双足机器人力传感器仿真及平衡检测研究
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摘要
模块化双足机器人在快速行走和越障过程中都有着无可比拟的优越性。根据运动学参数和动力学行为的要求,可以采用标准的连杆模块和关节模块快速装配成满足用户需求的机器人构型。它具有环境适应能力强、维护简单、可实现清洁生产、成本低廉、装配方便等优点。本文研究的模块化双足机器人采用德国工业自动化公司生产的PowerCube模块组装而成,腿部具有12个自由度,上身采用类人形质量块代替,不具备自由度。
本文首先对模块化双足机器人的概况进行介绍,通过D-H表示法研究了机器人正运动学并求解出其运动变换矩阵,基于拉格朗日方程推导出机器人的动力学方程,为后期的运动仿真和动态平衡控制提供理论依据。
在对F/T传感器仿真研究过程中,通过对传感器本体模型的合理简化,将测力模块简化成弹簧-阻尼-质量块系统,把测力矩模块简化成反力矩测试装置,进行数学建模分析。采用线性二次最优控制理论对传感器控制系统进行建模并在Matlab软件simulink模块中进行仿真。应用PID校正方法来校正控制器系统的响应特性,最后以二阶倒立摆和车作为控制输入,对传感器控制系统进行仿真验证。
在对机器人动态平衡研究过程中,提出在单脚支撑期和双脚支撑期基于李群理论利用传感器检测信息实时检测机器人零力矩点(ZMP)的方法,并在实验研究中验证了检测方法的准确性。建立机器人参考坐标系,依据ZMP和质心(COM)约束条件,建立凸优化方程,利用matlab软件MOSEK工具箱进行凸优化编程运算,进而实现COM和ZMP循迹误差、髋关节、膝关节、踝关节关节轨迹规划研究,验证凸优化二阶锥优化算法的有效性和机器人动态平衡行走的可行性。
When walking fast or crossing obstacle, modular biped robot has several unparalleled advantages. It can adjust itself to different conditions. It is simply maintained, friendly to environment, cost-effective and easy to be assembled. According to kinematic and dynamic requirements, robot can be assembled by standard link and joint modules. Modular biped robot in this paper is assembled by PowerCube modules which are produced by Schunk company. It has twelve degrees of freedom for the legs and the upper body is simplified with no degree of freedom.
Firstly, we introduce the profile of modular biped robot. The forward kinematics of robot using D-H parameters and tansformation matrix are obtained. The dynamic equation of the robot is also attained based on Lagrange method which provides theoretical basis for further simulation.
For the F/T sensor simulation, mathematical modeling analysis is done by simplifying force module for spring-damper-mass system and moment module for countertorque detecting device. Then we establish Linear Quadratic optimal controller and simulate it in simulink module of matlab. The response of control system is corrected by PID. The simulation of sensor control system with second order inverted pendulum and cart as input is implemented and the simulation results show that the control method is correct.
When studying dynamic balance of the robot, a ZMP formula using Lie Group is given for detecting ZMP of robot in real time. This formula uses information from F/T sensor both in single support phase and in double support phase. ZMP point detecting experiment is carried out and detecting method is verified.
At last, convex optimization for balance control is studied. The ZMP and COM constraints are established. The trajectories of hip, knee and ankle joints are obtained using Mosek toolbox in Matlab. The simulation results show that Second Order Cone Convex Optimization is effective and stable walking of robot can be realized.
