考虑输出约束的冗余驱动绳索并联机器人预设性能控制

陈正升; 程玉虎; 王雪松

doi:10.16383/j.aas.c210949

考虑输出约束的冗余驱动绳索并联机器人预设性能控制

doi: 10.16383/j.aas.c210949

陈正升^{1, 2,},
程玉虎^{1, 2,},
王雪松^{1, 2,}

1.
地下空间智能控制教育部工程研究中心徐州 221116
2.
中国矿业大学信息与控制工程学院徐州 221116

基金项目: 国家自然科学基金(61903347, 61976215, 62176259), 江苏省自然科学基金(BK20200086)资助

详细信息

作者简介:
陈正升：中国矿业大学信息与控制工程学院讲师. 2016年获得哈尔滨工业大学博士学位. 主要研究方向为机器人动力学建模与控制. E-mail: chenzhengsheng@cumt.edu.cn

程玉虎：中国矿业大学信息与控制工程学院教授. 2005年获得中国科学院自动化研究所博士学位. 主要研究方向为机器学习, 智能优化与控制. E-mail: chengyuhu@163.com

王雪松：中国矿业大学信息与控制工程学院教授. 2002年获得中国矿业大学博士学位. 主要研究方向为机器学习, 模式识别. 本文通信作者. E-mail: wangxuesongcumt@163.com

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出版历程
- 收稿日期: 2021-10-08
- 录用日期: 2022-01-11
- 网络出版日期: 2022-05-06
- 刊出日期: 2022-07-01

Prescribed Performance Control of Redundantly-actuated Cable Driving Parallel Robots Subjected to Output Constraint

CHEN Zheng-Sheng^{1, 2
,},
CHENG Yu-Hu^{1, 2
,},
WANG Xue-Song^{1, 2
,}

1.
Engineering Research Center of Intelligent Control for Underground Space, Ministry of Education, Xuzhou 221116
2.
School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116

Funds: Supported by National Natural Science Foundation of China (61903347, 61976215, 62176259) and Natural Science Foundation of Jiangsu Province (BK20200086)

More Information

Author Bio:
CHEN Zheng-Sheng　Lecturer at the School of Information and Control Engineering, China University of Mining and Technology. He received his Ph.D. degree from Harbin Institute of Technology in 2016. His main research interest is dynamic modeling and control of robotics

CHENG Yu-Hu　Professor at the School of Information and Control Engineering, China University of Mining and Technology. He received his Ph.D. degree from the Institute of Automation, Chinese Academy of Sciences in 2005. His research interest covers machining learning, intelligent optimization and control

WANG Xue-Song　Professor at the School of Information and Control Engineering, China University of Mining and Technology. She received her Ph.D. degree from China University of Mining and Technology in 2002. Her research interest covers machine learning and pattern recognition. Corresponding author of this paper

摘要

摘要: 提出一种考虑输出约束的冗余驱动绳索并联机器人(Redundantly-actuated cable driving parallel robots, RCDPRs)预设性能有限时间控制算法. 首先, 采用Newton-Euler方程推导系统动力学模型, 并建立绳索拉力优化模型保证系统正常工作; 其次, 将输出约束问题转化为位置跟踪误差的坐标变换问题, 设计给定时间衰减函数与非对称变换函数, 将约束形式的跟踪误差转化为无约束变量, 实现给定时间的输出约束; 然后, 针对滑模控制的抖振问题, 在预设性能控制中采用模型不确定与扰动估计器进行扰动估计, 并通过自适应方法对扰动估计误差进行补偿; 以此为基础, 提出一种基于精度驱动且在分段点处三阶连续的终端滑模面进行控制算法设计; 最后, 采用Lyapunov函数证明算法的有限时间收敛特性, 并以7自由度冗余驱动绳索并联机器人为控制对象进行仿真研究, 对算法进行验证.
- 滑模控制 /
- 有限时间收敛 /
- 输出约束 /
- 给定时间预设性能控制 /
- 冗余驱动绳索并联机器人
Abstract: This paper proposed a prescribed performance finite-time control algorithm of redundantly-actuated cable driving parallel robots (RCDPRs) considering output constraint. Firstly, the Newton-Euler equation is employed to establish the dynamic model of the system, and the optimization model for all cables was constructed to guarantee properly operation. Then, the output constraint problem is transformed into coordinate transformation problem of the position tracking errors, also the appointed time decay function and the asymmetric transformation function are designed to transform the tracking errors into unconstraint variables, thus the output constraint is realized. Meanwhile, aiming at the chattering problem, the uncertainty and disturbance estimator is proposed, and the adaptive algorithm is designed to compensate the estimation error, on the basis of which, the accuracy-driven terminal sliding mode surface with three-order continuity on the segment point is proposed and applied in controller design. Finally, the Lyapunov function is used to prove that the proposed algorithm has finite-time convergence characteristics, and a seven-degrees-of-freedom RCDPR is used as the control object for simulation research to demonstrate the effectiveness of the proposed controller.
- Sliding mode control /
- finite-time convergence /
- output constraint /
- appointed time prescribed performance control /
- redundantly-actuated cable driving parallel robots (RCDPRs)

