六轴机械臂非奇异快速积分终端滑模轨迹跟踪控制研究

doi:10.16182/j.issn1004731x.joss.24-1027

摘要/Abstract

摘要：

针对机械臂建模参数精准性与扰动不确定性的轨迹跟踪控制问题，提出一种非奇异快速积分终端滑模控制方案。设计一种新型非奇异快速积分终端滑模控制器，非奇异快速终端滑模保证系统快速收敛的同时避免收敛中的奇异性问题，积分项用于提高对扰动的抑制能力，保证控制器对误差的快速响应；通过李雅普诺夫稳定性理论对控制器进行收敛性分析。仿真结果表明：所提控制方案能在有外部干扰的情况下保证关节轨迹精确跟踪，验证了方案的有效性。

关键词: 机械臂, 非奇异快速积分终端滑模控制, 轨迹跟踪, 李雅普诺夫稳定性理论

Abstract:

To address the trajectory tracking control challenges caused by modeling parameter inaccuracies and disturbance uncertainties in robotic arms, a non-singular fast integral terminal sliding mode control scheme was developed. A new type of non-singular fast integral terminal sliding mode controller was designed. The non-singular fast terminal sliding mode ensured the rapid convergence of the system while avoiding the singularity during convergence. The integral term was used to enhance the suppression ability of disturbances and ensure the rapid response of the controller to errors. Lyapunov stability theory was applied to analyze the controller's convergence. The simulation results show that the proposed control scheme can ensure the precise tracking of the joint trajectory even in the presence of external disturbances, thereby verifying the effectiveness of the scheme.

Key words: robotic arm, non-singular fast integral terminal sliding mode control, trajectory tracking, Lyapunov stability theory

中图分类号:

TP241

陈涛,刘建璇,王立忠等 . 六轴机械臂非奇异快速积分终端滑模轨迹跟踪控制研究[J]. 系统仿真学报, 2025, 37(8): 2115-2123.

Chen Tao,Liu Jianxuan,Wang Lizhong,et al . Research on Non-singular Fast Integral Terminal Sliding Mode Trajectory Tracking Control of Six-axis Robotic Arm[J]. Journal of System Simulation, 2025, 37(8): 2115-2123.

图/表 12

图1

图2

表1

改进DH参数表

连杆	连杆长度 $a i / m$	连杆扭转角 $α i / r a d$	关节偏移量 $d i / m$
1	0	0	0.121 5
2	0	$π / 2$	0
3	-0.3	0	0
4	-0.267	0	0.110 5
5	0	$π / 2$	0.09
6	0	$- π / 2$	0.082

表1

图3

表2

主要参数取值表

参数	值	参数	值
$α$	1	$η$	0.1
$β$	1	$m$	10
$r 1$	1.5	$n$	3
$r 2$	1.3	$λ$	2
$k$	$d i a g (40,40,40, 40,40,40)$	$μ$	$d i a g (0.001,0.001,0.001, 0.001,0.001,0.001)$