本文首先对模块化双足机器人的概况进行介绍,通过D-H表示法研究了机器人正运动学并求解出其运动变换矩阵,基于拉格朗日方程推导出机器人的动力学方程,为后期的运动仿真和动态平衡控制提供理论依据。
在对F/T传感器仿真研究过程中,通过对传感器本体模型的合理简化,将测力模块简化成弹簧-阻尼-质量块系统,把测力矩模块简化成反力矩测试装置,进行数学建模分析。采用线性二次最优控制理论对传感器控制系统进行建模并在Matlab软件simulink模块中进行仿真。应用PID校正方法来校正控制器系统的响应特性,最后以二阶倒立摆和车作为控制输入,对传感器控制系统进行仿真验证。
在对机器人动态平衡研究过程中,提出在单脚支撑期和双脚支撑期基于李群理论利用传感器检测信息实时检测机器人零力矩点(ZMP)的方法,并在实验研究中验证了检测方法的准确性。建立机器人参考坐标系,依据ZMP和质心(COM)约束条件,建立凸优化方程,利用matlab软件MOSEK工具箱进行凸优化编程运算,进而实现COM和ZMP循迹误差、髋关节、膝关节、踝关节关节轨迹规划研究,验证凸优化二阶锥优化算法的有效性和机器人动态平衡行走的可行性。
When walking fast or crossing obstacle, modular biped robot has several unparalleled advantages. It can adjust itself to different conditions. It is simply maintained, friendly to environment, cost-effective and easy to be assembled. According to kinematic and dynamic requirements, robot can be assembled by standard link and joint modules. Modular biped robot in this paper is assembled by PowerCube modules which are produced by Schunk company. It has twelve degrees of freedom for the legs and the upper body is simplified with no degree of freedom.
Firstly, we introduce the profile of modular biped robot. The forward kinematics of robot using D-H parameters and tansformation matrix are obtained. The dynamic equation of the robot is also attained based on Lagrange method which provides theoretical basis for further simulation.
For the F/T sensor simulation, mathematical modeling analysis is done by simplifying force module for spring-damper-mass system and moment module for countertorque detecting device. Then we establish Linear Quadratic optimal controller and simulate it in simulink module of matlab. The response of control system is corrected by PID. The simulation of sensor control system with second order inverted pendulum and cart as input is implemented and the simulation results show that the control method is correct.
When studying dynamic balance of the robot, a ZMP formula using Lie Group is given for detecting ZMP of robot in real time. This formula uses information from F/T sensor both in single support phase and in double support phase. ZMP point detecting experiment is carried out and detecting method is verified.
At last, convex optimization for balance control is studied. The ZMP and COM constraints are established. The trajectories of hip, knee and ankle joints are obtained using Mosek toolbox in Matlab. The simulation results show that Second Order Cone Convex Optimization is effective and stable walking of robot can be realized.
引文
[1]张焕.六自由度机器人结构设计、运动学分析及仿真[D](硕士学位论文).西安理工大学.2004:1-2
[2]李忠智.经典倒立摆模型在双足步行机器人系统中的应用[D](硕士学位论文).西南大学.2009：1-5
[3]阮晓钢,仇忠臣等.双足行走机器人研发状况及我见[J].农业机械学报[J].2006,37(9)
[4]杨新海.双足步行方法与控制研究[D].哈尔滨工程大学.2006
[5]吴立勤.双足步行机器人步行步态研究及仿真[D].上海大学.2002
[6]解仑,王志良等.双足步行机器人制作技术.机械工业出版社.2008:19-22
[7]SonyCorp. A Small Biped Entertainment Robot SDR-4Ⅻ. RISSP2003, Changsha, China
[8]Shuuji Kajita ect. Balancing a Humanoaid Robot Using Backdrive Concerned Torque Control and Direct Angular Momentum Feedbaek. Mechanical Engineering Laboratory Namiki. Tsukuba Ibaraki
[9]K.Hirai,M.Hirose and T.Takenaka.Current and Future Perspective of Honda Humanoid Robot EEE/RSJ International Intelligent Robots and Systems.1998, OTkyo:500—510
[10]Kazuo Hiari, R&D Co.Ltd Wako Reseach Center. Current and Futtrie Perspetive of Honda of Dynamic Biped Locomotion Journal of dynamic Systems, Measurement and Control. June 1987:109— 150
[11]F.Pfeiffer,K.Loffler,M.Gienger. The Concept of Jogging JOHNNIE.2002 IEEE International Confer-ence on Robotics and Automation. Washington DC,2002,3129—3135
[12]Q.Li, A T kanishi,I.Kato. Development of ZMP measurement for Biped Humanoid walking Robot using universal force-moment sensors. Jounral of RSJ, Vol.10,No.6,pp,828,
[13]www. humanoid. waseta.jp.
