用于四足机器人的离散式串联弹性脊柱关节设计

doi:10.12382/bgxb.2024.0350

摘要/Abstract

摘要：

为提高四足机器人的运动步幅和在运动中的抗冲击性能,以猎豹为仿生对象进行运动机理分析,设计一种具有串联弹性驱动器(Series Elastic Actuator,SEA)的离散式仿生脊柱关节。采用SEA为驱动单元,布置在脊柱箱体与腿足关节之间,模拟生物肌肉特性提供被动柔顺性。脊柱整体设计采用2自由度离散式构型,实现伸展和蜷曲两种奔跑姿态,提高运动步幅。基于D-H参数法,建立了2自由度离散式脊柱四足机器人的运动学模型,并对四足机器人的运动步幅进行了对比分析。搭建四足机器人实验平台,开展性能测试实验。在bound步态下的实验结果表明:在步幅测试实验中,含脊柱的四足机器人运动步幅提高了73.72%;对比刚性躯干,在跳跃过程中可以减少前腿大腿电机峰值力矩35.2%、前腿小腿峰值力矩12.0%、后腿大腿峰值力矩45.7%以及后腿小腿峰值力矩10.3%,且各关节电机输出力矩的均值、标准差均明显降低。

关键词: 离散式脊柱, 串联弹性驱动器, 步幅提升, 力矩缓冲

Abstract:

In order to improve the stride length and impact resistance of quadruped robots during movement,a cheetah is used as a bionic object to analyze the motion mechanism,and a discrete bionic spine joint with series elastic actuator (SEA) is designed.The SEA is used as the driving unit,which is arranged between the spinal box and leg joints to simulate the characteristics of biological muscles and provide passive compliance.The overall design of the spine adopts 2-DoFs discrete configuration to achieve two running postures of extension and curling,thus improving the stride length.Based on the D-H parameter method,a kinematic model of quadruped robot with 2-DoF discrete spine is established,and the stride length of quadruped robot is analyzed.An experimental platform of quadruped robots with SEA spine is constructed for performance testing experiment.The experimental results under the bound gait show that the stride length of quadruped robot with SEA spine is increased by 73.72%.Compared with the rigid trunk,the SEA spine joint can reduce the peak torques of front leg thigh motor,front leg calf motor,hind leg thigh motor and hind leg calf motor by 35.2%,12.0%,45.7% and 10.3%,respectively,during jumping.And the mean and standard deviation of the output torque of each joint motor are significantly reduced.

Key words: discrete spine, series elastic actuator, stride length increase, torque buffering

中图分类号:

TP242

苏家豪, 刘思宇, 卢春雷, 郭朝, 王志瑞, 闫曈, 党睿娜, 苏波. 用于四足机器人的离散式串联弹性脊柱关节设计[J]. 兵工学报, 2025, 46(4): 240350-.

SU Jiahao, LIU Siyu, LU Chunlei, GUO Zhao, WANG Zhirui, YAN Tong, DANG Ruina, SU Bo. Design of a Discrete Series Elastic Actuated Spine for Quadruped Robots[J]. Acta Armamentarii, 2025, 46(4): 240350-.

图/表 25

图1 猎豹奔跑过程中的疾驰步态

Fig.1 Two gaits of a cheetah during running

图2 脊柱整体结构设计

Fig.2 Overall structural design of spine

图3 SEA结构

Fig.3 SEA structure

图4 SEA安装示意图

Fig.4 Installation diagram of SEA

图5 实验整体样机

Fig.5 Experimental overall prototype

图6 SEA压缩过程

Fig.6 Compression process of SEA

图7 SEA原理示意图

Fig.7 Schematic diagram of SEA

图8 单腿运动学坐标系建立

Fig.8 Establishment of single-leg kinematic coordinate system

表1 单腿D-H参数

Table 1 Single leg D-H parameters

i	θ_i/(°)	d_i/mm	α_i/(°)	∂_i/mm
1		d₀		∂₁
1'	θ₁+90		90
2		d₁
3	θ₂	d₂	-90
4	θ₃	d₃		∂₃
5	θ₄-90			∂₄

