基于递归Gibbs-Appell的柔性空间机器人建模与特性分析

张福礼; 袁朝辉

doi:10.13224/j.cnki.jasp.20220052

基于递归Gibbs-Appell的柔性空间机器人建模与特性分析

doi: 10.13224/j.cnki.jasp.20220052

西北工业大学自动化学院，西安 710072

基金项目: 国家自然科学基金（51505381）

详细信息

作者简介:
张福礼（1986-），男，博士生，主要从事空间机器人动力学建模与控制方法研究。E-mail：zhangfuli2007@sina.com

中图分类号: V414.2
计量
- 文章访问数: 637
- HTML浏览量: 359
- PDF量: 50
- 被引次数: 0
出版历程
- 收稿日期: 2022-01-31
- 网络出版日期: 2023-08-29

Flexible space robot modeling and characteristic analysis based on recursive Gibbs-Appell

School of Automation，Northwestern Polytechnical University，Xi’an 710072，China

摘要

摘要:
利用递归Gibbs-Appell方法研究了多重柔性的空间机器人动力学建模与特性分析。首先，根据Timoshenko beam theory与集中刚度分别对连杆与关节进行柔性描述，其次，利用旋转矩阵R_3×3与平移向量L_1×3的简化了齐次变换矩阵T_4×4以降低递推运动学难度，利用递归Gibbs函数与势能函数推导了柔性空间机器人的逆向动力学模型，再次，利用反向递归法获取了惯量矩阵与耦合矩阵，并构建了正向动力学模型。最后数值仿真结果表明，Matlab与Adams的仿真结果相对偏差不超过0.1%，Z弯曲变形相对于X剪切变形与Y扭转变形数量级超过了10³，这验证所建模型的正确性。在一定范围内，关节刚度增加50 N·m/rad时，连杆最大变形增量不超过1.5×10⁻³ m，关节摩擦成5倍增长时，连杆最大变形增量不超过2×10⁻³ m，帆板的增量变形具有相同变化趋势。
- 空间机器人 /
- 柔性机械臂 /
- 递归 Gibbs-Appell /
- 多体动力学建模 /
- 特性分析
Abstract:
Dynamic modeling and characteristic analysis of space robots with multiple flexible factors were studied by Recursive Gibbs-Appell modeling method. Firstly, the deformation of link and joints was described by concentrated stiffness and Timoshenko beam theory. Secondly, the homogeneous transformation matrix T_4×4 was simplified by using the rotation matrix R_3×3 and the translation vector L_1×3, and the difficulty of recursive kinematics was reduced. The inverse dynamics model of the flexible space robot was derived by using the recursive Gibbs function and the potential energy function. Thirdly, the mass inertia matrix and coupling matrix were obtained by inverse recursive method. The forward dynamic model of the space robot was obtained. The numerical simulation results showed that the relative deviation between Matlab and Adams simulation results did not exceed 0.1%, and the Z bending deformation was more than 10³ orders of magnitude relative to the X shear deformation and Y torsional deformation, which verified the correctness of the model. Within a certain range, when the joint stiffness increased by 50 N·m/rad, the maximum deformation increment of the connecting rod did not exceed 1.5×10⁻³ m, and when the joint friction increased by 5 times, the maximum deformation increment of the link did not exceed 2×10⁻³ m, the incremental deformation of the windsurfing board had the same trend.
- space robot /
- flexible manipulator /
- recursive Gibbs-Appell /
- multi-body dynamics modeling /
- characteristic analysis

HTML

图 1 柔性空间机器人的结构与变形描述

Figure 1. Structure and deformation description of flexible space robot

下载: 全尺寸图片幻灯片

图 2 空间柔性机器人整体系统结构

Figure 2. The system structure of space flexible robot

下载: 全尺寸图片幻灯片

图 3 基于Gibbs-Appell的递归动力学计算流程

Figure 3. Recursive dynamics calculation flow based on Gibbs-Appell

下载: 全尺寸图片幻灯片

图 4 载体的位姿变化

Figure 4. Pose change of carrier

下载: 全尺寸图片幻灯片

图 5 机械臂关节角度变化

Figure 5. Changes of joint angles

下载: 全尺寸图片幻灯片

图 6 机械臂关节柔性变化

Figure 6. Changes of joint flexibilit

下载: 全尺寸图片幻灯片

图 7 机械臂末端变形

Figure 7. Deformation at the end of the manipulator

下载: 全尺寸图片幻灯片

图 8 帆板中心点变形

Figure 8. Deformation of solar panel center point

下载: 全尺寸图片幻灯片

图 9 机械臂末端变形（不同关节刚度）

Figure 9. End deformation of manipulator （different joint stiffnesses）

下载: 全尺寸图片幻灯片

图 10 帆板中心点变形（不同关节刚度）

Figure 10. Deformation of solar panel center point （different joint stiffnesses）

下载: 全尺寸图片幻灯片

图 11 机械臂末端变形（不同关节摩擦因数）

Figure 11. End deformation of manipulator （different joint friction coefficients）

