KATZ B , DI C J , KIM S . Mini cheetah: a platform for pushing the limits of dynamic quadruped control [C ] // Proceedings of the 2019 International Conference on Robotics and Automation. Montreal , Canada : IEEE , 2019 : 6295 - 6301 .

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

HOELLER D , RUDIN N , SAKO D , et al. ANYmal parkour: learning agile navigation for quadrupedal robots [J ] . arXiv preprint arXiv:2306.14874, 2023 .

李姗姗 , 王洪波 , 陈建宇 , 等 . 新型四足并联军用机器人步态控制算法及仿真 [J ] . 兵工学报 , 2023 , 44 ( 3 ): 895 - 909 . DOI: 10.12382/bgxb.2021.0796 http://doi.org/10.12382/bgxb.2021.0796 在多关节步行机器人控制策略中，全部采用中央模式(CPG)网络进行控制的方法具有参数繁多、网络结构复杂的特点；机器人的工作环境通常多变且复杂，对机器人的灵活性和抗干扰能力提出了更高的要求，故仅采用单一的控制模式很难满足上述需求。针对上述问题，在机器人控制上把基于CPG的控制方法和基于虚拟模型的控制方法进行综合，对单腿为3-UPS机构的四足并联军用机器人设计了一种新型步态控制算法，用CPG完成机器人的基础步态，完成输入输出之间的非线性振荡器网络模型的搭建，并将模型的输出与关节电机的驱动力矩构成映射关系；再用虚拟模型生成行走时保持机器人平稳姿态所需要的足端虚拟力，并将足端虚拟力映射为关节驱动力矩。通过V-REP与MATLAB软件对该步态控制算法进行联合仿真实验。仿真结果表明：所提出的步态控制算法有效；新算法的优势在于简化控制网络的同时还能保证机器人在行走过程中拥有较强的灵活性和抗干扰能力，这种新型控制模式为四足并联军用机器人的步态控制提供了新的思路与方法。

LI S S , WANG H B , CHEN J Y , et al. Gait control algorithm and simulation of new parallel quadruped military robot [J ] . Acta Armamentarii , 2023 , 44 ( 3 ): 895 - 909 . (in Chinese) DOI: 10.12382/bgxb.2021.0796 http://doi.org/10.12382/bgxb.2021.0796 In the multi-joint walking robot control strategy, when only the CPG network control is used, there will be problems of various parameter and complex network structure. In addition, the robot’s work environment is usually varied and complex, requiring higher flexibility of robots and stronger anti-interference ability. So using a single control mode is difficult to meet the above requirements. To address these problems, by combining the CPG control method and the control method based on the virtual model, a new gait control algorithm is designed for parallel quadruped military robots whose each leg is a 3-UPS mechanism. CPG is used to complete the basic walking gait and the construction of the nonlinear oscillator network model between input and output, and then the output is mapped to the driving moment of the joint motor. The foot virtual force required to maintain the robot’s stable posture during walking is generated by the virtual model, and the foot virtual force is mapped to the joint’s driving moment. Finally, V-REP and MATLAB are used to simulate the proposed gait control algorithm, and the simulation results verify its effectiveness. The advantage of the proposed gait control algorithm is that it can simplify the control network and ensure the robot’s strong flexibility and anti-interference ability during walking, thus providing new insights into the gait control of parallel quadruped military robots.

王琪 , 张秀丽 , 江磊 , 等 . 具有2DOF铰接式躯干的仿猎豹四足奔跑机器人 [J ] . 机器人 , 2022 , 44 ( 3 ): 257 - 266 . DOI: 10.13973/j.cnki.robot.210101 http://doi.org/10.13973/j.cnki.robot.210101 为了探索脊柱运动对腿运动的增强机理，设计了具有2自由度铰接式躯干的仿猎豹四足奔跑机器人。对带腾空相的跳跃（bound）步态奔跑运动的力学过程进行描述，采用阻尼型弹性负载倒立摆（D-SLIP）模型建立了四足机器人动力学模型。依据猎豹的奔跑运动模式，对四足机器人脊柱关节与腿关节的耦合运动进行了轨迹规划。提出一种改进的粒子群优化（PSO）算法，解决了机器人脊柱关节驱动机构尺寸和运动轨迹控制参数之间目标互斥的嵌套优化问题。对四足机器人跳跃奔跑运动进行动力学仿真，结果表明：脊柱与腿的协调运动可以增大奔跑步幅，使机器人产生腾空相，从而提高机器人的奔跑速度。