[14]Jung-hoonKimn And Jun-Ho Oh. Torque Feedback Control of the Humannoid platform KRH-1 Maehine Control Laboratory, Department of Mechanical Engineering,KAIST.
[15]M.Vukobratovic. Biped Locomotion:Dynamics, Stability, Control and Application [M].Spring-Verlag, Berlin,1990
[16]Juyong Park, Jaeyoung Haan, and F.C.park. Convex Optimization Algorithms for Active Balancing of Humanoid Robots. IEEE TRANSACTIONS ON ROBOTICS, VOL.23, NO.4, AUGUST 2007
[17]Q.Huang, S.Sugano and K.Tanie. A High Stbaility Smooth Walking pattern of Biped Robot. IEEE Int. Conf.on Robotics and Automation,1999:65-71
[18]J.H.Park and H.C.Cho. An online ZMP Compensation of Stable Locomotion of Biped Robots. Second International symposium on Humnaoid Robot, Tokyo:65-70
[19]谢涛.仿人机器人的研究历史、现状及展望.机器人[J].2002,7
[20]刘莉等.THBIP-1拟人机器人研究进展.机器人[J].2002,5
[21]张志强.Powercube可重构模块化机器人研究[M](硕士学位论文).西华大学.2008,5:1-2.
[22]李树军.可重构模块化机器人模块及构型设计[J].东北大学学报(自然科学版).2004,1.
[23]张艳丽.可重构模块化机器人逆运动学建模.机械设计[J].2008,11
[24]胡俊杰.可重构模块化机器人逆运动学与构型优化设计方法研究[M].吉林大学.2009,5:31-38.
[25]任敬轶.一种9-DOF模块化机器人得运动学反解.机器人[J].2001,7
[26]朱明超.可重构模块化机器人运动学-动力学与控制方法研究[M].吉林大学.2006,5:49-55
[27]李海滨,段志信.基于坐标变换的六维力传感器静态标定方法.传感器与微系统[J].2006,3
[28]姚智慧,张付祥.机器人六维力传感器研究概况与发展预测.广东自动化与信息工程[J].2002,3
[29]干方建,刘正士.一种应变式六维力传感器的设计.中国机械工程[J].2007,4
[30]张付祥.仿人行走机器人脚步六维力传感器研究[D](硕士学位论文).哈尔滨工业大学,2004.
[31]James. Robot Technology[M]. London:Kegon page Ltd,1983.
[32]V. Scheinman. Design of a computer controlled manipulator [D]. M.S. Thesis, Mechanical Engineering Dept Standford University,1969.
[33]P.C.Watson, S.H.Drake, Pedestal. Wrist Force Sensors for Industrial Assembly[J]. Proc.of the 5th.Int.Symp on Industrial Robots, Chicago,1975:501-5
[34]E.Kroll. Decoupling Load Components and Improving Robot Interfacing with as Easy-to-use 6-axis Wrist Force Sensor[J]. Proc.of the 7th World Congress,1986:327-331
[35]王嘉力,江力.一种用于微型六维力传感器的集成式应变计设计.机器人[J].2007,7
[36]ATI Automation Company. Six-Axis Force/Torque Sensor System Complication of Manuals[J].2008
[37]邵长胜,邓正隆.卫星姿控仿真系统中的力矩传感器[J].宇航学报.2000,21(4):92-101
[38]熊磊,张朋好等.速度计力矩器设计[J].新技术新仪器,2008年第28卷第2期
[39]沈辉,吉爱红等.一种二维力-扭矩传感器设计.传感器与微系统[J].2006,7
[40]贾荣从.基于双足机器人的倒立摆系统的研究[M](硕士学位论文).山东大学.2007,5:23-35
[41]薛安克,王惠蛟.二级倒立摆的鲁棒建模及鲁棒H∞最优控制[J].计算机技术与自动化.2003,6
[42]张立迎.直线二级倒立摆稳定控制研究[M](硕士学位论文).山东大学.2009,5:7-18
[43]蒲昌玖.双足步行机器人运动规划方法研究[M](硕十学位论文).西南大学.2009,5:36-38
[44]Rong Xiong, Yichao Sun, Jian Chu, Changjiu Zhou. An Inverted Pendulum Model Based Humanoid Gait Generation Using Convex Optimization. Journal of Information & Computational Science[J]. 7(12):2529-2538,2010
[45]Rong Xiong, Changjiu Zhou, Liandong Zhang. A Convex Optimation Approach for Online Walking Pattern Generation. Proceedings of the Eleventh International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines.1207-1215, Coimbra, Portugal,8-10 September 2008
[46]郭彩芬,李祥全.凸优化方法及其在排队系统中的应用研究[J].系统工程.2004,4.
