RUBIO F , VALERO F , LLOPIS-ALBERT C . A review of mobile robots: concepts, methods, theoretical framework, and applications [J ] . International Journal of Advanced Robotic Systems , 2019 , 16 ( 2 ): 1729881419839596.

TODD D J . The mechanics of legged vehicles [M ] //TODD D J. Walking Machines:an Introduction to Legged Robots . Boston, MA, US : Springer 1985 : 63 - 89 .

ZHONG Y H , WANG R X , FENG H S , et al . Analysis and research of quadruped robot’s legs: a comprehensive review [J ] . International Journal of Advanced Robotic Systems , 2019 , 16 ( 3 ): 1729881419844148.

BISWAL P , MOHANTY P K . Development of quadruped walking robots: a review [J ] . Ain Shams Engineering Journal , 2021 , 12 ( 2 ): 2017 - 2031 . DOI: 10.1016/j.asej.2020.11.005 http://doi.org/10.1016/j.asej.2020.11.005 https://linkinghub.elsevier.com/retrieve/pii/S2090447920302501 https://linkinghub.elsevier.com/retrieve/pii/S2090447920302501

ZHUANG H C , GAO H B , DENG Z Q , et al . A review of heavy-duty legged robots [J ] . Science China Technological Sciences , 2014 , 57 ( 2 ): 298 - 314 . DOI: 10.1007/s11431-013-5443-7 http://doi.org/10.1007/s11431-013-5443-7 http://link.springer.com/10.1007/s11431-013-5443-7 http://link.springer.com/10.1007/s11431-013-5443-7

丁良宏 . BigDog四足机器人关键技术分析 [J ] . 机械工程学报 , 2015 , 51 ( 7 ): 1 - 23 . DOI: 10.3901/JME.2015.07.001 http://doi.org/10.3901/JME.2015.07.001 对BigDog四足机器人的核心技术进行分析，适应复杂地形是BigDog的设计主线。提高横、纵自由度联动能力是BigDog结构设计主要突破点。机体重心颠簸起伏、机体重心自扰动等不良运动特性是四足机器人控制难度大的主要原因。液压动力系统的构成和优点将被剖析，解决腿类移动装置的驱动问题是液压系统研发的根本目的。支撑腿打滑及俯仰和横滚角度是否过大作为监测机体运动安全状态的参数。惯导和关节编码器可检测机身与肢体的状态，借助压力传感器可还原落足点地形，三者合一可构建虚拟模型。借助虚拟模型可求算机体重心等关键控制处理中间参数，运动控制系统可实施粗略的动作预演及精确的运动学和动力学规划。规划模型与样机模型的偏差作为反馈值实施闭环控制。建立以三维激光扫描仪和双目视觉为主的导航系统，视觉地形还原功能可帮助LS3安全跨越岩石地形，软件系统将各种基本功能整合为有机的整体。机器人的自主性与智能性被讨论，利用BigDog/LS3与好奇号火星探测器作对比并加以分析。BigDog目前存在的几个主要问题：液压系统无法瞬时大幅增压、机械传动各种损伤、仿生设计的不彻底性。LS3机器人针对BigDog的不足，多个改进环节被分析。猎豹、野猫、Petman等机器人被简要分析。阿特拉斯双足机器人借助虚拟模型可实现机械臂碰撞保护功能，遭受外力撞击可迅速恢复平衡状态。

DING L H . Key technology analysis of BigDog quadruped robot [J ] . Journal of Mechanical Engineering , 2015 , 51 ( 7 ): 1 - 23 . (in Chinese) DOI: 10.3901/JME.2015.07.001 http://doi.org/10.3901/JME.2015.07.001 The core technology of the BigDog quadruped robot is analyzed. Adapting to the rough terrain is the main design clues of the BigDog. Improving horizontal and vertical degrees of freedom linkage ability is the main innovation of structure design. Not good motion characteristics, such as robot’s center of gravity ups and downs and self disturbance are the main reasons for being difficult to control. The components and advantage of the hydraulic power system are analyzed. Solving the driver problem of legged vehicles is the fundamental goal of the hydraulic system development. Supporting leg slipping or not, pitch and roll angle of the body too large or not are the main parameters as monitoring robot’s movement condition. IMU and joint encoder can detect the state parameters of the body and limbs. Terrain of foot placement can be restored by pressure sensor. Three-in-one can build a virtual model. By the virtual model, robot’s center of gravity and other key control process parameters can be calculated. At the same time, locomotion control system can do action drill roughly and accurate planning of kinematics or dynamics. The deviation of planning and prototype model is taken as the feedback for closed-loop control. LS3 constructs the navigation system of three-dimensional laser scanner and binocular vision as the main. LS3 can stride across rocky terrain by visual terrain reconstruction. Software system can integrate all the basic functions as an organic whole. Autonomy and intelligence of robot are discussed. BigDog/LS3 and Curiosity Mars Rover are compared and analyzed. BigDog has three big problems currently: instantaneously unable to increase hydraulic value significantly, all kinds of damage in mechanical transmission, bionic design not thoroughness. For the inadequacies of BigDog, several improvements are analyzed on the LS3. Petman, Cheetah and Wildcat robot are briefly analyzed. Atlas biped robot has crash protection function and can recovery equilibrium status quickly after external force hitting by virtual model.