WANG Q , ZHANG X L , JIANG L , et al. A cheetah-mimicking quadruped running robot with 2DOF qrticulated trunk [J ] . Robot , 2022 , 44 ( 3 ): 257 - 266 . (in Chinese) DOI: 10.13973/j.cnki.robot.210101 http://doi.org/10.13973/j.cnki.robot.210101 In order to explore the mechanism of leg movements enhanced by spinal movements, a cheetah-mimicking quadruped running robot with 2-DOF (degree of freedom) articulated trunk is designed. The mechanical processes of the running motion in bound gait with flying phase are described. The dynamics model of the quadruped robot is established using a damped spring loaded inverted pendulum (D-SLIP) model. Referring to the running mode of cheetahs, the trajectories of the coupled motions of the spine joints and leg joints of the quadruped robot are planned. An improved PSO (particle swarm optimization) algorithm is proposed to solve the nested optimization problem with target mutual exclusion between the dimensional parameters of actuation mechanism of robot spine joint and the control parameters of motion trajectory. The dynamic simulations of the running motion of the quadruped robot in bound gait are carried out. The results show that the coordinated movements between the spine and the legs can increase the stride length of the quadruped robot and allow the robot generating flying phases, so as to improve the running speed of the robot.

FELLER D . Kinematics of a novel serial-parallel, compliant, three-legged robot [J ] . IEEE Access , 2023 .DOI: 10.1109/ACCESS.2023.3313981 https://dx.doi.org/10.1109/ACCESS.2023.3313981 .

LI J Q , CONG D C , YANG Y , et al. A new bionic hydraulic actuator system for legged robots with impact buffering, impact energy absorption, impact energy storage, and force burst [J ] . Robotica , 2022 , 40 ( 7 ): 2485 - 2502 . DOI: 10.1017/S0263574721001752 http://doi.org/10.1017/S0263574721001752 https://www.cambridge.org/core/product/identifier/S0263574721001752/type/journal_article https://www.cambridge.org/core/product/identifier/S0263574721001752/type/journal_article It is a big challenge for bionic legged robots to realize desired jumping heights and forward-running speeds, let alone achieve springbok-style jump-running. A key limitation is that there is no actuator system that can mimic the springbok’s muscle system to drive leg–foot system movements. In this paper, we analyze the movement process of springboks and summarize some key characteristics of actuator systems. Some key concepts are then identified based on these key characteristics. Next, we propose a new bionic hydraulic joint actuator system with impact buffering, impact energy absorption, impact energy storage, and force burst, which can be applied to various legged robots to achieve higher running speeds, higher jumping heights, longer endurance, heavier loads, and lighter mass.

MOHSENI O , SHAHRI M A , DAVOODI A , et al. Adaptation in a variable parallel elastic actuator for rotary mechanisms towards energy efficiency [J ] . Robotics and Autonomous Systems , 2021 , 143 : 103815 . DOI: 10.1016/j.robot.2021.103815 http://doi.org/10.1016/j.robot.2021.103815 https://linkinghub.elsevier.com/retrieve/pii/S0921889021001007 https://linkinghub.elsevier.com/retrieve/pii/S0921889021001007

DEL F F , SESSELMANN A , ROA M A . Influence of variable leg elasticity on the stability of quadrupedal gaits [C ] // Proceedings of 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems. Kyoto , Japan : IEEE , 2022 : 5869 - 5876 .

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 . 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

魏敦文 , 葛文杰 , 高涛 . 仿生灵感下的弹性驱动器的研究综述 [J ] . 机器人 , 2017 , 39 ( 4 ): 541 - 550 . DOI: 10.13973/j.cnki.robot.2017.0541 http://doi.org/10.13973/j.cnki.robot.2017.0541 近年来有关仿生灵感下弹性驱动器的理论和应用研究越来越多，有必要将现有的研究成果加以分析和总结，对未来的发展趋势进行展望，以促进弹性驱动器的相关理论和仿生工程应用的进一步发展．首先，介绍基于仿生灵感的弹性驱动器的起源和意义．然后，在弹性驱动器相关研究的基础上，对串联弹性驱动器（series elastic actuator，SEA）、并联弹性驱动器（parallel elastic actuator，PEA）、离合弹性驱动器（clutchable elastic actuator，CEA）和多构态弹性驱动器（multi-configuration elastic actuator，MEA）4种典型的弹性驱动模式的结构组成、功能特性和应用等方面的研究现状进行阐述．最后，对弹性驱动器的关键技术进行分析，对未来发展趋势进行构想和展望，并提出未来潜在的几个研究方向．