下载: 全尺寸图片幻灯片

图 12 帆板中心点变形（不同关节摩擦因数）

Figure 12. Deformation of solar panel center point （different joint friction coefficients）

下载: 全尺寸图片幻灯片

表 1 坐标系的意义

Table 1. Significance of coordinate systems

名称	实际坐标x_i、y_i、z_i	浮动坐标$ {\hat x_i} $、$ {\hat y_i} $、${\hat {\textit{z} }_i}$
说明	轴X与关节轮毂平行，并与（i+1）关节轮毂方向平行； Z轴与平行电动机轴转动关节；Y轴由右手定律决定	轴$ \hat X $与变形连杆平行，并与（i+1）关节的轮毂方向平行；$ \hat Z $轴与平行电动机轴转动关节；$ \hat Y $轴由右手定律决定

下载: 导出CSV

表 2 空间柔性机器人关节机构物理参数

Table 2. Physical parameters of joint mechanism of space flexible robot

关节	质量/kg	尺寸/m		惯量/（kg·m²）			阻尼系数/ （N·m·s/rad）	刚度系数/ （N·m/rad）
关节	质量/kg	长度	半径	I_xx	I_yy	I_zz	阻尼系数/ （N·m·s/rad）	刚度系数/ （N·m/rad）
J₁，J₂	2.3	0.06	0.07	0.0745	0.0745	0.0100	0.05	1000
J₃，J₄，J₅, J₆	2.3	0.06	0.07	0.0745	0.0745	0.0100	0.05	800

下载: 导出CSV

表 3 空间柔性机器人机构物理参数

Table 3. Physical parameters of spatial flexible robot mechanism

机械臂	质量/kg	尺寸/m			惯量/（kg·m²）			弹性模量/ 10⁹ Pa
机械臂	质量/kg	长度	宽或半径	高	I_xx	I_yy	I_zz	弹性模量/ 10⁹ Pa
B₀	1.58×10³	1.5	1.5	1.5	1.481×10³	1.481×10³	0.592×10³	210
B₁	10	0.256	0.063		0.0745	0.0745	0.0397	210
B₂	17	1.774	0.063		4.492	0.0675	4.492	70
B₃, B₅	5	0.128	0.063		0.0331	0.0331	0.0397	210
B₄	16	1.604	0.063		3.462	0.0635	3.462	70
B₆	7	0.294	0.063		0.0643	0.0643	0.0278	210
B_p	162	4	1	0.02	9.000	56.456	47.627	0.37

下载: 导出CSV

参考文献(20)