表2

图4

图5

表3

图6

图7

图8

图9

参考文献 19

[1]	Bi Zhuming, Luo Chaomin, Miao Zhonghua, et al. Safety Assurance Mechanisms of Collaborative Robotic Systems in Manufacturing[J]. Robotics and Computer-Integrated Manufacturing, 2021, 67: 102022.
[2]	蒋泽睿, 杨立军, 李俊, 等. 自动跟踪口腔手术灯的运动学分析与仿真[J]. 系统仿真学报, 2021, 33(12): 2864-2879.
	Jiang Zerui, Yang Lijun, Li Jun, et al. Kinematics Analysis and Simulation of Automatically Tracking Dental Surgery Lamp[J]. Journal of System Simulation, 2021, 33(12): 2864-2879.
[3]	Wen Zunwang, Wang Yaoyao, Fu Hao, et al. Non-singular Terminal Sliding Mode Compliance Control of Aerial Manipulator Based on Disturbance Observer[J]. Transactions of Nanjing University of Aeronautics & Astronautics, 2023, 40(S2): 69-76.
[4]	鲍秀兰, 马志涛, 马萧杰, 等. 丘陵果园自然环境下柑橘采摘机器人设计与试验[J]. 农业机械学报, 2024, 55(4): 124-135.
	Bao Xiulan, Ma Zhitao, Ma Xiaojie, et al. Design and Experiment of Citrus Picking Robot in Hilly Orchard Natural Environment[J]. Transactions of the Chinese Society for Agricultural Machinery, 2024, 55(4): 124-135.
[5]	赵京, 周振勇, 张自强. 冗余度机械臂的自运动流形计算及关节轨迹规划[J]. 机械工程学报, 2023, 59(5): 77-88.
	Zhao Jing, Zhou Zhenyong, Zhang Ziqiang. Self-motion Manifolds Calculation and Joint Trajectory Planning of Redundant Manipulators[J]. Journal of Mechanical Engineering, 2023, 59(5): 77-88.
[6]	Qiao Lei, Zhao Min, Wu Chao, et al. Adaptive PID Control of Robotic Manipulators Without Equality/Inequality Constraints on Control Gains[J]. International Journal of Robust and Nonlinear Control, 2022, 32(18): 9742-9760.
[7]	Yang Xiaohang, Zhao Zhiyuan, Li Yuntao, et al. Adaptive Neural Network Control of Manipulators with Uncertain Kinematics and Dynamics[J]. Engineering Applications of Artificial Intelligence, 2024, 133, Part A: 107935.
[8]	Chávez-Vázquez Samuel, Jorge E Lavín-Delgado, Gómez-Aguilar José F, et al. Trajectory Tracking of Stanford Robot Manipulator by Fractional-order Sliding Mode Control[J]. Applied Mathematical Modelling, 2023, 120: 436-462.
[9]	Samer Said Saab, Shen Dong, Orabi Mohamad, et al. Iterative Learning Control: Practical Implementation and Automation[J]. IEEE Transactions on Industrial Electronics, 2022, 69(2): 1858-1866.
[10]	尚东阳, 李小彭, 尹猛, 等. 采用模糊补偿滑模控制器的空间柔性机械臂振动抑制方法[J]. 振动与冲击, 2024, 43(7): 175-185, 204.
	Shang Dongyang, Li Xiaopeng, Yin Meng, et al. Vibration Suppression Method for Space-flexible Manipulator Using Fuzzy Compensation Sliding Mode Controller[J]. Journal of Vibration and Shock, 2024, 43(7): 175-185, 204.
[11]	Zhou Yujian, She Jinhua, Wang Feng, et al. Disturbance Rejection for Stewart Platform Based on Integration of Equivalent-input-disturbance and Sliding-mode Control Methods[J]. IEEE/ASME Transactions on Mechatronics, 2023, 28(4): 2364-2374.
[12]	Cruz-Ortiz David, Chairez Isaac, Poznyak Alexander. Non-singular Terminal Sliding-mode Control for a Manipulator Robot Using a Barrier Lyapunov Function[J]. ISA Transactions, 2022, 121: 268-283.
[13]	Guo Keyou, Shi Peipeng, Wang Pengshuo, et al. Non-singular Terminal Sliding Mode Controller with Nonlinear Disturbance Observer for Robotic Manipulator[J]. Electronics, 2023, 12(4): 849.
[14]	杜宝林, 朱大昌, 盘意华. 机械臂模糊超螺旋二阶滑模轨迹跟踪控制[J]. 系统仿真学报, 2022, 34(6): 1343-1352.
	Du Baolin, Zhu Dachang, Pan Yihua. Fuzzy Super-twisting Second Order Sliding Mode Trajectory Tracking Control for Robotic Manipulator[J]. Journal of System Simulation, 2022, 34(6): 1343-1352.
[15]	梁捷, 陈力. 柔性空间机械臂系统的双环积分滑模控制[J]. 中国机械工程, 2011, 22(16): 1906-1912.
	Liang Jie, Chen Li. Dual-loop Integral Sliding Mode Control for Flexible Space Manipulator[J]. China Mechanical Engineering, 2011, 22(16): 1906-1912.
[16]	Xu Jianliang, Sui Zhen, Wang Wenduo, et al. An Adaptive Discrete Integral Terminal Sliding Mode Control Method for a Two-joint Manipulator[J]. Processes, 2024, 12(6): 1106.
[17]	刘金琨. 机器人控制系统的设计与MATLAB仿真: 基本设计方法[M]. 北京: 清华大学出版社, 2016.
	Liu Jinkun. Robot Control System Design and MATLAB Simulation: The Basic Design Method[M]. Beijing: Tsinghua University Press, 2016.
[18]	贾华, 刘延俊, 王雨, 等. 六轴机械臂神经网络自适应终端滑模控制[J]. 西安交通大学学报, 2022, 56(11): 21-30.
	Jia Hua, Liu Yanjun, Wang Yu, et al. Adaptive-neural-network-based Terminal Sliding Mode Control for Six-axis Robotic Manipulators[J]. Journal of Xi'an Jiaotong University, 2022, 56(11): 21-30.
[19]	康惠骏. 非线性系统理论[M]. 北京: 机械工业出版社, 2010.
	Kang Huijun. Nonlinear System Theory[M]. Beijing: China Machine Press, 2010.

关节	NFTSMC
Ⅰ	0.000 54	0.000 25	0.000 36
Ⅱ	0.001 46	0.001 25	0.001 07
Ⅲ	0.000 44	0.000 71	0.000 37
Ⅳ	0.001 10	0.000 80	0.000 70
Ⅴ	0.000 27	0.000 18	0.000 12
Ⅵ	0.204 00	0.019 00	0.014 00