两轮自平衡小车系统
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摘要
本质不稳定两轮小车是一种特殊轮式移动机器人,其动力学系统具有多变量、非线性、强耦合、参数不确定性等特性,是研究各种控制方法的一个理想平台。其体积小、结构简单、运动灵活,适于在狭小和危险的空间内工作,在民用和军事上有着广泛的应用前景；本课题旨在研制一种两轮自平衡小车。该系统是一种两轮左右平行布置的,像传统的倒立摆一样,本身是一个自然不稳定体,必须施加强有力的控制手段才能使之稳定。其工作原理是系统以姿态传感器(陀螺仪、加速度计)来监测车身所处的俯仰状态和状态变化率,通过高速中央处理器计算出适当数据和指令后,驱动电动机产生前进或后退的加速度来达到车体前后平衡的效果。
本文在总结和归纳国内外两轮自平衡小车的研究现状后,在缺少所需的成形的实验对象的情况下,选用适当的控制器、执行电机和传感器,设计出两轮自平衡小车的驱动电路,实现了两轮小车的硬件控制系统。
陀螺仪存在漂移的问题及加速度计的动态响应慢,对于系统的姿态检测而言,单独使用陀螺仪或者加速度计,都不能提供有效和可靠的信息来反映车体的实时状态。本文对传感器两者所采集的数据进行了优化处理,补偿陀螺仪的漂移误差和加速度计的动态误差,得到一个更优的倾角近似值。
由于实际的小车本体未加工完成,不能在此基础上进行其控制算法的研究。为了提前研究其控制策略同时缩短设计周期,本文选用LEGO机器人为试验平台,搭建所需的小车模型,利用牛顿运动定律对该系统进行数学建模,并对其线性化处理,得到相应的状态方程。在此基础之上详细介绍了两种不同的控制策略,即PID技术和极点配置技术,并通过实验来验证了极点配置方法对该系统有更好的控制效果。
The natural unstable two-wheel vehicle is a special kind of wheeled mobile robot. Its dynamics equations are multi-variable, non-linear, serious coupling and uncertain parameters etc. So it is ideal that various control methods are studied on this platform. The robot is small in mechanism and can make a flexible motion. So it is fit for tasks in narrow and dangerous space and has a wide foreground both in civilian and military application. The subject aims to develop a two-wheel self-balancing vehicle. The device of this system is a parallel arrangement of two single wheels, like a traditional inverted pendulum. Because of itself natural instability, it must be exerted strong control to make it stable. It works as follows:system attitude sensors (gyroscopes and accelerometers) monitor body condition and the state in which the pitch change rate, high-speed central processing unit to calculate the appropriate data and instructions, the motor produces forward or backward to achieve the body balancing result.
In this paper, studies on self-balancing two-wheel vehicle at home and abroad are summarized. And in the absence of subjects required and formed, we select the appropriate controller, motors and sensors to design two-wheel self-balancing vehicle drive circuit. And it accomplishes the entire hardware control system.
Because of gyro drift problems and slow dynamic response of the accelerometer, for gesture detection system, separate usage of gyro or accelerometer can not provide effective or reliable information to reflect the real state of its body. In this paper, the data collected by the two sensors are optimized to compensate the drift error of gyroscope and accelerometer dynamic error so that the inclination of its body can be approximated better.
Since that the real vehicle body is not accomplished, the control algorithms can not be studied on this basis. In order to study the control strategy in advance and shorten the design cycle, the paper has to take advantage of the LEGO robot as test platform, build vehicle model required, get mathematical modeling of the system by Newton's laws and obtain the corresponding state equation through its linearization. On this basis, the two different control strategies, namely, PID technology and pole placement technique are described in details, and finally the pole configuration is verified that it has better control effect through experiments.
