基于IMU的双足机器人动态平衡控制
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摘要
随着科学技术的发展,机器人逐渐地走进了人类的生活。国内外很多学者进行步态规划方面的研究,大多数情况没有考虑外力作用,这与人类真正意义的行走还有很大的区别。为了使其更好的适应环境,双足机器人动态平衡控制已经成为机器人学中一个非常重要的研究领域。本文以德国AMTEC公司生产的PowerCube模块设计的16自由度模块化双足机器人为蓝本,进行动态平衡控制研究。
本文首先总结了IMU惯性测量单元的发展情况,根据数学表达式和受力情况的不同,在Matlab软件Simulink中对其进行建模和仿真,并验证建立模型的正确性。分析了其控制系统的响应特性,采用PID控制器进行校正,建立校正系统仿真模型。把模块化双足机器人的结构简化为19杆连杆模型,按照Denavit-Hartenberg法则,分别推导出模块化双足机器人上肢和下肢的数学模型,进行了运动学分析,分别得出上肢和下肢运动学的正解和逆解。
在模块化双足机器人动态平衡控制研究中,首先总结了双足机器人的基本控制方法,将模块化双足机器人简化为三阶倒立摆模型,采用最优控制进行控制研究。将IMU惯性测量单元应用到模块化双足机器人上,对外力进行分类,设计控制流程图和控制结构图,以及后退动作。稳定性是机器人控制的基础,根据ZMP理论研究其稳定性,求出取值范围。以重心的位移在空间运动的距离最短为优化目标,根据静态等价尺寸链法,求解出重心的位移和加速度,采用五次多项式曲线拟合方法对各个运动关节进行轨迹规划。利用Matlab软件对模块化双足机器人的各个关节的位移、速度、加速度,进行仿真。对仿真结果进行分析,检验运动关节轨迹规划结果的合理性。
With the development of modern science and technology, the robots have stepped into our lives gradually. Most of schoolars at home and abroad research on gait planning, but the function of external force is not considerated in most cases. This is different from real meaning human walking. In order to make the robot adapt to exteral environment, dynamic balance control of biped humanoid robot has become a vital research rigion of robotics. The dynamic balance control is researched basing on 16 DOFs module biped humanoid robot with powercub, which is produced by AMTEC Corporation from German.
Firstly, the development of IMU is introduced. It is modeled and simulated in simulink of Matlab, and the model’s accuracy is demonstrated according to mathematical expression and different force conditions. The reponse of control system is analyzed, and the PID controller is used to regulate the model. The simulation model is established. The module biped humanoid robot is simplified for 19 links. According to Denavit-Hartenberg rule, the module biped humanoid robot’s upper and lower limbs’mathematical model is derived.
At frist, the basic control methods of biped robot are summarized in dynamic balance control. The module biped humanoid robot is simplified for third-order inverted pendulum model, whose control research is based on optimal control. The IMU is used on module biped humanoid robot, the external force is classed, the control flowchart and structure are designed, and recession movement is planned. Becased the stability is the base of robot’s control, according to ZMP theory, the value range is figured out. The optimal target is the displacement of COM’s motion is the shortest. According to Statically Equivallent Serial Chains, the displacement and acceleration of COM is figured out, and the fifth degree polynomial curve is used to plan the each link’s trajectory. The dispalcement and velocity and acceleration are simulated in Matlab. Accordingly to analysis of simulation results, the rationality of link’s trajectory planning is verified.
本文首先总结了IMU惯性测量单元的发展情况,根据数学表达式和受力情况的不同,在Matlab软件Simulink中对其进行建模和仿真,并验证建立模型的正确性。分析了其控制系统的响应特性,采用PID控制器进行校正,建立校正系统仿真模型。把模块化双足机器人的结构简化为19杆连杆模型,按照Denavit-Hartenberg法则,分别推导出模块化双足机器人上肢和下肢的数学模型,进行了运动学分析,分别得出上肢和下肢运动学的正解和逆解。
在模块化双足机器人动态平衡控制研究中,首先总结了双足机器人的基本控制方法,将模块化双足机器人简化为三阶倒立摆模型,采用最优控制进行控制研究。将IMU惯性测量单元应用到模块化双足机器人上,对外力进行分类,设计控制流程图和控制结构图,以及后退动作。稳定性是机器人控制的基础,根据ZMP理论研究其稳定性,求出取值范围。以重心的位移在空间运动的距离最短为优化目标,根据静态等价尺寸链法,求解出重心的位移和加速度,采用五次多项式曲线拟合方法对各个运动关节进行轨迹规划。利用Matlab软件对模块化双足机器人的各个关节的位移、速度、加速度,进行仿真。对仿真结果进行分析,检验运动关节轨迹规划结果的合理性。
With the development of modern science and technology, the robots have stepped into our lives gradually. Most of schoolars at home and abroad research on gait planning, but the function of external force is not considerated in most cases. This is different from real meaning human walking. In order to make the robot adapt to exteral environment, dynamic balance control of biped humanoid robot has become a vital research rigion of robotics. The dynamic balance control is researched basing on 16 DOFs module biped humanoid robot with powercub, which is produced by AMTEC Corporation from German.
