不确定非完整动力学系统的自适应模糊滑模控制器

为研究不确定非完整动力学系统的收敛性, 根据速度跟踪原理, 对其提出一种新的自适应模糊滑模控制器. 该控制器在存在的参数不确定性与外界干扰的情况下, 能使系统的广义坐标与广义速度收敛到预先给定的界内. 仿真算例验证了所提出方法的有效性.     

非定常完整约束系统的线性映射方法

通过一阶线性映射可以从非定常完整约束系统的位形空间映射出一个时空Π,并诱导出时空Π上的附加几何结构(度规和联络),由此可以写出约束系统在时空Π中的运动方程.当一阶线性映射不可积时,时空Π是一个Riemann Cartan空间;当一阶线性映射可积时,时空Π将退化为一个Riemann空间,且此时由这种线性映射方法得到的时空Π中的运动方程等价于用广义坐标表示的约束系统的Lagrange方程.     

并联预紧式六维力传感器动态力响应分析

提出一种并联预紧式双层结构六维力传感器,介绍了该传感器的结构特点和优点.并基于多自由度系统振动力学对该六维力传感器进行动态力响应分析.首先结合该传感器的结构特点对其进行静力学分析,在此基础上建立了传感器系统的振动力学模型;然后推导出系统的运动微分方程,通过求解运动微分方程,得到了系统在动态力作用下广义坐标的响应以及各分...     

基于Hermite 插值的多体系统动力学离散变分方法

针对多体系统动力学数值仿真问题,研究基于Hermite插值的离散变分方法.首先对广义坐标和广义速度进行Hermite插值,结合Gauss数值积分方法,利用Hamilton原理和离散力学变分原理,建立了含已知导数信息和含未知导数信息的Hermite插值离散变分数学模型,求解得到精确度较高的动力学仿真结果.该方法可以在步长较大时精确保持约束方程,并保持系统总能量在一定范围内有界变化,适用于长时间仿真情况.     

萤火虫算法求解多体系统动力学微分-代数方程

针对多体系统动力学微分-代数方程求解问题,研究基于萤火虫算法的求解方法.首先将广义坐标和广义速度进行Lagrange插值,结合Gauss数值积分方法,将微分-代数方程求解问题转化成求解最优化问题.然后用萤火虫算法对问题进行优化求解.最后,通过对平面双连杆机械臂的多体系统仿真实验,验证了萤火虫算法在求解动力学方程中既保持了约束又较好地保证了能量精度.结果表明智能优化算法在求解多体动力学问题上具有较好的应用前景.     

机器人及机械系统自适应控制的研究

本文给出了作者在机器人控制领域所做的以下工作: 1)针对机器人杆身结构上的特点,首先提出一种利用输入输出积分寻求自适应控制律的新方法;2)将负载质量从机器人动力学方程中分离出来,给出其一般的表现形式。在此基础上,利用作者提出的输入输出积分寻求自适应控制律的方法,得到了针对负载未知时在广义坐标空间和任务坐标空间中的轨迹跟踪、点到点以及模型参考自适应控制,并研究了在有界扰动时的鲁棒自适应控制;3)研究了除负载质量未知外还有其它参数未知时,在广义坐标空间和任务坐标空     

欠驱动旋转双摆系统的建模与仿真

研究倒立摆控制问题,针对旋转双摆系统这一新颖的欠驱动机械系统,而旋转双摆系统是由一个驱动的旋转臂和两个未驱动的旋转摆杆组成,选取驱动臂和两个摆杆的旋转角度作为系统的广义坐标,系统存在不稳定平衡点.为对系统进行稳定性控制,采用拉格朗日方程的方法建立了其动力学模型并总结了系统模型的特殊性质.为了便于进行稳定控制器的设计,给出了近似条件下旋转双摆系统的线性化.对动力学模型进行了仿真实验,仿真结果表明实现了系统的稳定性控制,说明了模型的有效性.     

考虑几何非线性和热效应的刚柔耦合系统的频域特性研究

研究温度场中旋转刚体-梁系统的刚-柔耦合动力学特性.考虑几何非线性和热效应,从精确的应变-位移关系式出发,用虚功原理和有限单元法建立了旋转刚体-梁系统的刚-柔耦合动力学方程.由于非线性刚度阵与变形的高次项有关,将非线性刚度阵的各元素表示为广义坐标阵和常值阵的乘积.数值计算表明,该方法可避免重复积分,提高计算效率.在此基础上研究了在温度递增的情况下几何非线性对系统的刚-柔耦合动力学特性的影响,用频谱分析方法研究了系统的固有频率随中心刚体转动惯量和温度的变化.     