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图 1 冗余驱动绳索并联机器人结构原理图

Fig. 1 Structural schematic diagram of the RCDPR

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图 2 带有7个驱动绳索的RCDPR

Fig. 2 The RCDPR with 7 driving cables

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图 3 位置与角度跟踪误差

Fig. 3 Positional and angular tracking errors

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图 4 速度跟踪误差

Fig. 4 Velocity tracking error

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图 5 冗余驱动绳索并联机器人驱动力矩及其差值

Fig. 5 Torques and torque deviations of the RCDPR

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图 6 采用本文算法时RCDPR各绳索拉力

Fig. 6 RCDPR＇s pull forces of the proposed controller

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图 7 采用本文算法时自适应项系数

Fig. 7 Adaptive coefficients of the proposed controller

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图 8 采用ASTUDESMC时自适应项系数

Fig. 8 Adaptive coefficients of ASTUDESMC

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图 9 基于跟踪误差e的滑模面数值

Fig. 9 Sliding mode surface for tracking error e

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图 10 基于跟踪误差z的滑模面数值

Fig. 10 Sliding mode surface for tracking error z

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表 1 RCDPR运动学参数(mm)

Table 1 Kinematic parameters of the RCDPR (mm)

参数	数值	参数	数值
b₁	[0, 0, 1000]	a₁	[−150, −100, 50]
b₂	[100, 0, 1000]	a₂	[150, −100, 50]
b₃	[1000, 1000, 1000]	a₃	[150, 100, 50]
b₄	[0, 1000, 1000]	a₄	[−150, 100, 50]
b₅	[500, 0, 0]	a₅	[0, −100, −50]
b₆	[1000, 1000, 0]	a₆	[150, 100, −50]
b₇	[0, 1000, 0]	a₇	[−150, 100, 50]
r	20

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表 2 RCDPR惯性参数

Table 2 Inertial parameters of the RCDPR

参数	描述	数值
m_p	动平台质量	1.67 kg
I_p	动平台转动惯量矩阵	diag{2.78×10⁴, 5.56×10⁴, 7.26×10⁴} kg·mm²
I_b	滑轮转动惯量	1.2×10⁴kg·mm²

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表 3 各控制器参数

Table 3 Parameters of all controllers

控制器	参数	值
PPSMC	K₁, K₂, α₁, α₂, α₃, Δ₁₁, Δ₁₂, Δ₁₃, Δ₁₄, Δ₁₅, Δ₁₆, β₄, β₅, K₃, γ₀, T, λ₁, λ₂, T_e, ε_1i, ε_2i, μ₀, μ_∞, k	100I₆, 50I₆, 0.5, 1.5, 1.8, 0.01, 0.01, 0.01, 0.001, 0.001, 0.001, 5, 5, 10I₆, 10, 0.001 s, 0.001, 0.01, 0.2 s, 0.5, 1, [0.2, 0.2, 0.2, 0.02, 0.02, 0.02]^T, 0.002[1, 1, 1, 0.01, 0.01, 0.01]^T, 30
ASTUDESMC	k₁, k₂, α_i, T, ε, $ {\omega _1}\sqrt {{{{\gamma _1}} \mathord{\left/ {\vphantom {{{\gamma _1}} 2}} \right. } 2}} $, λ+4ε²	100I₆, 50I₆, 0.5, 0.001 s, 0.5, 500, 10
TDENFTSMC	ρ₁, ρ₂, α_1i, α_2i, k₁, k₂, L	100I₆, 50I₆, 0.5, 1.8, 0.001 s
UDESMC	c, 1/a, k	160, 0.001 s, 20

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