Firstly, the development of IMU is introduced. It is modeled and simulated in simulink of Matlab, and the model’s accuracy is demonstrated according to mathematical expression and different force conditions. The reponse of control system is analyzed, and the PID controller is used to regulate the model. The simulation model is established. The module biped humanoid robot is simplified for 19 links. According to Denavit-Hartenberg rule, the module biped humanoid robot’s upper and lower limbs’mathematical model is derived.
At frist, the basic control methods of biped robot are summarized in dynamic balance control. The module biped humanoid robot is simplified for third-order inverted pendulum model, whose control research is based on optimal control. The IMU is used on module biped humanoid robot, the external force is classed, the control flowchart and structure are designed, and recession movement is planned. Becased the stability is the base of robot’s control, according to ZMP theory, the value range is figured out. The optimal target is the displacement of COM’s motion is the shortest. According to Statically Equivallent Serial Chains, the displacement and acceleration of COM is figured out, and the fifth degree polynomial curve is used to plan the each link’s trajectory. The dispalcement and velocity and acceleration are simulated in Matlab. Accordingly to analysis of simulation results, the rationality of link’s trajectory planning is verified.
引文
[1]包志军,马培荪.从两足机器人到仿人机器人的研究历史及其问题[J].机器人.1999,21(4):312-319
[2] Toby Daniel Low.Active balabnce for humanoid robot [D].The university of queensland.2003:9-10
[3]阮小刚,仇忠臣,关佳亮.双足行走机器人发展现状和展望[J].机械工程师.2007,2:18-19
[4]陈建.基于智能体的仿人机器人控制系统设计[D].硕士学位论文.上海交通大学.2007:2-3
[5]廖绍辉.双足机器人几何建模及运动轨迹规划的研究[D].硕士学位论文.大连交通大学.2007:5-6
[6] Yariv Bachar. Develop controller of biped humanoid locomotion [D].School of informatics university of Edinburgh.2004:2-3
[7]付成龙,陈恳.双足机器人稳定性与控制策略研究进展[J].高技术通讯.2006,16(3):320
[8] Albertus Hendrawan Adiwahono Chee-Meng ChewWeiwei Huang etal. Push Recovery Controller for Bipedal Robot Walking. IEEE International Conference on Humanoid Robots, 2008:2-3
[9]李增刚.一种基于神经网络感知器的双足行走机器人稳定性控制方法[J].智能控制技术.2002,2: 15-16
[10]边琦,魏世民,周晓光.神经网络在双足机器人稳定性研究中的应用[J].科学技术与工程.2008,8 (17):4838-4839
[11]殷晨波,周庆敏,徐海涵等.基于虚拟零力矩点FZMP的拟人机器人行走稳定性仿真[J].系统仿真学报.2006,18(9):2593
[12]王志越.IC&MEMS制造技术及其发展趋势[J].电子工业专用设备.2003,102:15-16
[13] OliverJ.Woodman. An introduction to inertial navigation [D].University of Cambridge.2007:4-9