四旋翼吊挂运输系统动态反馈线性化轨迹控制

三维空间下的四旋翼吊挂运输系统是一种欠驱动、强耦合、多变量的非线性系统. 根据系统的动力学特点, 将系统分解为双质点系绳连接子系统和四旋翼姿态控制子系统. 选择与系统自由度维数相同的广义坐标并基于虚位移原理计算对应的广义力, 从而建立系统的拉格朗日动力学方程. 利用微分平滑特性证明了运输系统存在平凡零动态, 因此可通过动态反馈转化为线性和能控系统. 经过2次动态扩展和变量代换, 原系统扩展为总相对阶等于系统状态维度的线性能控系统. 基于赫尔维茨稳定性判据, 设计了跟踪误差指数收敛的动态反馈控制律. 该方法可作为一类非线性系统控制器设计的标准方法. 最后以三维空间的螺旋曲线及水平面内频率变化的圆周曲线为参考轨迹进行仿真, 仿真结果验证了控制系统的有效性.     

α方法在非完整力学系统数值积分中的应用

将源于直接积分方法的广义-α法和d—RATTLE法应用到非完整力学系统动力学方程数值积分中,直接求解指标-2的微分一代数方程（DAEs）,这两种方法的质量矩阵可以是常量,也可以与广义坐标相关．最后,文中通过一个非完整力学系统：Snakeboard模型,对这两种方法进行了验证,并且与DASSL算法包的结果进行了比较．     

Structure of optimized generalized coordinates partitioned vectors for holonomic and non-holonomic systems

The generalized coordinates partitioning is a well-known procedure that can be applied in the framework of a numerical integration of the DAE systems. However, although the procedure proves to be a very useful tool, it is known that an optimization algorithm for the coordinates partitioning is needed to obtain the best performance. In the paper, the optimized partitioning of the generalized coordinates is revisited in the context of a numerical forward dynamics of the holonomic and non-holonomic multibody systems. After a short presentation of the geometric background of the optimized coordinates partitioning, a structure of the optimally partitioned vectors is discussed on the basis of a gradient analysis of the separate constraint sub-manifolds at the configuration and the velocity levels when holonomic and non-holonomic constraints are present in the system. It is shown that, for holonomic systems, the vectors of optimally partitioned coordinates have the same structure for the generalized positions and velocities. On the contrary, in the case of non-holonomic systems, the optimally partitioned coordinates generally differ at the configuration and the velocity levels. The conclusions of the paper are illustrated within the framework of the presented numerical example.     

基于稀疏解组合优化的广义重心坐标

根据广义重心坐标线性运算的性质与特点,运用广义重心坐标的稀疏解权函数的 调和平均组合方法,对空间凸多面体顶点设计了一种求解广义重心坐标的算法,且权函数是带 有保形参数的一元函数,因而具有保形优化的特点。构造了 2 种不同类型的带形参权函数,运 用不同权函数及其参数的广义重心坐标将平面图形映射到空间曲面的实例进行了分析,并应用 重心坐标常用的等值线工具对保形性进行了比较。     

A procedure to find equivalences among dynamic models of planar biped robots

In this paper, a method to find equivalences among dynamic models is presented. The models are given in different generalized coordinates for the same mechanical system. This novel method is valid for planar biped robots, i.e., those whose motions are executed only in a plane. We show that no matter which generalized coordinates are used to get the dynamic models, there is always an equivalence among them by using a particular input matrix. We exhibit some advantages of getting the dynamic model using absolute coordinates instead of relative coordinates, and we show how to calculate the input matrix for getting the equivalence between these models. Because of its simplicity, a compass-like biped robot model is used as example to explain in detail the novel procedure. In order to appreciate the benefits of the proposed procedure in biped robots of high degrees of freedom, we also present the equivalence between two dynamic models for the single support phase of a 5 degrees of freedom biped robot using absolute coordinates and relative ones.     

Maximum Likelihood Coordinates

Any point inside a d-dimensional simplex can be expressed in a unique way as a convex combination of the simplex's vertices, and the coefficients of this combination are called the barycentric coordinates of the point. The idea of barycentric coordinates extends to general polytopes with n vertices, but they are no longer unique if n > d+1. Several constructions of such generalized barycentric coordinates have been proposed, in particular for polygons and polyhedra, but most approaches cannot guarantee the non-negativity of the coordinates, which is important for applications like image warping and mesh deformation. We present a novel construction of non-negative and smooth generalized barycentric coordinates for arbitrary simple polygons, which extends to higher dimensions and can include isolated interior points. Our approach is inspired by maximum entropy coordinates, as it also uses a statistical model to define coordinates for convex polygons, but our generalization to non-convex shapes is different and based instead on the project-and-smooth idea of iterative coordinates. We show that our coordinates and their gradients can be evaluated efficiently and provide several examples that illustrate their advantages over previous constructions.     