图9 有无脊柱足端工作空间对比

Fig.9 Comparison of foot-end workspaces with and without spine

图10 摆线轨迹

Fig.10 Cycloid trajectory

图11 bound步态下腿部关节运动轨迹

Fig.11 Motion trajectories of leg joints under bound gait

图12 猎豹奔跑步态

Fig.12 Motion trajectories of leg joints under running gait

图13 有无脊柱步幅对比

Fig.13 Comparison of stride lengths with and without spine

图14 等效刚度测试平台

Fig.14 Equivalent stiffness test platform

图15 等效刚度

Fig.15 Equivalent stiffness curve

图16 频率响应实验

Fig.16 Frequency response experiment

图17 冲击测试实验平台

Fig.17 Impact test experimental platform

图18 不同冲击下的电机力矩对比

Fig.18 Motor torques under different impacts

表2 有SEA和无SEA下的峰值力矩实验

Table 2 Experiments of torque buffering with SEA and without SEA in terms of peak torque

下落高度mm	有SEA峰值力矩/ (N·m)	无SEA峰值力矩/(N·m)	减少百分比/%
200	6.97	13.30	47.6%
400	8.78	17.93	51.0%
600	9.10	21.76	58.2%

图19 样机步幅测试平台

Fig.19 Prototype stride test platform

图20 bound步态步幅对比

Fig.20 Stride length comparison of bound gait

图21 跳跃缓冲实验

Fig.21 Jump buffer experiment

图22 各电机位置与力矩对比

Fig.22 Comparison of position and torque of each motor

表3 有、无SEA脊柱时各电机力矩数据对比

Table 3 Comparison of motor torque data with and without SEA spine N·m

电机	有SEA脊柱			无SEA脊柱			有SEA脊柱峰值力矩减少百分比/%
电机	峰值		标准差	峰值		标准差	有SEA脊柱峰值力矩减少百分比/%
前腿大腿	3.70	-3.42	1.09	5.71	-2.80	1.60	35.2
前腿小腿	0.52	-16.94	2.41	2.23	-19.23	3.31	12.0
后腿大腿	0.37	-6.64	1.18	1.32	-12.23	1.81	45.7
后腿小腿	0.54	-15.80	2.88	1.11	-17.61	3.15	10.3
脊柱	1.36	-3.51	1.02