[14]王洪志,王彦国.新一代陀螺的发展及应用分析[J].光学仪器.2004,26(1):14-15
[15]朱绍箕,李立新,张绍武.从西欧三国考察看惯性技术的发展[J].制导与控制.1999,1:34-37
[16]牟淑志.无陀螺惯性测量组合仿真及实验研究[D].硕士学位论文.南京理工大学.2006,8-10
[17]解旭辉,刘危,张明亮等.微惯性测量组合关键技术与应用[J].光学精密工程.2002,10(4):154-155
[18]陈伟平,赵振刚,刘晓为等.力平衡框架结构加速度计的设计[J].传感器技术学报.2006,19(5): 2194-2195
[19]陈雪冬.力平衡式加速度计闭环伺服系统动态数学模型[J].传感器技术.2001,20(5):5-6
[20]李彩华.力平衡加速度传感器设计分析[J].传感器技术.2005,24(8):46-47
[21] S.Saad, Z.Ghemari, L.Herou.Transducer (Accelerometer) Modeling and Simulation.Asian Journal of Information Technology.2007,6(1):54-57
[22]于治会.关于加速度计参数的选定[J].电气传动自动化.2003,25(3):59-61
[23] D.Prasanna Kumar and Kirat Pal.System Level Simulation of Servo Accelerometer in Simulink [J].Journal of Physical Sciences.2006,1(10):145-146
[24]董景新,赵长德,熊沈蜀等.控制工程基础[M].第二版.清华大学出版社,2003:220-221
[25]王丽飞.PID控制器参数整定方法研究[D].硕士学位论文.中国石油大学.2008:4-9
[26]张志强.PowerCube可重构模块化机器人研究[J].机器人.2006,25(1):74-76
[27] http:∥www.amtec-robotics.com
[28]熊有伦.机器人技术基础[M].第1版.华中科技大学出版社,1996:34-35
[29]霍伟编.机器人动力学与控制[M].第1版.高等教育出版社,2005:123-124
[30]丁学恭.机器人控制研究[M].第一版.浙江大学出版社,2006: 64-93
[31] (美)HaganM T,DemuthH B,BealeM H.神经网络设计[M].戴葵,李伯民译.机械工业出版社,2006: 35-82
[32]谭民,徐德后,李增广等.先进机器人控制[M].第一版.高等教育出版社,2007:430-457
[33]姚丽萍.双足机器人的设计与研究[D].硕士学位论文.江南大学.2007:36-37
[34]但远宏.小车三级倒立摆摆起倒立的仿人智能控制[D].硕士学位论文.重庆大学.2006:1-2
[35]宴安.小车三级倒立摆系统模型参数精确辨识及其摆起倒立控制器的设计与参数整定[D].硕士学位论文.重庆大学.2006:3-4
[36] Sebastien Cotton, Andrew Murray, Philippe Fraisse.Statically Equivallent Serial Chains for Modelling the Center of Mass of Humanoid Robot [J]. IEEE International Conference on Humanoid Robots, 2008:1-3
[37] Sebastien Cotton, Andrew Murray, Philippe Fraisse.Center of Mass Acceleration Characteristics of Humanoids. IEEE International Conference on Humanoid Robots.2008:3-4
[38]陈丹.基于遗传算法B样条曲线优化机器人轨迹规划中的应用[D].硕士学位论文.武汉科技大学.2007:3
[39]许英,封立耀,戚晓艳等.基于曲线等弧长分割的机器人轨迹规划[J].南昌航空工业学院学报.2004,18(3):12
[40]张海荣,舒志兵.BP神经网络在机器人运动轨迹规划中的应用[J].机械与电子.2006,11:56
[41]张连东,王德伦.一种基于测地线的机器人轨迹规划方法[J].机器人.2006,26(1):83-84
[42]刘晓平,田西勇,庄未.基于非对称组合正弦函数的机器人轨迹规划方法[J].电子机械工程.2008,24(1):56
[2] Toby Daniel Low.Active balabnce for humanoid robot [D].The university of queensland.2003:9-10
[3]阮小刚,仇忠臣,关佳亮.双足行走机器人发展现状和展望[J].机械工程师.2007,2:18-19
[4]陈建.基于智能体的仿人机器人控制系统设计[D].硕士学位论文.上海交通大学.2007:2-3
[5]廖绍辉.双足机器人几何建模及运动轨迹规划的研究[D].硕士学位论文.大连交通大学.2007:5-6
[6] Yariv Bachar. Develop controller of biped humanoid locomotion [D].School of informatics university of Edinburgh.2004:2-3
[7]付成龙,陈恳.双足机器人稳定性与控制策略研究进展[J].高技术通讯.2006,16(3):320
