基于Stewart平台的六维加速度传感器研究
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摘要
类人机器人灵巧手在抓取物体的过程中,手抓的惯性力会影响抓取的鲁棒性,惯性导航系统中需要测量空间加速度经过积分计算获得载体的位置和姿态,武器制导、汽车碰撞、医学和体育等领域也都对六维加速度传感器有着迫切的需求。但是沿x、y、z正交分解布置敏感元件的传统方法很难构造能同时测量三维线加速度和三维角加速度的弹性元件结构,并联机构的发展和Stewart平台的结构特点为该课题的研究提供了新的思路。论文中采用基于Stewart平台的柔性并联机构作为弹性元件对六维加速度传感器从基础理论、关键技术、标定和实验等方面进行研究,解决并联机构刚度大导致传感器信噪比低不能用于小量程传感器弹性元件、传感器弹性元件理论简化模型实体化后带来的结构误差影响传感器测量精度等关键科学问题,为六维加速度传感器的研究提供理论依据和实验指导。主要研究了以下内容：
(1)在定义了六维加速度传感器系统静态模型的基础上,应用空间模型理论建立了传感器的静态数学模型,推导了无量纲尺寸参数的三维空间和二维平面的模型转换方程,依据矢量积法和并联机构理论推导了同机构尺寸参数相关的加速度雅可比矩阵。
(2)提出把影响传感器测量精度的基本特性误差和影响误差与传感器的加速度雅可比矩阵和弹性连接杆的输出应变矩阵相关联,全面研究误差对传感器测量精度的影响规律。分析了影响传感器信噪比的因素,全面定义了传感器的静态特性和动态特性性能指标,尤其是传感器的各向同性和灵敏度特性性能指标。
(3)基于各向同性和灵敏度特性性能指标的定义,绘制了各性能指标同理论模型参数之间关系的性能图谱,通过建立各性能指标的单目标和多目标优化函数对理论模型参数进行了尺寸优化研究,并将优化结果与其它优化方法的结果进行了全面对比。
(4)针对弹性元件理论简化模型实体化后带来的结构误差对传感器测量精度的影响问题和目前柔性并联机构建模方法存在的局限性,提出应用有限元法研究了弹性元件实体化模型参数的刚度对传感器测量精度和动态特性的影响问题,鉴于刚度对二者的影响存在矛盾,提出应用正交试验和极差分析法对实体化模型参数的尺寸进行了优化研究。
(5)针对并联机构刚度大导致传感器信噪比低影响传感器测量精度的问题,提出了应用应力集中系数法研究弹性元件结构的研究方法,定义了适合弹性元件结构研究的应力集中系数,应用穆斯海里什维里算法研究了引入应力集中的弹性连接杆结构的数学模型。在应力集中系数法研究的基础上,提出了一种双悬臂梁S型的弹性连接杆结构,建立了其受力情况的力学模型,并应用有限元法对其力学模型进行了分析。
(6)从理论上分析了基于Stewart平台的六维加速度传感器耦合误差产生的原因,并对解耦的方法进行了研究。基于论文中提出的理论设计、加工了传感器弹性元件,搭建了传感器的测量系统进行标定试验和测量精度验证,并对六维加速度传感器的动态特性进行了研究。
In the course of grasping objects by the dexterous hands of humanoid robot, the inertial force caused by the spacial acceleration imposed on the hands will affect the grasping robustness. The spacial acceleration need to be measured so as to calculate the position and attitude of the carrier with the method of integration the spacial acceleration in inertial navigation systems. And there is an urgent need of six-axis accelerometers in the other fields such as weapons guidance, car collision and sports. Nevertheless, it is difficult to fabricate the elastic element to simultaneously sense the three linear accelerations and three angular accelerations with the method of placing the sensing elements along the x, y, and z-orthogonal decomposition. With the development of parallel mechanism, the structural features of Stewart platform provide a new approach to study on a six-axis accelerometer. Using the compliant mechanism based on Stewart plarform as elasitc element,This paper studied a six-axis accelerometer on the theory and calibration experiment in order to solve the key science questions such as parallel mechanism not used as the elastic element of sensor with small range because of high rigidity causing low singal to noise(S/N) and the structural errors by the solid model instead of the simplified theoretical model affecting sensor measurement accuracy, and provide a theoretical basis and experimental guidance for study on the six-axis accelerometer. Research the following:
(l)Based on the definition of the static model for the six-axis accelerometer, the mathematic static model of sensor war established with the method of the physical model of solution space and changed3D nondimensional parameters into2D by the conversion formulas. According to the method of vector product and theory of parallel mechanism, acceleration Jacobian matrix was detailedly deduced and expressed by the nondimensional parameters.