Time-optimal control in regions where all state coordinates have the same sign

For a plant consisting of pure integrators it is shown that, in the region of state space where all state coordinates have a given sign, the time-optimal control has the opposite sign. This result is generalized to regions where the state coordinates are all non. positive or all non-negative.     

基于四边形面积坐标法的广义协调薄板单元

为克服等参坐标的缺点,采用四边形面积法构造一系列4节点12自由度的广义协调任意面积坐标四边形薄板(Area-coordinate Quadrilateral Plate,AQP)单元.对广义协调条件、边界位移场和试函数的选取规律进行深入探讨.该系列单元克服等参单元易网格畸变的缺点,在推导过程中引入广义位移的特征矩阵、节点位移的特征矩阵以及转换矩阵的概念,以使推导过程简单化、通用化.数值算例表明,此方法通用性强、易于程序化,所构造的单元自由度少、效率和精度较高.     

基于测地线距离的广义高斯型Laplacian 特征映射

传统的Laplacian 特征映射是基于欧氏距离的近邻数据点的保持,近邻的高维数据点映射到内在低维空间后仍为近邻点,高维数据点的近邻选取最终将影响全局低维坐标.将测地线距离和广义高斯函数融合到传统的Laplacian 特征映射算法中,首先提出了一种基于测地线距离的广义高斯型Laplacian 特征映射算法(geodesicdistance-based generalized Gaussian LE,简称GGLE),该算法在用不同的广义高斯函数度量高维数据点间的相似度时,获得的全局低维坐标呈现出不同的聚类特性;然后,利用这种特性进一步提出了它的集成判别算法,该集成判别算法的主要优点是:近邻参数K 固定,邻接图和测地线距离矩阵都只构造一次.在木纹数据集上的识别实验结果表明,这是一种有效的基于流形的集成判别算法.     

结合广义重心坐标与Voronoi 剖分的函数分片逼近

结合广义重心坐标理论,提出了一个新方法,以解决在平面区域上的函数逼近问题。 该方法通过构建基于广义重心坐标的最优分片函数来逼近目标函数。采用Voronoi 图来划分区域, 并提出一个度量逼近误差的能量函数。推导出该函数的导数后,采用一种高效的Voronoi 节点更 新方法来获得区域的最优剖分,并通过最优剖分构建最优分片函数。由于该方法对不连续函数具 有良好地逼近能力,因此将其应用在图像逼近问题中。分别在解析函数和彩色图像上对该方法进 行实验,均获得了很好的逼近效果。     

Subsystem synthesis method with approximate function approach for a real-time multibody vehicle model

This paper presents the subsystem synthesis method with approximate function approach for a real-time multibody vehicle dynamics model. In the subsystem synthesis method, equations of motion for the car body of a vehicle and the equations of motion for suspension subsystems are formed separately for efficient computation. Joint coordinates are used to construct suspension subsystem equations of motion. Since these joint coordinates must satisfy the loop closure constraint equations that represent suspension linkage kinematics, they are not all independent. Using the generalized coordinate partitioning method, suspension subsystem equations of motion can be represented only in terms of independent generalized coordinates. To represent dependent coordinates as a function of independent coordinates in the generalized coordinate partitioning method, expensive numerical approaches, such as the Newton–Raphson method, must be applied. For real-time computation of the multibody vehicle model, an approximate function approach is proposed to express the dependent coordinates as polynomial functions of the independent coordinates within the framework of the subsystem synthesis method. Different orders of candidate polynomial functions are investigated for solution accuracy. Efficiency of the proposed method has been studied theoretically by counting arithmetic operators. By measuring actual CPU times of the simulations with a quarter car and a full car model, efficiency of the proposed method has also been investigated.     

一种适用于无线传感器网络的健壮的有序定位算法

提出了一种分布式无线传感器网络有序定位算法,利用邻居节点间的测量距离和两跳邻居的坐标信息来对网络中的节点进行定位,在测量距离误差较大的情况下仍然能够比较理想地估算出节点的地理位置.先对约束条件比较多的节点进行定位,这样该节点的定位精度就比较高,一个节点得到坐标后又会引入若干约束条件,这些条件又作为定位其他节点的约束,就这样一直定位下去.实验证明此种优化手段可以显著改善定位精度.详细分析了该定位算法中采用的各种技术,并针对邻居数目和测量距离精度做了很多实验来研究其对定位结果的影响.