WEI D W , GE W J , GAO T . Review of elastic actuator research from bionic inspiration [J ] . Robot , 2017 , 39 ( 4 ): 541 - 550 . (in Chinese) DOI: 10.13973/j.cnki.robot.2017.0541 http://doi.org/10.13973/j.cnki.robot.2017.0541 Because there are more and more theoretical and applied researches of elastic actuators from bionic inspiration in recent years, it is necessary to summarize and analyze the existing research results and to point out the development trends in the future, so as to promote the further developments of the related theories and bionic engineering applications of elastic actuators. Firstly, the origin and significance of the elastic actuators from bionic inspiration are introduced. Based on the research of elastic actuators, four typical elastic actuators, including the series elastic actuator (SEA), the parallel elastic actuator (PEA), the clutchable elastic actuator (CEA) and the multi-configuration elastic actuator (MEA), are introduced from the structures, features and applications aspects. Finally, the key technologies of elastic actuators are analyzed, the conception and prospect for the future development trends are proposed, and several potential future research directions are put forward.

MATHEWS C W , BRAUN D J . Parallel variable stiffness actuators [C ] // Proceedings of the 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems. Prague , Czech Republic : IEEE , 2021 : 8225 - 8231 .

CHAICHAOWARAT R , KINUGAWA J , SEINO A , et al. A spring-embedded planetary-geared parallel elastic actuator [C ] // Proceedings of the 2020 IEEE/ASME International Conference on Advanced Intelligent Mechatronics. Boston, MA , US : IEEE , 2020 : 952 - 959 .

LIU X , ROSSI A , POULAKAKIS I . A switchable parallel elastic actuator and its application to leg design for running robots [J ] . IEEE/ASME Transactions on Mechatronics , 2018 , 23 ( 6 ): 2681 - 2692 . DOI: 10.1109/TMECH.2018.2871670 http://doi.org/10.1109/TMECH.2018.2871670 https://ieeexplore.ieee.org/document/8470106/ https://ieeexplore.ieee.org/document/8470106/

PLOOIJ M , WISSE M , VALLERY H . Reducing the energy consumption of robots using the bidirectional clutched parallel elastic actuator [J ] . IEEE Transactions on Robotics , 2016 , 32 ( 6 ): 1512 - 1523 . DOI: 10.1109/TRO.2016.2604496 http://doi.org/10.1109/TRO.2016.2604496 http://ieeexplore.ieee.org/document/7587409/ http://ieeexplore.ieee.org/document/7587409/

CHATZIANDREOU E , MATHEWS C W , BRAUN D J . Design of a parallel elastic actuator with a continuously-adjustable equilibrium position:arXiv:2212.07601 [R/OL ] . Ithaca, NY , US : Cornell University , 2022 :2212.07601 (2023-01-17). https://arxiv.org/abs/2212.07601v2 https://arxiv.org/abs/2212.07601v2 https://arxiv.org/abs/2212.07601v2.

韩亚丽 , 贾山 , 王兴松 . 基于人体生物力学的低功耗踝关节假肢的设计与仿真 [J ] . 机器人 , 2013 , 35 ( 3 ): 276 - 282 .

HAN Y L , JIA S , WANG X S . Design and simulation of an ankle prosthesis with lower power based on human biomechanics [J ] . Robot , 2013 , 35 ( 3 ): 276 - 282 . (in Chinese) DOI: 10.3724/SP.J.1218.2013.00276 http://doi.org/10.3724/SP.J.1218.2013.00276 http://robot.sia.cn/CN/10.3724/SP.J.1218.2013.00276 http://robot.sia.cn/CN/10.3724/SP.J.1218.2013.00276

BJELONIC F , LEE J , ARM P , et al. Learning-based design and control for quadrupedal robots with parallel-elastic actuators [J ] . IEEE Robotics and Automation Letters , 2023 , 8 ( 3 ): 1611 - 1618 . DOI: 10.1109/LRA.2023.3234809 http://doi.org/10.1109/LRA.2023.3234809 https://ieeexplore.ieee.org/document/10008034/ https://ieeexplore.ieee.org/document/10008034/

