NI L W , MA F W , GE L H , et al . Design and posture control of a wheel-legged robot with actively passively transformable suspension system [J ] . Journal of Mechanisms and Robotics: Transactions of the ASME , 2021 , 13 ( 1 ): 1 - 10 .

BJELONIC M , SANKAR P K , BELLICOSO C D , et al . Rolling in the deep-hybrid locomotion for wheeled-legged robots using online trajectory optimization [J ] . IEEE Robotics and Automation Letters , 2020 , 5 ( 2 ): 3626 - 3633 . 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

LIU H , LIU B S , HAN Z Y , et al . Attitude control strategy for unmanned wheel-legged hybrid vehicles considering the contact of the wheels and ground [J ] . Proceedings of the Institution of Mechanical Engineers, Part D:Journal of Automobile Engineering , 2022 , 236 ( 10/11 ): 2294 - 2305 . DOI: 10.1177/09544070211058382 http://doi.org/10.1177/09544070211058382 http://journals.sagepub.com/doi/10.1177/09544070211058382 http://journals.sagepub.com/doi/10.1177/09544070211058382 During patrol and surveillance tasks, attitude control is crucial for improving the terrain adaptability of unmanned wheel-legged hybrid vehicles. This paper proposes an attitude control strategy for unmanned wheel-legged hybrid vehicles, considering the contact of the wheels and ground. The proposed method can naturally achieve torque control efficiently of each joint actuator and wheel-side actuator and avoid the discrepancy between off-road terrain and stability. First, an inverse kinematics model is established to resolve the body and each joint rotation angle, and the dynamic model is built based on the multi rigid body theory, considering the contact points planning of wheel and ground. Considering the nonholonomic constraint of the structure scheme, a hierarchical real-time attitude controller for a wheel-legged vehicle is proposed. The upper layer calculates the contact points of each wheel and the ground through the quadratic programming algorithm, and the lower layer is divided into a legged motion generator and a wheel motion generator by a mathematical analysis method. Finally, the proposed method is applied to achieve the tracking and control of the whole-body trajectory. The proposed strategy can achieve the decoupling of wheeled motion generator and legged motion generator, and improve control efficiency.

BJELONIC M , GRANDIA R , HARLEY O , et al . Whole-body MPC and online gait sequence generation for wheeled-legged robots [C ] //Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. Prague , Czech Republic : IEEE , 2021 : 8388 - 8395 .

KLEMM V , MORRA A , GULICH L , et al . LQR-assisted whole-body control of a wheeled bipedal robot with kinematic loops [J ] . IEEE Robotics and Automation Letters , 2020 , 5 ( 2 ): 3745 - 3752 . 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

刘冬琛 , 王军政 , 汪首坤 , 等 . 基于速度矢量的电动并联式轮足机器人全方位步态切换方法 [J ] . 机械工程学报 , 2019 , 55 ( 1 ): 17 - 24 . DOI: 10.3901/JME.2019.01.017 http://doi.org/10.3901/JME.2019.01.017 搭建了电动并联式轮足机器人的运动学模型，在单腿工作空间约束和行走稳定性约束条件下完成了间歇步态和旋转步态的基本步态设计，保证机器人在大负重情况下的全方位稳定行走。分析了机器人运动速度矢量与不同基本步态之间的对应关系。提出了基于速度矢量的电动并联式轮足机器人全方位步态切换方法，分析了步态切换的最佳时机，详细介绍了不同种步态之间的步态切换过程。通过虚拟样机和物理样机试验平台对本步态切换方法进行仿真分析和试验验证。仿真与试验的结果表明，电动并联式轮足机器人在基本步态行走和步态切换过程中，稳定裕度始终不小于零，且机器人机身的横滚角和俯仰角分别在-1.5°~4°和-2.8°~2.5°范围内变化，该方法能够保证电动并联式轮足机器人稳定的完成步态切换。

LIU D C , WANG J Z , WANG S K , et al . Omnidirectionalgait switching method of electric parallel wheel-foot robot based on velocity vector [J ] . Journal of Mechanical Engineering , 2019 , 55 ( 1 ): 17 - 24 . (in Chinese)