本文在总结和归纳国内外两轮自平衡小车的研究现状后,在缺少所需的成形的实验对象的情况下,选用适当的控制器、执行电机和传感器,设计出两轮自平衡小车的驱动电路,实现了两轮小车的硬件控制系统。
陀螺仪存在漂移的问题及加速度计的动态响应慢,对于系统的姿态检测而言,单独使用陀螺仪或者加速度计,都不能提供有效和可靠的信息来反映车体的实时状态。本文对传感器两者所采集的数据进行了优化处理,补偿陀螺仪的漂移误差和加速度计的动态误差,得到一个更优的倾角近似值。
由于实际的小车本体未加工完成,不能在此基础上进行其控制算法的研究。为了提前研究其控制策略同时缩短设计周期,本文选用LEGO机器人为试验平台,搭建所需的小车模型,利用牛顿运动定律对该系统进行数学建模,并对其线性化处理,得到相应的状态方程。在此基础之上详细介绍了两种不同的控制策略,即PID技术和极点配置技术,并通过实验来验证了极点配置方法对该系统有更好的控制效果。
The natural unstable two-wheel vehicle is a special kind of wheeled mobile robot. Its dynamics equations are multi-variable, non-linear, serious coupling and uncertain parameters etc. So it is ideal that various control methods are studied on this platform. The robot is small in mechanism and can make a flexible motion. So it is fit for tasks in narrow and dangerous space and has a wide foreground both in civilian and military application. The subject aims to develop a two-wheel self-balancing vehicle. The device of this system is a parallel arrangement of two single wheels, like a traditional inverted pendulum. Because of itself natural instability, it must be exerted strong control to make it stable. It works as follows:system attitude sensors (gyroscopes and accelerometers) monitor body condition and the state in which the pitch change rate, high-speed central processing unit to calculate the appropriate data and instructions, the motor produces forward or backward to achieve the body balancing result.
In this paper, studies on self-balancing two-wheel vehicle at home and abroad are summarized. And in the absence of subjects required and formed, we select the appropriate controller, motors and sensors to design two-wheel self-balancing vehicle drive circuit. And it accomplishes the entire hardware control system.
Because of gyro drift problems and slow dynamic response of the accelerometer, for gesture detection system, separate usage of gyro or accelerometer can not provide effective or reliable information to reflect the real state of its body. In this paper, the data collected by the two sensors are optimized to compensate the drift error of gyroscope and accelerometer dynamic error so that the inclination of its body can be approximated better.
Since that the real vehicle body is not accomplished, the control algorithms can not be studied on this basis. In order to study the control strategy in advance and shorten the design cycle, the paper has to take advantage of the LEGO robot as test platform, build vehicle model required, get mathematical modeling of the system by Newton's laws and obtain the corresponding state equation through its linearization. On this basis, the two different control strategies, namely, PID technology and pole placement technique are described in details, and finally the pole configuration is verified that it has better control effect through experiments.
引文
[1]徐国华,谭民.移动机器人的发展现状及其趋势[J].机器人技术与应用,2001,14(3)：7—14
[2]刘金琨.智能控制.北京：电子工业出版社,2005：1—2
[3]Rich Chi Ooi, Balancing a Two-Wheeled Autonomous Robot. Final Year Thesis of USQ, 2003
[4]Colette Shen, Jinger Zhao. Brave New Machine:Will Ginger Revolutionize the way We Move? Havard Science Review,2002:57-60
[5]刘斌.两轮自平衡小车软硬件研发与基于模糊线性化模型的变结构控制研究.西安电子科技大学工学硕士学位论文.2009
[6]黎田.两轮自平衡机器人自适应控制算法的研究.哈尔滨工业大学工学硕士学位论文.2007
[7]Googol Technology. Control & network factories of the future.2007
[8]梅晓榕.自动控制元件及线路.哈尔滨工业大学出版社.2004
[9]张琛.直流无刷电动机原理及应用.机械工业出版社.2007
[10]尔桂花,窦曰轩.运动控制系统.清华大学出版社.2002
[11]阮毅,陈伯时.电力拖动自动控制系统：运动控制系统(第4版).机械工业出版社.2009
[12]陈永军,黄声华,翁惠辉,李俊杰.基于dsPIC的无刷直流电机调速系统方案[J].电机与控制应用,2006.33(8)：32-34.
[13]International Rectifier. IRFB4310 datasheet.2004
[14]ON Semiconductor. MC33035 Brushless DC Motor Controller datasheet.2006
[15]Motorola, Inc. MC33039 Closed Loop Brushless Motor Adapter.1996
[16]陈永军,黄声华,翁惠辉,李俊杰.基于dsPIC的无刷直流电机调速系统方案[J].电机与控制应用,2006,33(8)：32-34.