HUANG Y H , BING Z S , WALTER F , et al . Enhanced quadruped locomotion of a rat robot based on the lateral flexion of a soft actuated spine [C ] // Proceedings of 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems . Kyoto, Japan : IEEE , 2022 : 2622 - 2627 .

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[JL] . Scientific Reports , 2021 , 11 ( 1 ): 9631 . DOI: 10.1038/s41598-021-88879-0 http://doi.org/10.1038/s41598-021-88879-0 Cheetahs use a galloping gait in their fastest speed range. It has been reported that cheetahs achieve high-speed galloping by performing two types of flight through spine movement (gathered and extended). However, the dynamic factors that enable cheetahs to incorporate two types of flight while galloping remain unclear. To elucidate this issue from a dynamical viewpoint, we developed a simple analytical model. We derived possible periodic solutions with two different flight types (like cheetah galloping), and others with only one flight type (unlike cheetah galloping). The periodic solutions provided two criteria to determine the flight type, related to the position and magnitude of ground reaction forces entering the body. The periodic solutions and criteria were verified using measured cheetah data, and provided a dynamical mechanism by which galloping with two flight types enhances speed. These findings extend current understanding of the dynamical mechanisms underlying high-speed locomotion in cheetahs.

TAO Y , WANG T M , WANG Y Q , et al . A new variable stiffness robot joint [J ] . Industrial Robot: an International Journal , 2015 , 42 ( 4 ): 371 - 378 . DOI: 10.1108/IR-11-2014-0422 http://doi.org/10.1108/IR-11-2014-0422 https://www.emerald.com/insight/content/doi/10.1108/IR-11-2014-0422/full/html https://www.emerald.com/insight/content/doi/10.1108/IR-11-2014-0422/full/html – This study aims to propose a new variable stiffness robot joint (VSR-joint) for operating safely. More and more variable stiffness actuators are being designed and implemented because of their ability to minimize large forces due to shocks, to safely interact with the user and their ability to store and release energy in passive elastic elements.

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 http://doi.org/10.3969/j.issn.1000-1093.2022.01.015 A frog-shaped bionic soft robot with a dielectric elastomer as the actuator is designed based on the advantages of frog propulsion method and soft materials for realizing the miniaturization of robot and enhancing its environmental adaptability. According to the tensile properties of material, the manufacturing process was determined and the actuator was simulated by finite element method, and the motion trajectory planning and real underwater test of robot legs were carried out. A propulsion efficiency model was constructed by considering various parameters during swimming, and the most efficient motion parameters were determined. Experimental results show that the maximum swimming speed of the robot is as high as 132 mm/s at a frequency of 2 Hz and a voltage of 5 kV. Compared with the dimensionless model parameters of amphibians, the motion characteristics of the robot are close to those of real creatures, and it has good motion capability.

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 , 2023 , 28 ( 3 ): 1730 - 1741 . DOI: 10.1109/TMECH.2022.3224423 http://doi.org/10.1109/TMECH.2022.3224423 https://ieeexplore.ieee.org/document/9967017/ https://ieeexplore.ieee.org/document/9967017/

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 2021 IEEE/ASME International Conference on Advanced Intelligent Mechatronics . Delft, the Netherlands : IEEE , 2021 : 566 - 571 .

刘畅 , 毕树生 , 赵宏哲 , 等 . 基于折叠式串联簧片的可调刚度致动器设计 [J ] . 机械工程学报 , 2017 , 53 ( 17 ): 70 - 77 . DOI: 10.3901/JME.2017.17.070 http://doi.org/10.3901/JME.2017.17.070 可调刚度致动器能为机器人动态性能和人机交互安全性带来显著提升。在对常见簧片型变结构式刚度调节机理进行分析总结的基础上设计一种基于折叠串联型平行排布簧片组的新型旋转式可调刚度致动器，分析其刚度调节原理并介绍样机机械结构。针对实际刚度调节机构中簧片与滑块滚子的间隙，建立修正的关节旋转刚度解析模型。通过系统试验证明了模型的准确性和整体方案的可行性。折叠式串联簧片的应用使系统在有限的尺寸和足够的承载能力下获得了更大的刚度调节范围。簧片的平行排布设计则实现了多组柔性单元滑块滚子运动的同步及关节驱动与刚度控制的解耦。