[47]李冲,王兴华.复合凸优化问题的.Gause-Newton法的收敛性.计算数学[J].2002,11
[48]郜丽鹏,林云.基于凸优化理论的多传感器故障检测技术.电子测量与仪器学报[J].2009,8
[2]李忠智.经典倒立摆模型在双足步行机器人系统中的应用[D](硕士学位论文).西南大学.2009：1-5
[3]阮晓钢,仇忠臣等.双足行走机器人研发状况及我见[J].农业机械学报[J].2006,37(9)
[4]杨新海.双足步行方法与控制研究[D].哈尔滨工程大学.2006
[5]吴立勤.双足步行机器人步行步态研究及仿真[D].上海大学.2002
[6]解仑,王志良等.双足步行机器人制作技术.机械工业出版社.2008:19-22
[7]SonyCorp. A Small Biped Entertainment Robot SDR-4Ⅻ. RISSP2003, Changsha, China
[8]Shuuji Kajita ect. Balancing a Humanoaid Robot Using Backdrive Concerned Torque Control and Direct Angular Momentum Feedbaek. Mechanical Engineering Laboratory Namiki. Tsukuba Ibaraki
[9]K.Hirai,M.Hirose and T.Takenaka.Current and Future Perspective of Honda Humanoid Robot EEE/RSJ International Intelligent Robots and Systems.1998, OTkyo:500—510
[10]Kazuo Hiari, R&D Co.Ltd Wako Reseach Center. Current and Futtrie Perspetive of Honda of Dynamic Biped Locomotion Journal of dynamic Systems, Measurement and Control. June 1987:109— 150
[11]F.Pfeiffer,K.Loffler,M.Gienger. The Concept of Jogging JOHNNIE.2002 IEEE International Confer-ence on Robotics and Automation. Washington DC,2002,3129—3135
[12]Q.Li, A T kanishi,I.Kato. Development of ZMP measurement for Biped Humanoid walking Robot using universal force-moment sensors. Jounral of RSJ, Vol.10,No.6,pp,828,
[13]www. humanoid. waseta.jp.
[14]Jung-hoonKimn And Jun-Ho Oh. Torque Feedback Control of the Humannoid platform KRH-1 Maehine Control Laboratory, Department of Mechanical Engineering,KAIST.
[15]M.Vukobratovic. Biped Locomotion:Dynamics, Stability, Control and Application [M].Spring-Verlag, Berlin,1990
[16]Juyong Park, Jaeyoung Haan, and F.C.park. Convex Optimization Algorithms for Active Balancing of Humanoid Robots. IEEE TRANSACTIONS ON ROBOTICS, VOL.23, NO.4, AUGUST 2007
[17]Q.Huang, S.Sugano and K.Tanie. A High Stbaility Smooth Walking pattern of Biped Robot. IEEE Int. Conf.on Robotics and Automation,1999:65-71
[18]J.H.Park and H.C.Cho. An online ZMP Compensation of Stable Locomotion of Biped Robots. Second International symposium on Humnaoid Robot, Tokyo:65-70
[19]谢涛.仿人机器人的研究历史、现状及展望.机器人[J].2002,7
[20]刘莉等.THBIP-1拟人机器人研究进展.机器人[J].2002,5
[21]张志强.Powercube可重构模块化机器人研究[M](硕士学位论文).西华大学.2008,5:1-2.