[8] Albertus Hendrawan Adiwahono Chee-Meng ChewWeiwei Huang etal. Push Recovery Controller for Bipedal Robot Walking. IEEE International Conference on Humanoid Robots, 2008:2-3
[9]李增刚.一种基于神经网络感知器的双足行走机器人稳定性控制方法[J].智能控制技术.2002,2: 15-16
[10]边琦,魏世民,周晓光.神经网络在双足机器人稳定性研究中的应用[J].科学技术与工程.2008,8 (17):4838-4839
[11]殷晨波,周庆敏,徐海涵等.基于虚拟零力矩点FZMP的拟人机器人行走稳定性仿真[J].系统仿真学报.2006,18(9):2593
[12]王志越.IC&MEMS制造技术及其发展趋势[J].电子工业专用设备.2003,102:15-16
[13] OliverJ.Woodman. An introduction to inertial navigation [D].University of Cambridge.2007:4-9
[14]王洪志,王彦国.新一代陀螺的发展及应用分析[J].光学仪器.2004,26(1):14-15
[15]朱绍箕,李立新,张绍武.从西欧三国考察看惯性技术的发展[J].制导与控制.1999,1:34-37
[16]牟淑志.无陀螺惯性测量组合仿真及实验研究[D].硕士学位论文.南京理工大学.2006,8-10
[17]解旭辉,刘危,张明亮等.微惯性测量组合关键技术与应用[J].光学精密工程.2002,10(4):154-155
[18]陈伟平,赵振刚,刘晓为等.力平衡框架结构加速度计的设计[J].传感器技术学报.2006,19(5): 2194-2195
[19]陈雪冬.力平衡式加速度计闭环伺服系统动态数学模型[J].传感器技术.2001,20(5):5-6
[20]李彩华.力平衡加速度传感器设计分析[J].传感器技术.2005,24(8):46-47
[21] S.Saad, Z.Ghemari, L.Herou.Transducer (Accelerometer) Modeling and Simulation.Asian Journal of Information Technology.2007,6(1):54-57
[22]于治会.关于加速度计参数的选定[J].电气传动自动化.2003,25(3):59-61
[23] D.Prasanna Kumar and Kirat Pal.System Level Simulation of Servo Accelerometer in Simulink [J].Journal of Physical Sciences.2006,1(10):145-146
[24]董景新,赵长德,熊沈蜀等.控制工程基础[M].第二版.清华大学出版社,2003:220-221
[25]王丽飞.PID控制器参数整定方法研究[D].硕士学位论文.中国石油大学.2008:4-9
[26]张志强.PowerCube可重构模块化机器人研究[J].机器人.2006,25(1):74-76
[27] http:∥www.amtec-robotics.com
[28]熊有伦.机器人技术基础[M].第1版.华中科技大学出版社,1996:34-35
[29]霍伟编.机器人动力学与控制[M].第1版.高等教育出版社,2005:123-124
[30]丁学恭.机器人控制研究[M].第一版.浙江大学出版社,2006: 64-93
[31] (美)HaganM T,DemuthH B,BealeM H.神经网络设计[M].戴葵,李伯民译.机械工业出版社,2006: 35-82
[32]谭民,徐德后,李增广等.先进机器人控制[M].第一版.高等教育出版社,2007:430-457
[33]姚丽萍.双足机器人的设计与研究[D].硕士学位论文.江南大学.2007:36-37
[34]但远宏.小车三级倒立摆摆起倒立的仿人智能控制[D].硕士学位论文.重庆大学.2006:1-2
[35]宴安.小车三级倒立摆系统模型参数精确辨识及其摆起倒立控制器的设计与参数整定[D].硕士学位论文.重庆大学.2006:3-4
[36] Sebastien Cotton, Andrew Murray, Philippe Fraisse.Statically Equivallent Serial Chains for Modelling the Center of Mass of Humanoid Robot [J]. IEEE International Conference on Humanoid Robots, 2008:1-3
[37] Sebastien Cotton, Andrew Murray, Philippe Fraisse.Center of Mass Acceleration Characteristics of Humanoids. IEEE International Conference on Humanoid Robots.2008:3-4
[38]陈丹.基于遗传算法B样条曲线优化机器人轨迹规划中的应用[D].硕士学位论文.武汉科技大学.2007:3
[39]许英,封立耀,戚晓艳等.基于曲线等弧长分割的机器人轨迹规划[J].南昌航空工业学院学报.2004,18(3):12
[40]张海荣,舒志兵.BP神经网络在机器人运动轨迹规划中的应用[J].机械与电子.2006,11:56
[41]张连东,王德伦.一种基于测地线的机器人轨迹规划方法[J].机器人.2006,26(1):83-84
[42]刘晓平,田西勇,庄未.基于非对称组合正弦函数的机器人轨迹规划方法[J].电子机械工程.2008,24(1):56