参考文献 35

[1]	SEMINI C, TSAGARAKIS N G, GUGLIELMINO E, et al. Design of HyQ-a hydraulically and electrically actuated quadruped robot[J]. Proceedings of the Institution of Mechanical Engineers,Part I:Journal of Systems and Control Engineering, 2011, 225(6):831-849.
[2]	HUTTER M, GEHRING C, JUD D, et al. Anymal-a highly mobile and dynamic quadrupedal robot[C]// Proceedings of the 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems.Daejeon, South Korea: IEEE, 2016:38-44.
[3]	荣学文. SCalf 液压驱动四足机器人的机构设计与运动分析[D]. 济南: 山东大学, 2013.
	RONG X W. Mechanism design and kinematics analysis of a hydraulically actuated quadruped robot SCalf[D]. Jinan: Shandong University, 2013. (in Chinese)
[4]	柴汇, 孟健, 荣学文, 等. 高性能液压驱动四足机器人 SCalf 的设计与实现[J]. 机器人, 2014, 36(4):385-391.
	CHAI H, MENG J, RONG X W, et al. Design and implementation of SCalf,an advanced hydraulic quadruped robot[J]. Robot, 2014, 36(4):385-391. (in Chinese)
[5]	Unitree Aliengo[EB/OL]. 杭州: 杭州宇树科技有限公司, 2019 (2019-05-20) [2024-10-21]. https://www.unitree.com/cn/aliengo.
	Unitree Aliengo[EB/OL]. Hangzhou: Hangzhou Yushu Technology CO., LTD., 2019 (2019-05-20) [2024-10-21]. https://www.unitree.com/cn/aliengo. in Chinese)
[6]	绝影 X30[EB/OL]. 杭州: 杭州云深处科技有限公司, 2023 (2023-10-09) [2024-10-21]. https://www.deeprobotics.cn/robot/index/product3.html.
	Jueying X30[EB/OL]. Hangzhou: Hangzhou Yunshenchu Technology Co., Ltd., 2023 (2023-10-09) [2024-10-21]. https://www.deeprobotics.cn/robot/index/product3.html. in Chinese)
[7]	HILDEBRAND M. Motions of the running cheetah and horse[J]. Journal of Mammalogy, 1959, 40(4):481-495.
[8]	HILDEBRAND M. Further studies on locomotion of the cheetah[J]. Journal of Mammalogy, 1961, 42(1):84-91.
[9]	GALBUSERA F, WILKE H J. Biomechanics of the spine[M]. Pittsburgh,PA,US: Academic Press, 2018:279-296.
[10]	REITMAIER S, SCHMIDT H, IHLER R, et al. Preliminary investigations on intradiscal pressures during daily activities:an in vivo study using the merino sheep[J]. PloS One, 2013, 8(7):e69610.
[11]	GAMBARYAN P P. How mammals run[M]. Jerusalem, Israel:IPST,1974.
[12]	SCHILLING N, HACKERT R. Sagittal spine movements of small therian mammals during asymmetrical gaits[J]. Journal of Experimental Biology, 2006, 209(19):3925-3939.
[13]	ALEXANDER R M N, DIMERY N J, KER R F. Elastic structures in the back and their role in galloping in some mammals[J]. Journal of Zoology, 1985, 207(4):467-482.
[14]	GRAY J. How animals move[M]. Cambridge,UK: Cambridge University Press, 2013.
[15]	LEESER K F. Locomotion experiments on a planar quadruped robot with articulated spine[D]. Cambridge,MA, US: Massachusetts Institute of Technology, 1996.
[16]	LEWIS M A. Self-organization of locomotory controllers in robots and animals[M]. Los Angeles,CA,US: University of Southern California, 1996.
[17]	JASON D. Boston dynamics robot Cheetah outruns swiftest human[EB/OL]. 2012 (2012-09-10) [2019-03-02]. https://singularityhub.com/2012/09/10/boston-dynamics-robot-cheetah-outruns-swiftest-human/.
[18]	LIU J Y. From big dog to spot mini:evolution of boston powered quadruped robot[J]. Robot Industry, 2018,2:109-116.
[19]	SEOK S, WANG A, CHUAH M Y, et al. Design principles for highly efficient quadrupeds and implementation on the MIT Cheetah robot[C]// Proceedings of the 2013 IEEE International Conference on Robotics and Automation.Karlsruhe, Germany:IEEE, 2013:3307-3312.
[20]	SEOK S, WANG A, CHUAH M Y, et al. Design principles for energy-efficient legged locomotion and implementation on the MIT cheetah robot[J]. IEEE/ASME Transactions on Mechatronics, 2014, 20(3):1117-1129.