(2)Based on deviding the errors affecting measurement accuracy into basic errors associated with the acceleration Jacobian matrix and impact errors associated with the output strain matrix of the elastic leg, this paper analyzed the impact law caused by the errors affecting measurement accuracy and factors affecting S/N of sensor. And then, the sensor performance indexes were difined such as the static and dynamic characteristics, especially in isotropy and sensitivity characteristics expressed by nondimensional parameters of simplified theoretical model.
(3)The performance atlases were drawn and used to express the relationship among all kinds of indexes to theoretical parameters based on the definition of isotropy and sensitivity characteristics. Then, the single-objective optimization functions and multi-objective optimization functions were constructed so as to optimize the theoretical parameters, and the results were compared with those obtained by other optimization methods.
(4)In order to solve the questions such as the structural errors by the solid model instead of the simplified theoretical model affecting sensor measurement accuracy and he limitations of modeling methods for compliant parallel mechanism, the finite element method of numerical solution was utilized to study the structural rigidy affecting measurement accuracy and dynamic characteristics of the sensor. Taking the contradictions bring by structural rigidy affecting measurement accuracy and dynamic characteristics into account, this paper presented to optimize the solid model parameters by orthogonal test and extreme difference analysis.
(5)So as to solve the questions such that parallel mechanism not used as the elastic element of sensor with small range because of high rigidity causing low singal to noise(S/N), the method of stress concentration factor was applied to study the elastic element structure based on the redefinition stress concentration factor in order to establish the mathematic model for he elastic element structure with the method of Muskhelishvili. According to the method of stress concentration factor, this paper presented a structure of elastic element with double cantilever beam, constructed force model and calculated by the finite element method.
(6)Based on the anslysis mechanism of coupling errors for the six-axis acclelerometer with Stewart platform, this paper studied the decoupling method, designed the measuring system for sensor based on the prototype processed, calibrated the measurement accuracy by calibration experiment and,finally, silmulated dynamic characteristics.
(1)在定义了六维加速度传感器系统静态模型的基础上,应用空间模型理论建立了传感器的静态数学模型,推导了无量纲尺寸参数的三维空间和二维平面的模型转换方程,依据矢量积法和并联机构理论推导了同机构尺寸参数相关的加速度雅可比矩阵。
(2)提出把影响传感器测量精度的基本特性误差和影响误差与传感器的加速度雅可比矩阵和弹性连接杆的输出应变矩阵相关联,全面研究误差对传感器测量精度的影响规律。分析了影响传感器信噪比的因素,全面定义了传感器的静态特性和动态特性性能指标,尤其是传感器的各向同性和灵敏度特性性能指标。
(3)基于各向同性和灵敏度特性性能指标的定义,绘制了各性能指标同理论模型参数之间关系的性能图谱,通过建立各性能指标的单目标和多目标优化函数对理论模型参数进行了尺寸优化研究,并将优化结果与其它优化方法的结果进行了全面对比。
(4)针对弹性元件理论简化模型实体化后带来的结构误差对传感器测量精度的影响问题和目前柔性并联机构建模方法存在的局限性,提出应用有限元法研究了弹性元件实体化模型参数的刚度对传感器测量精度和动态特性的影响问题,鉴于刚度对二者的影响存在矛盾,提出应用正交试验和极差分析法对实体化模型参数的尺寸进行了优化研究。
(5)针对并联机构刚度大导致传感器信噪比低影响传感器测量精度的问题,提出了应用应力集中系数法研究弹性元件结构的研究方法,定义了适合弹性元件结构研究的应力集中系数,应用穆斯海里什维里算法研究了引入应力集中的弹性连接杆结构的数学模型。在应力集中系数法研究的基础上,提出了一种双悬臂梁S型的弹性连接杆结构,建立了其受力情况的力学模型,并应用有限元法对其力学模型进行了分析。
(6)从理论上分析了基于Stewart平台的六维加速度传感器耦合误差产生的原因,并对解耦的方法进行了研究。基于论文中提出的理论设计、加工了传感器弹性元件,搭建了传感器的测量系统进行标定试验和测量精度验证,并对六维加速度传感器的动态特性进行了研究。