LIU C , BI S S , ZHAO H Z , et al . Novel variable stiffness actuator based on folded serial leaf springs [J ] . Journal of Mechanical Engineering , 2017 , 53 ( 17 ): 70 - 77 . (in Chinese) DOI: 10.3901/JME.2017.17.070 http://doi.org/10.3901/JME.2017.17.070 Variable stiffness actuators can significantly improve the dynamic performance of robots and ensure safety in human robot interaction. An overview of different principles working on most structure controlled variable stiffness mechanisms is presented. The design of a novel variable stiffness actuator and its working principle is described. Considering the gap between leaves and rollers in the real mechanism, the analytical joint stiffness model is modified to get a more accurate estimation of the prototype. Experiments are conducted to validate the model and the feasibility of the design. The application of folded serial leaf springs leads to an increased stiffness range while the size and load capacity remains unchanged. Motion synchronization of rollers and the decoupling of joint motion and stiffness adjustment are easily achieved by the parallel assembling of leaves.

TRIGILI E , CREA S , MOISÈ M , et al . Design and experimental characterization of a shoulder-elbow exoskeleton with compliant joints for post-stroke rehabilitation [J ] . IEEE/ASME Transactions on Mechatronics , 2019 , 24 ( 4 ): 1485 - 1496 . DOI: 10.1109/TMECH.3516 http://doi.org/10.1109/TMECH.3516 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=3516 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=3516

SHINTAKE J , SCHUBERT B , ROSSET S , et al . Variable stiffness actuator for soft robotics using dielectric elastomer and low-melting-point alloy [C ] // Proceedings of 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems . Hamburg, Germany : IEEE , 2015 : 1097 - 1102 .

BIGGE B , HARVEY I R . Programmable springs: developing actuators with programmable compliance for autonomous robots [J ] . Robotics and Autonomous Systems , 2007 , 55 ( 9 ): 728 - 734 . DOI: 10.1016/j.robot.2007.05.013 http://doi.org/10.1016/j.robot.2007.05.013 https://linkinghub.elsevier.com/retrieve/pii/S0921889007000656 https://linkinghub.elsevier.com/retrieve/pii/S0921889007000656

BILANCIA P , BERSELLI G , PALLI G . Virtual and physical prototyping of a beam-based variable stiffness actuator for safe human-machine interaction [J ] . Robotics and Computer-Integrated Manufacturing , 2020 , 65 : 101886 . DOI: 10.1016/j.rcim.2019.101886 http://doi.org/10.1016/j.rcim.2019.101886 https://linkinghub.elsevier.com/retrieve/pii/S0736584519303850 https://linkinghub.elsevier.com/retrieve/pii/S0736584519303850

王伟 , 刘立冬 , 魏来 , 等 . 柔性齿条式变刚度关节驱动器设计与研究 [J ] . 机械工程学报 , DOI: 10.3901/JME.2016.01.026 https://dx.doi.org/10.3901/JME.2016.01.026 .

WANG W , LIU L D , WEI L , et al . Design and research of rack-based variable stiffness actuator [J ] . Journal of Mechanical Engineering , DOI: 10.3901/JME.2016.01.026 https://dx.doi.org/10.3901/JME.2016.01.026 . (in Chinese)

WOLF S , GRIOLI G , EIBERGER O , et al . Variable stiffness actuators: review on design and components [J ] . IEEE/ASME Transactions on Mechatronics , 2016 , 21 ( 5 ): 2418 - 2430 . DOI: 10.1109/TMECH.2015.2501019 http://doi.org/10.1109/TMECH.2015.2501019 http://ieeexplore.ieee.org/document/7330025/ http://ieeexplore.ieee.org/document/7330025/

GROOTHUIS S S , CARLONI R , STRAMIGIOLI S . Single motor-variable stiffness actuator using bistable switching mechanisms for independent motion and stiffness control [C ] // Proceedings of 2016 IEEE International Conference on Advanced Intelligent Mechatronics . Banff, AB, Canada : IEEE , 2016 : 234 - 239 .