[17]Microchip Technology Inc. dsPIC33FJ128MCX02/X04 Data Sheet.2009
[18]包国彬,张建民,刘赢.单片机复位电路的设计与分析.光电技术应用.第20卷第3期.2005.6：3-4
[19]Formulations Media Inc. Butterworth Filters.2002
[20]孔祥宣.自主式双轮动态平衡移动机器人的控制系统研究.上海交通大学硕士学位论文.2007
[21]孙环忠.客车外摆门控制系统的研究与开发.东南大学硕士学位论文.2004
[22]张吉昌.单轴双轮自平衡代步车的研究与设计.中国海洋大学硕士论文.2009
[23]王巍,徐长智,赵采凡.陀螺加速度计输出装置设计与测试.导弹与航天运载技术.1995.3：36-44
[24]谭卢敏,冯新刚MEMS陀螺仪在检测小车运动状态中的应用.科技广场.2009.1：184-185
[25]N. Yazdi, F. Ayazi, and K. Najafi. MICROMACHINED INERTIAL SENSORS, Proceedings of the IEEE, Aug.1998.vol.86, No.8, Page(s):1640-1659
[26]Analog Devices, Inc. ±50°/s Yaw Rate Gyro ADXRS614.2007
[27]周振宇.一种用于车载导航系统的MEMS陀螺性能研究.天津大学硕士论文.2007
[28]霍贝Kalman线性滤波在非线性动态系统中的运用[J].雷达与对抗.2003.2：24-29
[29]Analog Devices Inc. Single/Dual Axis Accelerometer ADXL103/ADXL203.2004
[30]孙华,陈俊风,吴林.多传感器信息融合技术及其在机器人中的应用[J].传感器技术.2003：1-4
[31]陈俊风.多传感器信息融合及其在机器人中的应用.哈尔滨理工大学硕士论文.2004
[32]Greg Welch, Gary Bishop. An Introduction to the Kalman Filter. Department of Computer Science, University of North Carolina at Chapel Hill,2004
[33]The Balance Filter.web.mit.edu/first/segway.
[34]http://en.wikipedia.org/wiki/Low-pass_filter#Passive_digital_realization
[35]张陪仁,杨兴明.机器人系统设计与算法[M].中国科技技术大学出版社.2008
[36]Thomas Braunl, Jie Pan. Balancing a Two-Wheeled Autonomous Robot. The University of Western Australia School of Mechanical Engineering Final Year Thesis.2003.1-10,23-43
[37]F.Grasser, A.D'Arrigo etc. A Mobile Inverted Pendulum, IEEE Trans. Industrial Electronics,vol.39, No.1, February 2002. Page(s):107-114
[38]王瑜.两轮自平衡机器人的控制技术研究.哈尔滨工程大学硕士学位论文.2009
[39]袁泽睿.两轮自平衡机器人控制算法的研究.哈尔滨工业大学硕士论文.2006
[40]谢世杰,陈生潭,楼顺天.数字PID算法在无刷直流电机控制器中的应用[J].现代电子技术.200427(2)：59-61
[41]胡晓磊,喻俊志.一种新型模糊PID控制器在伺服系统的应用[J].电力电子技术.200943(11)：35-37
[42]曹青松,黎林.具时滞单级倒立摆系统的稳定性分析[J].煤矿机械.2009.4：85-89
[43]胡寿松.自动控制原理(第五版)[M].科学出版社.2007
[44]刘豹.现代控制理论(第二版).机械工业出版社.2003
[45]Shankar Sastry. Nonlinear systems:analysis, stability, and control, New York:Springer, 1999
[2]刘金琨.智能控制.北京：电子工业出版社,2005：1—2
[3]Rich Chi Ooi, Balancing a Two-Wheeled Autonomous Robot. Final Year Thesis of USQ, 2003
[4]Colette Shen, Jinger Zhao. Brave New Machine:Will Ginger Revolutionize the way We Move? Havard Science Review,2002:57-60
[5]刘斌.两轮自平衡小车软硬件研发与基于模糊线性化模型的变结构控制研究.西安电子科技大学工学硕士学位论文.2009
[6]黎田.两轮自平衡机器人自适应控制算法的研究.哈尔滨工业大学工学硕士学位论文.2007
[7]Googol Technology. Control & network factories of the future.2007
[8]梅晓榕.自动控制元件及线路.哈尔滨工业大学出版社.2004
[9]张琛.直流无刷电动机原理及应用.机械工业出版社.2007
[10]尔桂花,窦曰轩.运动控制系统.清华大学出版社.2002
[11]阮毅,陈伯时.电力拖动自动控制系统：运动控制系统(第4版).机械工业出版社.2009
[12]陈永军,黄声华,翁惠辉,李俊杰.基于dsPIC的无刷直流电机调速系统方案[J].电机与控制应用,2006.33(8)：32-34.