曲梦可 , 王洪波 , 荣誉 . 军用轮 、 腿混合四足机器人设计 [J ] . 兵工学报 , 2018 , 39 ( 4 ): 787 - 797 . DOI: 10.3969/j.issn.1000-1093.2018.04.019 http://doi.org/10.3969/j.issn.1000-1093.2018.04.019 为设计一种可以在迈步行走、有动力轮式机动、无动力轮旱冰式滑行3种运动方式之间灵活转换的轮、腿混合四足机器人，提出一种采用3-PUPS机构的超冗余、可变胞并联机械腿，其构型可以通过伺服电机的抱闸锁定实现变胞变换，从而使机械腿能根据任务需求实时改变自身构型和性能。在建立机械腿3-PUPS机构的运动学和静力学模型基础上，通过定义运动学和静力学性能评价指标，分析了机械腿尺寸参数对其各性能评价指标的影响规律，从而确定机械腿一组使机械腿运动学和静力学性能较为均衡的结构参数，并研制出机械腿的实验样机。建立轮、腿混合四足机器人整机的通用运动学模型，定义机器人整机的性能评价指标，分析机器人整机尺寸参数对其各性能评价指标的影响规律，并确定整机尺寸参数值，在此基础上完成了轮、腿混合四足机器人整机的设计方案。通过一套专用机器人标定系统对机械腿的实验样机进行位姿测量实验。研究结果表明：机械腿运动平台的实际运动沿x轴方向最大偏差为0.041 mm，沿y轴方向最大偏差为0.040 mm，沿 z轴方向最大偏差为0.040 mm；绕z轴姿态角最大偏差为0.041°，绕y轴姿态角最大偏差为0.043°，绕x轴姿态角最大偏差为0.045°；机械腿实验样机达到了通用式工业机器人的精度水平。

QU M K , WANG H B , RONG Y . Design of military wheel-leg hybrid quadruped robot [J ] . Acta Armamentarii , 2018 , 39 ( 4 ): 787 - 797 . (in Chinese)

姜祎 , 王挺 , 邵沛瑶 , 等 . 一种轮腿复合型机器人的步态研究与越障性能分析 [J ] . 兵工学报 , 2023 , 44 ( 1 ): 247 - 259 . DOI: 10.12382/bgxb.2022.0823 http://doi.org/10.12382/bgxb.2022.0823 为实现地面移动机器人在复杂地形下的环境探索需求，结合轮式机器人的高速特性和足式机器人对地形适应性强的特征，提出一种轮幅型轮腿复合型机器人，并针对其在移动过程中的振动问题以及爬梯过程中的越障问题，对机器人进行步态研究及性能分析。从静力学分析中得出机器人轮腿结构以不同姿态着地时的受力情况，结合实际情况中机器人运动约束对机器人在前进、转向和越障等任务中的步态进行分析，并基于动力学仿真ADAMS软件建立动力学模型来模拟机器人不同步态下的振动情况以及越障性能。研究结果表明，结合本文提出的步态控制方法，该轮腿复合型机器人在复杂地形环境中具有较好的行进效率和越障能力。

JIANG Y , WANG T , SHAO P Y , et al . Gaitstudy and obstacle-surmounting performance analysis of a wheel-leg hybrid robot [J ] . Acta Armamentarii , 2023 , 44 ( 1 ): 247 - 259 . (in Chinese) DOI: 10.12382/bgxb.2022.0823 http://doi.org/10.12382/bgxb.2022.0823 In order for ground mobile robots to fulfil the requirements of environmental exploration in complex terrain, considering the high speed characteristic of wheeled robots and the strong environmental adaptability of legged robots, a wheel-leg hybrid robot is proposed. To address the vibration problem in moving and the obstacle surmounting problem in ladder climbing, the gait study and performance analysis of the robot are carried out. The force conditions of the wheel-leg structure of the robot in different landing postures are obtained from the static analysis, and combined with the motion constraints in the actual situation, the robot gaits in the tasks of moving forward, turning and obstacle-surmounting are analyzed. Then, with the ADAMS simulation software, the dynamic model is established to simulate the robot vibration and obstacle-surmounting performance in different gaits. The results show that combined with the proposed gait control method, the wheel-leg hybrid robot has better traveling efficiency and obstacle surmounting ability in complex terrain environment.