SHAO Y X , ZHANG W X , SU Y J , et al . Design and optimisation of load-adaptive actuator with variable stiffness for compact ankle exoskeleton [J ] . Mechanism and Machine Theory , 2021 , 161 : 104323 . DOI: 10.1016/j.mechmachtheory.2021.104323 http://doi.org/10.1016/j.mechmachtheory.2021.104323 https://linkinghub.elsevier.com/retrieve/pii/S0094114X21000811 https://linkinghub.elsevier.com/retrieve/pii/S0094114X21000811

LIU Y W , LIU X G , YUAN Z Q , et al . Design and analysis of spring parallel variable stiffness actuator based on antagonistic principle [J ] . Mechanism and Machine Theory , 2019 , 140 : 44 - 58 . DOI: 10.1016/j.mechmachtheory.2019.05.016 http://doi.org/10.1016/j.mechmachtheory.2019.05.016 https://linkinghub.elsevier.com/retrieve/pii/S0094114X18317488 https://linkinghub.elsevier.com/retrieve/pii/S0094114X18317488

PETIT F , FRIEDL W , HÖPPNER H , et al . Analysis and synthesis of the bidirectional antagonistic variable stiffness mechanism [J ] . IEEE/ASME Transactions on Mechatronics , 2015 , 20 ( 2 ): 684 - 695 . DOI: 10.1109/TMECH.2014.2321428 http://doi.org/10.1109/TMECH.2014.2321428 http://ieeexplore.ieee.org/document/6824187/ http://ieeexplore.ieee.org/document/6824187/

JAFARI A , TSAGARAKIS N G , CALDWELL D G . A novel intrinsically energy efficient actuator with adjustable Stiffness (AwAS) [J/OL ] . IEEE/ASME Transactions on Mechatronics , 2013 , 18 ( 1 ): 355 - 365 .

JAFARI A , TSAGARAKIS N G , SARDELLITTI I , et al . A new actuator with adjustable stiffness based on a variable ratio lever mechanism [J ] . IEEE/ASME Transactions on Mechatronics , 2014 , 19 ( 1 ): 55 - 63 . DOI: 10.1109/TMECH.2012.2218615 http://doi.org/10.1109/TMECH.2012.2218615 http://ieeexplore.ieee.org/document/6327673/ http://ieeexplore.ieee.org/document/6327673/

TSAGARAKIS N G , SARDELLITTI I , CALDWELL D G . A new variable stiffness actuator (CompAct-VSA): Design and modelling [C ] // Proceedings of 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems . San Francisco, CA, US : IEEE , 2011 : 378 - 383 .

孙剑韬 , 周江琛 , 郭朝 , 等 . 面向柔性机器人的串联式变刚度驱动器设计 [J ] . 华中科技大学学报(自然科学版) , 2019 , 47 ( 1 ): 7 - 12 .

SUN J T , ZHOU J C , GUO Z , et al . Design of serial variable stiffness actuator for compliant robots [J ] . Journal of Huazhong University of Science & Technology (Natural Science Edition) , 2019 , 47 ( 1 ): 7 - 12 . (in Chinese)

SUN J T , GUO Z , ZHANG Y B , et al . A novel design of serial variable stiffness actuator based on an archimedean spiral relocation mechanism [J ] . IEEE/ASME Transactions on Mechatronics , 2018 , 23 ( 5 ): 2121 - 2131 . DOI: 10.1109/TMECH.3516 http://doi.org/10.1109/TMECH.3516 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=3516 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=3516

LI Z Y , CHEN W H , ZHANG J B , et al . A novel cable-driven antagonistic joint designed with variable stiffness mechanisms [J ] . Mechanism and Machine Theory , 2022 , 171 : 104716 . DOI: 10.1016/j.mechmachtheory.2021.104716 http://doi.org/10.1016/j.mechmachtheory.2021.104716 https://linkinghub.elsevier.com/retrieve/pii/S0094114X21004432 https://linkinghub.elsevier.com/retrieve/pii/S0094114X21004432

MENGACCI R , KEPPLER M , PFANNE M , et al . Elastic structure preserving control for compliant robots driven by agonistic-antagonistic actuators (ESPaa) [J ] . IEEE Robotics and Automation Letters , 2021 , 6 ( 2 ): 879 - 886 . DOI: 10.1109/LSP.2016. http://doi.org/10.1109/LSP.2016. https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7083369 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7083369

MENGACCI R , GARABINI M , GRIOLI G , et al . Overcoming the torque/stiffness range tradeoff in antagonistic variable stiffnessactuators [J ] . IEEE/ASME Transactions on Mechatronics , 2021 , 26 ( 6 ): 3186 - 3197 . DOI: 10.1109/TMECH.2021.3055364 http://doi.org/10.1109/TMECH.2021.3055364 https://ieeexplore.ieee.org/document/9339937/ https://ieeexplore.ieee.org/document/9339937/