[13]International Rectifier. IRFB4310 datasheet.2004
[14]ON Semiconductor. MC33035 Brushless DC Motor Controller datasheet.2006
[15]Motorola, Inc. MC33039 Closed Loop Brushless Motor Adapter.1996
[16]陈永军,黄声华,翁惠辉,李俊杰.基于dsPIC的无刷直流电机调速系统方案[J].电机与控制应用,2006,33(8)：32-34.
[17]Microchip Technology Inc. dsPIC33FJ128MCX02/X04 Data Sheet.2009
[18]包国彬,张建民,刘赢.单片机复位电路的设计与分析.光电技术应用.第20卷第3期.2005.6：3-4
[19]Formulations Media Inc. Butterworth Filters.2002
[20]孔祥宣.自主式双轮动态平衡移动机器人的控制系统研究.上海交通大学硕士学位论文.2007
[21]孙环忠.客车外摆门控制系统的研究与开发.东南大学硕士学位论文.2004
[22]张吉昌.单轴双轮自平衡代步车的研究与设计.中国海洋大学硕士论文.2009
[23]王巍,徐长智,赵采凡.陀螺加速度计输出装置设计与测试.导弹与航天运载技术.1995.3：36-44
[24]谭卢敏,冯新刚MEMS陀螺仪在检测小车运动状态中的应用.科技广场.2009.1：184-185
[25]N. Yazdi, F. Ayazi, and K. Najafi. MICROMACHINED INERTIAL SENSORS, Proceedings of the IEEE, Aug.1998.vol.86, No.8, Page(s):1640-1659
[26]Analog Devices, Inc. ±50°/s Yaw Rate Gyro ADXRS614.2007
[27]周振宇.一种用于车载导航系统的MEMS陀螺性能研究.天津大学硕士论文.2007
[28]霍贝Kalman线性滤波在非线性动态系统中的运用[J].雷达与对抗.2003.2：24-29
[29]Analog Devices Inc. Single/Dual Axis Accelerometer ADXL103/ADXL203.2004
[30]孙华,陈俊风,吴林.多传感器信息融合技术及其在机器人中的应用[J].传感器技术.2003：1-4
[31]陈俊风.多传感器信息融合及其在机器人中的应用.哈尔滨理工大学硕士论文.2004
[32]Greg Welch, Gary Bishop. An Introduction to the Kalman Filter. Department of Computer Science, University of North Carolina at Chapel Hill,2004
[33]The Balance Filter.web.mit.edu/first/segway.
[34]http://en.wikipedia.org/wiki/Low-pass_filter#Passive_digital_realization
[35]张陪仁,杨兴明.机器人系统设计与算法[M].中国科技技术大学出版社.2008
[36]Thomas Braunl, Jie Pan. Balancing a Two-Wheeled Autonomous Robot. The University of Western Australia School of Mechanical Engineering Final Year Thesis.2003.1-10,23-43
[37]F.Grasser, A.D'Arrigo etc. A Mobile Inverted Pendulum, IEEE Trans. Industrial Electronics,vol.39, No.1, February 2002. Page(s):107-114
[38]王瑜.两轮自平衡机器人的控制技术研究.哈尔滨工程大学硕士学位论文.2009
[39]袁泽睿.两轮自平衡机器人控制算法的研究.哈尔滨工业大学硕士论文.2006
[40]谢世杰,陈生潭,楼顺天.数字PID算法在无刷直流电机控制器中的应用[J].现代电子技术.200427(2)：59-61
[41]胡晓磊,喻俊志.一种新型模糊PID控制器在伺服系统的应用[J].电力电子技术.200943(11)：35-37
[42]曹青松,黎林.具时滞单级倒立摆系统的稳定性分析[J].煤矿机械.2009.4：85-89
[43]胡寿松.自动控制原理(第五版)[M].科学出版社.2007
[44]刘豹.现代控制理论(第二版).机械工业出版社.2003
[45]Shankar Sastry. Nonlinear systems:analysis, stability, and control, New York:Springer, 1999