[21]	张秀丽, 谭小康, 吴海波. 可变刚度的四足机器人被动柔顺脊柱设计与应用[J]. 北京交通大学学报, 2018, 42(6):111-118. doi: 10.11860/j.issn.1673-0291.2018.06.016
	ZHANG X L, TAN X K, WU H B. Design and application of passive compliant spine of quadruped robot with variable stiffness[J]. Journal of Beijing Jiaotong University, 2018, 42(6):111-118. (in Chinese) doi: 10.11860/j.issn.1673-0291.2018.06.016
[22]	雷静桃, 俞煌颖. 四足机器人气动人工肌肉驱动的仿生柔性机体动力学分析[J]. 上海交通大学学报, 2014, 48(12):1688-1693.
	LEI J T, YU H Y. Dynamics analysis of bionic flexible body driven by pneumatic artificial muscle for quadruped robot[J]. Journal of Shanghai Jiaotong University, 2014, 48(12):1688-1693. (in Chinese)
[23]	ZHAO Q, SUMIOKA H, YU X, et al. The function of the spine and its morphological effect in quadruped robot locomotion[C]// Proceedings of the 2012 IEEE International Conference on Robotics and Biomimetics.Guangzhou, China: IEEE, 2012:66-71.
[24]	李庆中, 李晓丹, 于福杰, 等. 介电弹性体式蛙型仿生软体机器人设计[J]. 兵工学报, 2022, 43(1):140-147.
	LI Q Z, LI X D, YU F J, et al. Dielectric elastomer-driven frog-shaped bionic soft robot[J]. Acta Armamentarii, 2022, 43(1):140-147. (in Chinese) doi: 10.3969/j.issn.1000-1093.2022.01.015
[25]	QIAN W, LIAO J B, LU L J, et al. CURER:a lightweight cable-driven compliant upper limb rehabilitation exoskeleton robot[J]. IEEE/ASME Transactions on Mechatronics, 2022, 28(3):1730-1741.
[26]	ZHAO W H, WANG J C, QIAN W, et al. Design of a compliant upper-limb rehabilitation exoskeleton based on novel series elastic actuators[C]// Proceedings of the/2021 IEEE/ASME International Conference on Advanced Intelligent Mechatronics.Delft, The Netherlands: IEEE, 2021:566-571.
[27]	ZHAO W H, LIAO J B, QIAN W, et al. A novel design of series elastic actuator using tensile springs array[J]. Mechanism and Machine Theory, 2024,192:105541.
[28]	廖峻北, 伊烁闻, 雷飞, 等. 连续变刚度仿生驱动关节的设计与建模分析[J]. 兵工学报, 2023, 44(11):3269-3278. doi: 10.12382/bgxb.2023.0730
	LIAO J B, YI S W, LEI F, et al. Design and modeling of a bionic joint with continuously variable stiffness[J]. Acta Armamentarii, 2023, 44(11):3269-3278. (in Chinese) doi: 10.12382/bgxb.2023.0730
[29]	刘思宇, 廖峻北, 雷飞, 等. 用于四足机器人的并联弹性腿足关节设计与优化[J]. 兵工学报, 2024, 44(增刊2):71-83.
	LIU S Y, LIAO J B, LEI F, et al. Design and optimization of a parallel elastic actuator leg for quadruped robots[J]. Acta Armamentarii, 2023, 44(S2):71-83. (in Chinese) doi: 10.12382/bgxb.2023.0897
[30]	KAMIMURA T, AOI S, HIGURASHI Y, et al. Dynamical determinants enabling two different types of flight in cheetah gallop to enhance speed through spine movement[J]. Scientific Reports, 2021, 11(1):9631. doi: 10.1038/s41598-021-88879-0 pmid: 33953253
[31]	CORKE P I. A simple and systematic approach to assigning Denavit-Hartenberg parameters[J]. IEEE Transactions on Robotics, 2007, 23(3):590-594.
[32]	MCGHEE R B, FRANK A A. On the stability properties of quadruped creeping gaits[J]. Mathematical Biosciences, 1968,3:331-351.
[33]	SPRÖWITZ A, TULEU A, VESPIGNANI M, et al. Towards dynamic trot gait locomotion:design,control,and experiments with Cheetah-cub,a compliant quadruped robot[J]. The International Journal of Robotics Research, 2013, 32(8):932-950.
[34]	蔡润斌. 四足机器人运动规划及协调控制[D]. 长沙: 国防科学技术大学, 2013.
	CAI R B. Quadruped robot motion planning and coordinated control[D]. Changsha: National University of Defense Technology, 2013. (in Chinese)
[35]	PAINE N, OH S, SENTIS L. Design and control considerations for high-performance series elastic actuators[J]. IEEE/ASME Transactions on Mechatronics, 2013, 19(3):1080-1091.