[22]李树军.可重构模块化机器人模块及构型设计[J].东北大学学报(自然科学版).2004,1.
[23]张艳丽.可重构模块化机器人逆运动学建模.机械设计[J].2008,11
[24]胡俊杰.可重构模块化机器人逆运动学与构型优化设计方法研究[M].吉林大学.2009,5:31-38.
[25]任敬轶.一种9-DOF模块化机器人得运动学反解.机器人[J].2001,7
[26]朱明超.可重构模块化机器人运动学-动力学与控制方法研究[M].吉林大学.2006,5:49-55
[27]李海滨,段志信.基于坐标变换的六维力传感器静态标定方法.传感器与微系统[J].2006,3
[28]姚智慧,张付祥.机器人六维力传感器研究概况与发展预测.广东自动化与信息工程[J].2002,3
[29]干方建,刘正士.一种应变式六维力传感器的设计.中国机械工程[J].2007,4
[30]张付祥.仿人行走机器人脚步六维力传感器研究[D](硕士学位论文).哈尔滨工业大学,2004.
[31]James. Robot Technology[M]. London:Kegon page Ltd,1983.
[32]V. Scheinman. Design of a computer controlled manipulator [D]. M.S. Thesis, Mechanical Engineering Dept Standford University,1969.
[33]P.C.Watson, S.H.Drake, Pedestal. Wrist Force Sensors for Industrial Assembly[J]. Proc.of the 5th.Int.Symp on Industrial Robots, Chicago,1975:501-5
[34]E.Kroll. Decoupling Load Components and Improving Robot Interfacing with as Easy-to-use 6-axis Wrist Force Sensor[J]. Proc.of the 7th World Congress,1986:327-331
[35]王嘉力,江力.一种用于微型六维力传感器的集成式应变计设计.机器人[J].2007,7
[36]ATI Automation Company. Six-Axis Force/Torque Sensor System Complication of Manuals[J].2008
[37]邵长胜,邓正隆.卫星姿控仿真系统中的力矩传感器[J].宇航学报.2000,21(4):92-101
[38]熊磊,张朋好等.速度计力矩器设计[J].新技术新仪器,2008年第28卷第2期
[39]沈辉,吉爱红等.一种二维力-扭矩传感器设计.传感器与微系统[J].2006,7
[40]贾荣从.基于双足机器人的倒立摆系统的研究[M](硕士学位论文).山东大学.2007,5:23-35
[41]薛安克,王惠蛟.二级倒立摆的鲁棒建模及鲁棒H∞最优控制[J].计算机技术与自动化.2003,6
[42]张立迎.直线二级倒立摆稳定控制研究[M](硕士学位论文).山东大学.2009,5:7-18
[43]蒲昌玖.双足步行机器人运动规划方法研究[M](硕十学位论文).西南大学.2009,5:36-38
[44]Rong Xiong, Yichao Sun, Jian Chu, Changjiu Zhou. An Inverted Pendulum Model Based Humanoid Gait Generation Using Convex Optimization. Journal of Information & Computational Science[J]. 7(12):2529-2538,2010
[45]Rong Xiong, Changjiu Zhou, Liandong Zhang. A Convex Optimation Approach for Online Walking Pattern Generation. Proceedings of the Eleventh International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines.1207-1215, Coimbra, Portugal,8-10 September 2008
[46]郭彩芬,李祥全.凸优化方法及其在排队系统中的应用研究[J].系统工程.2004,4.
[47]李冲,王兴华.复合凸优化问题的.Gause-Newton法的收敛性.计算数学[J].2002,11
[48]郜丽鹏,林云.基于凸优化理论的多传感器故障检测技术.电子测量与仪器学报[J].2009,8