In the course of grasping objects by the dexterous hands of humanoid robot, the inertial force caused by the spacial acceleration imposed on the hands will affect the grasping robustness. The spacial acceleration need to be measured so as to calculate the position and attitude of the carrier with the method of integration the spacial acceleration in inertial navigation systems. And there is an urgent need of six-axis accelerometers in the other fields such as weapons guidance, car collision and sports. Nevertheless, it is difficult to fabricate the elastic element to simultaneously sense the three linear accelerations and three angular accelerations with the method of placing the sensing elements along the x, y, and z-orthogonal decomposition. With the development of parallel mechanism, the structural features of Stewart platform provide a new approach to study on a six-axis accelerometer. Using the compliant mechanism based on Stewart plarform as elasitc element,This paper studied a six-axis accelerometer on the theory and calibration experiment in order to solve the key science questions such as parallel mechanism not used as the elastic element of sensor with small range because of high rigidity causing low singal to noise(S/N) and the structural errors by the solid model instead of the simplified theoretical model affecting sensor measurement accuracy, and provide a theoretical basis and experimental guidance for study on the six-axis accelerometer. Research the following:
(l)Based on the definition of the static model for the six-axis accelerometer, the mathematic static model of sensor war established with the method of the physical model of solution space and changed3D nondimensional parameters into2D by the conversion formulas. According to the method of vector product and theory of parallel mechanism, acceleration Jacobian matrix was detailedly deduced and expressed by the nondimensional parameters.
(2)Based on deviding the errors affecting measurement accuracy into basic errors associated with the acceleration Jacobian matrix and impact errors associated with the output strain matrix of the elastic leg, this paper analyzed the impact law caused by the errors affecting measurement accuracy and factors affecting S/N of sensor. And then, the sensor performance indexes were difined such as the static and dynamic characteristics, especially in isotropy and sensitivity characteristics expressed by nondimensional parameters of simplified theoretical model.
(3)The performance atlases were drawn and used to express the relationship among all kinds of indexes to theoretical parameters based on the definition of isotropy and sensitivity characteristics. Then, the single-objective optimization functions and multi-objective optimization functions were constructed so as to optimize the theoretical parameters, and the results were compared with those obtained by other optimization methods.
(4)In order to solve the questions such as the structural errors by the solid model instead of the simplified theoretical model affecting sensor measurement accuracy and he limitations of modeling methods for compliant parallel mechanism, the finite element method of numerical solution was utilized to study the structural rigidy affecting measurement accuracy and dynamic characteristics of the sensor. Taking the contradictions bring by structural rigidy affecting measurement accuracy and dynamic characteristics into account, this paper presented to optimize the solid model parameters by orthogonal test and extreme difference analysis.
(5)So as to solve the questions such that parallel mechanism not used as the elastic element of sensor with small range because of high rigidity causing low singal to noise(S/N), the method of stress concentration factor was applied to study the elastic element structure based on the redefinition stress concentration factor in order to establish the mathematic model for he elastic element structure with the method of Muskhelishvili. According to the method of stress concentration factor, this paper presented a structure of elastic element with double cantilever beam, constructed force model and calculated by the finite element method.
(6)Based on the anslysis mechanism of coupling errors for the six-axis acclelerometer with Stewart platform, this paper studied the decoupling method, designed the measuring system for sensor based on the prototype processed, calibrated the measurement accuracy by calibration experiment and,finally, silmulated dynamic characteristics.
引文
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