GRAND C , BENAMAR F , PLUMET F , et al . Decoupled control of posture and trajectory of the hybrid wheel-legged robot Hylos [C ] //Proceedings of the IEEE International Conference on Robotics and Automation.New Orleans, LA, US:IEEE , 2004 : 1050 - 4729 .

DU W Q , FNADI M , BENAMAR F . Rolling based locomotion on rough terrain for a wheeled quadruped using centroidal dynamics [J ] . Mechanism and Machine Theory , 2020 , 153 : 103984 . DOI: 10.1016/j.mechmachtheory.2020.103984 http://doi.org/10.1016/j.mechmachtheory.2020.103984 https://linkinghub.elsevier.com/retrieve/pii/S0094114X20302056 https://linkinghub.elsevier.com/retrieve/pii/S0094114X20302056

刘本勇 , 高峰 , 姜惠 , 等 . 平衡摇臂式移动机器人姿态控制算法 [J ] . 北京航空航天大学学报 , 2018 , 44 ( 2 ): 391 - 398 .

LIU B Y , GAO F , JIANG H , et al . Attitude control algorithm of balancing-arm mobile robot [J ] . Journal of Beijing University of Aeronautics and Astronautics , 2018 , 44 ( 2 ): 391 - 398 . (in Chinese)

韩子勇 , 苑士华 , 裴伟亚 , 等 . 摇臂悬挂机动平台运动姿态调节最优控制研究 [J ] . 兵工学报 , 2019 , 40 ( 11 ): 2184 - 2194 . DOI: 10.3969/j.issn.1000-1093.2019.11.002 http://doi.org/10.3969/j.issn.1000-1093.2019.11.002 摇臂悬挂机动平台运动自由度多且运动姿态调节复杂，以机构运动学控制为主的运动控制方法，不能准确描述驱动关节力矩与车体轨迹和姿态的关系。基于质心动力学模型和二次规划方法，建立了一种适用于轮腿复合移动类型车辆整体运动姿态调节的通用动态优化控制框架；以基于动力学模型的二次规划方法为主，结合系统逆运动学控制，实现了对车轮地面反作用力的直接控制。利用上述控制方法，对机动平台的侧倾、俯仰、联合姿态调节及其在颠簸路面下的应用进行仿真。结果表明，该动力学运动姿态调节动态优化控制方法能够满足实时性和控制精度的需求。

HAN Z Y , YUAN S H , PEI W L , et al . Optimalcontrol of posture adjustment for articulated suspension vehicle [J ] . Acta Armamentarii , 2019 , 40 ( 11 ): 2184 - 2194 . (in Chinese)

CARLO J D , WENSING P M , KATZ B , et al . Dy namic locomotion in the MIT cheetah 3 through convex model-predictive control [C ] //Proceedings of the 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems. Madrid, Spain:IEEE , 2018 : 1 - 9 .

张国腾 , 荣学文 , 李贻斌 , 等 . 基于虚拟模型的四足机器人对角小跑步态控制方法 [J ] . 机器人 , 2016 , 38 ( 1 ): 64 - 74 . DOI: 10.13973/j.cnki.robot.2016.0064 http://doi.org/10.13973/j.cnki.robot.2016.0064 为提高四足机器人对角小跑运动的稳定性，实现机器人躯干 6 维运动方向控制的解耦，提出了一种基于虚拟模型的对角小跑步态控制方法．控制器主要包括支撑相虚拟模型控制和摆动相虚拟模型控制．在支撑相，建立了作用于躯干质心的虚拟力与对角支撑腿关节扭矩之间的数学关系，通过调整躯干虚拟力的大小控制躯干的高度与姿态，控制机器人前进速度和自转角速度．在摆动相，将机器人侧向速度控制引入到足端轨迹规划中，并通过虚拟的“弹簧－阻尼”元件驱动摆动足沿给定轨迹运动．此外，在控制器设计过程中，引入了状态机，用于监控机器人各腿的状态，并输出对角小跑步态相位切换指令．仿真实验结果表明，机器人能够以对角小跑步态在平地上进行全方位移动，跨越不平坦地形，并能够抵抗外部冲击，证明了文中控制方法的有效性和鲁棒性．

