boldsymbol{q}}\left(0\right)=[0.08, 0.08, 0.08, 0.08, 0.08, 0.08{]}^{{\rm T}} $

Fig.9 Angle tracking when

$ {\boldsymbol{q}}\left(0\right)=[0.3, 0.3, 0.3, 0.3, 0.3, 0.3{]}^{{\rm T}} $

Tab.2 Convergence time when

$ {\boldsymbol{q}}\left(0\right)=[0.08, 0.08, 0.08, 0.08, 0.08, $

$ 0.08{]}^{{\rm T}} $

Tab.3 Convergence time when

$ {\boldsymbol{q}}\left(0\right)=[0.3, 0.3, 0.3, 0.3, 0.3, 0.3{]}^{{\rm T}} $

Fig.10 Actual disturbance term and estimated disturbance term

Fig.11 Tracking error of joint angle

Fig.12 Desired velocity of end-effector

Fig.13 Angle tracking result after trajectory planning

Fig.14 Position and attitude change of base


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