HONG C , TANG D W , QUAN Q Q , et al. A combined series-elastic actuator & parallel-elastic leg no-latch bio-inspired jumping robot [J ] . Mechanism and Machine Theory , 2020 , 149 : 103814 . DOI: 10.1016/j.mechmachtheory.2020.103814 http://doi.org/10.1016/j.mechmachtheory.2020.103814 https://linkinghub.elsevier.com/retrieve/pii/S0094114X20300355 https://linkinghub.elsevier.com/retrieve/pii/S0094114X20300355

LINDA F S , WOUTER J W , MARTIJN W . Unparameterized optimization of the spring characteristic of parallel elastic actuators [J ] . IEEE Robotics and Automation Letters , 2019 , 4 ( 2 ): 854 - 861 . DOI: 10.1109/LRA.2019.2893425 http://doi.org/10.1109/LRA.2019.2893425 https://ieeexplore.ieee.org/document/8613810/ https://ieeexplore.ieee.org/document/8613810/

MATHEWS C W , BRAUN D J . Design of parallel variable stiffness actuators [J ] . IEEE Transactions on Robotics , 2023 , 39 ( 1 ): 768 - 782 . DOI: 10.1109/TRO.2022.3197088 http://doi.org/10.1109/TRO.2022.3197088 https://ieeexplore.ieee.org/document/9882183/ https://ieeexplore.ieee.org/document/9882183/

KAKOGAWA A , KAWABATA T , MA S G . Plate-springed parallel elastic actuator for efficient snake robot movement [J ] . IEEE/ASME Transactions on Mechatronics , 2021 , 26 ( 6 ): 3051 - 3063 . DOI: 10.1109/TMECH.2021.3052037 http://doi.org/10.1109/TMECH.2021.3052037 https://ieeexplore.ieee.org/document/9325915/ https://ieeexplore.ieee.org/document/9325915/

MENGACCI R , ZAMBELLA G , GRIOLI G , et al. An open-source ROS-gazebo toolbox for simulating robots with compliant actuators [J ] . Frontiers in Robotics and AI , 2021 , 8 : 713083 . DOI: 10.3389/frobt.2021.713083 http://doi.org/10.3389/frobt.2021.713083 https://www.frontiersin.org/articles/10.3389/frobt.2021.713083/full https://www.frontiersin.org/articles/10.3389/frobt.2021.713083/full To enable the design of planning and control strategies in simulated environments before their direct application to the real robot, exploiting the Sim2Real practice, powerful and realistic dynamic simulation tools have been proposed, e.g., the ROS-Gazebo framework. However, the majority of such simulators do not account for some of the properties of recently developed advanced systems, e.g., dynamic elastic behaviors shown by all those robots that purposely incorporate compliant elements into their actuators, the so-called Articulated Soft Robots ASRs. This paper presents an open-source ROS-Gazebo toolbox for simulating ASRs equipped with the aforementioned types of compliant actuators. To achieve this result, the toolbox consists of two ROS-Gazebo modules: a plugin that implements the custom compliant characteristics of a given actuator and simulates the internal motor dynamics, and a Robotic Operation System (ROS) manager node used to organize and simplify the overall toolbox usage. The toolbox can implement different compliant joint structures to perform realistic and representative simulations of ASRs, also when they interact with the environment. The simulated ASRs can be also used to retrieve information about the physical behavior of the real system from its simulation, and to develop control policies that can be transferred back to the real world, leveraging the Sim2Real practice. To assess the versatility of the proposed plugin, we report simulations of different compliant actuators. Then, to show the reliability of the simulated results, we present experiments executed on two ASRs and compare the performance of the real hardware with the simulations. Finally, to validate the toolbox effectiveness for Sim2Real control design, we learn a control policy in simulation, then feed it to the real system in feed-forward comparing the results.

MA B P , RUI Y F , WANG C L , et al. Research on leg transmission mechanism of quadruped robot [C ] // Proceedings of the 2021 6th International Conference on Control, Robotics and Cybernetics. Shanghai , China : IEEE , 2021 : 36 - 40 .

FARLEY A , WANG J , MARSHALL J A . How to pick a mobile robot simulator: a quantitative comparison of CoppeliaSim, Gazebo, MORSE and Webots with a focus on accuracy of motion [J ] . Simulation Modelling Practice and Theory , 2022 , 120 : 102629 . DOI: 10.1016/j.simpat.2022.102629 http://doi.org/10.1016/j.simpat.2022.102629 https://linkinghub.elsevier.com/retrieve/pii/S1569190X22001046 https://linkinghub.elsevier.com/retrieve/pii/S1569190X22001046