[1]	孟光,韩亮亮,张崇峰. 空间机器人研究进展及技术挑战[J]. 航空学报,2021,42(1): 523963. MENG Guang,HAN Liangliang,ZHANG Chongfeng. Research progress and technical challenges of space robot[J]. Acta Aeronautica et Astronautica Sinica,2021,42(1): 523963. (in Chinese)
[2]	刘宏,刘冬雨,蒋再男. 空间机械臂技术综述及展望[J]. 航空学报,2021,42(1): 524164. LIU Hong,LIU Dongyu,JIANG Zainan. Space manipulator technology: review and prospect[J]. Acta Aeronautica et Astronautica Sinica,2021,42(1): 524164. (in Chinese)
[3]	方五益,郭晛,黎亮,等. 柔性铰柔性杆机器人动力学建模、仿真和控制[J]. 力学学报,2020,52(4): 965-974. doi: 10.6052/0459-1879-20-067 FANG Wuyi,GUO Xian,LI Liang,et al. Dynamics modeling, simulation, and control of robots with flexible joints and flexible links[J]. Chinese Journal of Theoretical and Applied Mechanics,2020,52(4): 965-974. (in Chinese) doi: 10.6052/0459-1879-20-067
[4]	何俊培. 新型超冗余空间机械臂的关键技术研究[D]. 长春: 中国科学院大学(中国科学院长春光学精密机械与物理研究所), 2020. HE Junpei. Research on key technologies of new hyper-redundant space manipulator[D]. Changchun: Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, 2020. (in Chinese)
[5]	NANOS K, PAPADOPOULOS E. On parameter estimation of space manipulator systems with flexible joints using the energy balance[C]//2019 International Conference on Robotics and Automation. Piscataway, US: IEEE, 2019: 3570-3576.
[6]	KORAYEM M H,DEHKORDI S F,MEHRJOOEE O. Nonlinear analysis of open-chain flexible manipulator with time-dependent structure[J]. Advances in Space Research,2022,69(2): 1027-1049. doi: 10.1016/j.asr.2021.10.037
[7]	倪诗皓. 空间柔性机械臂动力学建模研究[D]. 南京: 南京航空航天大学, 2020. NI Shihao. Research on dynamic modeling of flexible space manipulator[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2020. (in Chinese)
[8]	陈志勇,陈力. 姿态受控柔性关节双臂空间机器人的抗力矩饱和控制与振动抑制[J]. 工程力学,2016,33(5): 227-233,256. CHEN Zhiyong,CHEN Li. Anti-torque-windup control and vibration suppression of flexible-joint dual-arm space robot with an attitude-controlled base[J]. Engineering Mechanics,2016,33(5): 227-233,256. (in Chinese)
[9]	谢立敏,陈力. 漂浮基柔性关节-柔性臂空间机器人运动非线性滑模控制及双重弹性振动主动抑制[J]. 中国机械工程,2013,24(19): 2657-2663. doi: 10.3969/j.issn.1004-132X.2013.19.020 XIE Limin,CHEN Li. Nonlinear sliding mode motion control and double elastic vibration active suppression of free-floating flexible-joint and flexible-link space robot[J]. China Mechanical Engineering,2013,24(19): 2657-2663. (in Chinese) doi: 10.3969/j.issn.1004-132X.2013.19.020
[10]	黄小琴,陈力. 基座、臂杆全弹性空间机器人抗死区动态面控制[J]. 哈尔滨工程大学学报,2019,40(12): 2063-2069. doi: 10.11990/jheu.201810012 HUANG Xiaoqin,CHEN Li. Anti-dead-zone control based on dynamic surface for space robot with flexible links and elastic base[J]. Journal of Harbin Engineering University,2019,40(12): 2063-2069. (in Chinese) doi: 10.11990/jheu.201810012
[11]	潘冬. 空间柔性机械臂动力学建模分析及在轨抓捕控制[D]. 哈尔滨: 哈尔滨工业大学, 2014. PAN Dong. Research on dynamics modeling and capture control of space flexible manipulator[D]. Harbin: Harbin Institute of Technology, 2014. (in Chinese)
[12]	余章卫. 六自由度空间机器人动力学建模与控制研究[D]. 上海: 上海交通大学, 2018: 10-50. YU Zhangwei. Dynamics modelling and control of a six DOF space robot[D]. Shanghai: Shanghai Jiao Tong University, 2018: 10-50. (in Chinese)
[13]	杜严锋. 柔性空间机器人动力学建模及振动控制研究[D]. 哈尔滨: 哈尔滨工业大学, 2020: 23-60. DU Yanfeng. Research on dynamic modeling and vibration control for flexible space robot[D]. Harbin: Harbin Institute of Technology, 2020: 23-60. (in Chinese)
[14]	RASTEGARI R,ALI A MOOSAVIAN S. Multiple impedance control of space free-flying robots via virtual linkages[J]. Acta Astronautica,2010,66(5/6): 748-759.
[15]	GOULIAEV V I,ZAVRAZHINA T V. Dynamics of a flexible multi-link cosmic robot-manipulator[J]. Journal of Sound and Vibration,2001,243(4): 641-657. doi: 10.1006/jsvi.2000.3409
[16]	KORAYEM M H,SHAFEI A M,ABSALAN F,et al. Kinematic and dynamic modeling of viscoelastic robotic manipulators using Timoshenko beam theory: theory and experiment[J]. The International Journal of Advanced Manufacturing Technology,2014,71(5/6/7/8): 1005-1018.
[17]	SHARIFNIA M,AKBARZADEH A. A constrained assumed modes method for dynamics of a flexible planar serial robot with prismatic joints[J]. Multibody System Dynamics,2017,40(3): 261-285. doi: 10.1007/s11044-016-9525-8
[18]	刘延柱, 潘振宽, 戈新生. 多体系统动力学[M]. 2版. 北京: 高等教育出版社, 2014.
[19]	SHAFEI A M,SHAFEI H R. Oblique impact of multi-flexible-link systems[J]. Journal of Vibration and Control,2018,24(5): 904-923. doi: 10.1177/1077546316654854
[20]	WU Yifei,WANG Zhihong,LI Yuanyuan,et al. Characteristic modeling and control of servo systems with backlash and friction[J]. Mathematical Problems in Engineering,2014,2014: 1-21.