ZHANG G T , RONG X W , LI Y B , et al. Control of the quadrupedal trotting based on virtual model [J ] . Robot , 2016 , 38 ( 1 ): 64 - 74 . (in Chinese) DOI: 10.13973/j.cnki.robot.2016.0064 http://doi.org/10.13973/j.cnki.robot.2016.0064 In order to improve the stability of the trotting quadruped robot and to decouple the control of the robot torso motion along six directions, an approach based on virtual model is presented for trot gait control. The controller mainly consists of two main modules: the virtual model control at support phase and the virtual model control at flight phase. During the support phase, the mathematical relationship are mapped between the joint torques of diagonal support legs and the virtual forces acted on the center-of-mass of the torso. And the values of virtual torso forces are regulated to control the torso attitude and height, as well as the forward velocity and the yaw angular velocity of the robot. During the flight phase, lateral velocity is introduced to plan the toe trajectory. And virtual spring-damper sections are implemented to drive the flight toes to track the planned trajectories. In addition, while designing the controller, a state machine is introduced to monitor the legs' states and output phase switching commands for trot gait regulation. The simulations show that the robot is able to trot omni-directionally on flat ground as well as uneven terrains, even suffering from external impacts. And thus the effectiveness and robustness of the controller are proved.

PENG H , WANG J Z , SHEN W , et al . Cooperative attitude control for a wheel-legged robot [J ] . Peer-to-Peer Networking and Applications , 2019 , 12 ( 6 ): 1741 - 1752 . DOI: 10.1007/s12083-019-00747-x http://doi.org/10.1007/s12083-019-00747-x Robot systems are complex systems which include many CPUs and communication networks. In order to control attitude of a wheel-legged robot, a cooperative control framework is designed. The wheel-legged robot has four legs and four wheels, and the wheels are installed on the foot. The wheel-legged robot can adjust its attitude by controlling the position of each leg when it is walking with wheels. In addition, in order to avoid the wheels dangling during the driving of the robot, an impedance control based on force method is applied. Moreover, the centroid height of the robot is controlled to guarantee that the robot has maximum motion space. The cooperative control framework is implemented in a host CPU and four slave CPUs. The host CPU calculates the position of each leg by combining the control variables of attitude controller, centroid height controller and impedance controller based on force. The slave CPUs receive the position command, and then control the position of each leg with active disturbance rejection control (ADRC). ADRC can deal with the internal modeling uncertainty and external disturbances. The application of the proposed method is illustrated in the electric parallel wheel-leg robot system. Experimental results are provided to verify the effectiveness of the proposed method.

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CAMURRI M , FALLON M , BAZEILLE S , et al . Probabilistic contact estimation and impact detection for state estimation of quadruped robots [J ] . IEEE Robotics and Automation Letters , 2017 , 2 ( 2 ): 1023 - 1030 . DOI: 10.1109/LRA.2017.2652491 http://doi.org/10.1109/LRA.2017.2652491 http://ieeexplore.ieee.org/document/7815333/ http://ieeexplore.ieee.org/document/7815333/

YANG S , KUMAR H , GU Z Y , et al . State estimation for legged robots using contact-centric leg odometry:arXiv : 1911 .05176[R ] . Ithaca,NY , US : Cornell University , 2019 :1911.05176.

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QIN M Y , YU Z G , CHEN X C , et al . A novel foot contact probability estimator for biped robot state estimation [C ] //Proceedings of IEEE International Conference on Mechatronics and Automation . Beijing, China : IEEE , 2020 : 1901 - 1906 .