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浙江大学学报(工学版)
浙江大学学报(工学版)  2025, Vol. 59 Issue (2): 351-361    DOI: 10.3785/j.issn.1008-973X.2025.02.013
机械工程、能源工程     
柔性空间机器人预定义时间自适应滑模控制
刘宜成(),杨迦凌,唐瑞,程靖
四川大学 电气工程学院，四川 成都 610065
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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摘要：

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    
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
收稿日期: 2023-12-26 出版日期: 2025-02-11
CLC:  TP 241  
基金资助: 清华大学横向协作项目（HG2020153）.
作者简介: 刘宜成（1975—），男，副教授，博士，从事柔性机器人、空间机器人建模和控制的研究. orcid.org/0000-0003-3571-3839. E-mail：liuyicheng@scu.edu.cn
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引用本文:

刘宜成,杨迦凌,唐瑞,程靖. 柔性空间机器人预定义时间自适应滑模控制[J]. 浙江大学学报(工学版), 2025, 59(2): 351-361.

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.

链接本文:

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

图 1  柔性空间机器人的三维模型
图 2  柔性机械臂
图 3  在轨服务任务场景
图 4  柔性臂弯曲的示意图
图 5  弯曲平面角$ \mathit{\varphi } $
图 6  弯曲平面角为0时的坐标变换
图 7  RBF神经网络的结构
参数数值说明
$ {m}_{0} /{{\mathrm{kg}}}$240基座质量
$ {I}_{0} /(\text{kg}\cdot {{\mathrm{m}}}^{2})$$ \left[\begin{array}{ccc}104.97& 0& 0\\ 0& 34.97& 0\\ 0& 0& 103.34\end{array}\right]\; $基座转动惯量
$ b/{\mathrm{m}} $$ [0.35,\;0,\;0.5{]}^{{\rm T}} $机械臂基座位置
$ \rho /(\text{kg}\cdot {{\mathrm{m}}}^{-3})$4510中心杆密度
$ E /({\mathrm{N}}\cdot {{\mathrm{m}}}^{-2})$$ 1.05\times 1{0}^{11} $弹性模量
$ A /{{\mathrm{m}}}^{2}$0.07中心杆截面积
$ l/{\mathrm{m}} $0.45中心杆长度
$ {I}_{xx}/{{\mathrm{m}}}^{4} $$ 3.98 \times 10^{-4} $中心杆惯性矩
$ {m}_{{\mathrm{d}}}/\text{kg} $0.117圆盘质量
$ {I}_{{\mathrm{d}}}/ (\rm{kg}\cdot {{\mathrm{m}}}^{2} )$$ \left[\begin{array}{*{20}{c}}5.42& 0& 0\\ 0& 10.64& 0\\ 0& 0& 5.42\end{array}\right]\times 1{0}^{-3} $圆盘转动惯量
表 1  柔性空间机器人的模型参数
图 8  $ {\boldsymbol{q}}\left(0\right)=[0.08,0.08,0.08,0.08,0.08,0.08{]}^{\mathit{{\rm T}}} $时的角度跟踪
图 9  $ {\boldsymbol{q}}\left(0\right)=[0.3,0.3,0.3,0.3,0.3,0.3{]}^{\mathit{{\rm T}}} $时的角度跟踪
关节$ {T}_{\text{r1}} $/s$ {T}_{\text{r2}} $/s
$ {\varphi }_{1} $0.0990.357
$ {\theta }_{1} $0.0990.458
$ {\varphi }_{2} $0.0990.357
$ {\theta }_{2} $0.0990.694
$ {\varphi }_{3} $0.0990.851
$ {\theta }_{3} $0.0990.358
表 2  $ {\boldsymbol{q}}\left(0\right)=[0.08,0.08,0.08,0.08,0.08,0.08{]}^{\mathit{{\rm T}}} $时的收敛时间
关节$ {T}_{\text{r3}} $/s$ {T}_{\text{r4}} $/s
$ {\varphi }_{1} $0.2590.392
$ {\theta }_{1} $0.2590.392
$ {\varphi }_{2} $0.2590.392
$ {\theta }_{2} $0.2590.392
$ {\varphi }_{3} $0.2590.761
$ {\theta }_{3} $0.2590.392
表 3  $ {\boldsymbol{q}}\left(0\right)=[0.3,0.3,0.3,0.3,0.3,0.3{]}^{\mathit{{\rm T}}} $时的收敛时间
图 10  实际的干扰项和估计的干扰项
图 11  关节角度的跟踪误差
图 12  末端的期望速度
图 13  轨迹规划后的角度跟踪结果
图 14  基座位姿变化
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