多智能体沿多条给定路径编队运动的有向协同控制

研究了在有向通信连接下二阶积分器描述的多智能体沿多条给定路径编队运动的控制器设计及其稳定性分析问题. 智能体的动态和指定路径都是在固定直角坐标系下描述的. 通过引入路径函数来设计路径跟踪控制, 根据路径函数与弧长的关系来设计编队控制律, 使得多智能体沿期望路径的位置和速度在规定队形下达到一致. 利用图论证明, 当通信拓扑对应的有向图具有全局可达点时, 设计的编队控制系统是渐近稳定的. 本文设计的有向协同控制律可以应用于区域的信息优化采集.     

跨座式捷运车辆编组分布式固定时间协同巡航控制

为解决跨座式捷运车辆编组协同巡航控制问题,本文提出了基于固定时间理论的跨座式捷运车辆编组分布式协同巡航控制方法.首先,文章建立了跨座式捷运车辆编组动力学模型,明确了编组队列的控制目标,构建了分布式固定时间协同巡航控制架构,提出了跨座式捷运车辆编组分布式固定时间协同巡航控制方法.然后,本文运用代数图论描述编组间的通讯拓扑关系,应用了分布式固定时间终端滑模估计器估计领航编组的位置和速度,设计了分布式固定时间滑模控制器,并基于Lyapunov稳定性理论证明了控制器的稳定性.最后,文章进行了加速–巡航常规工况仿真实验,验证了所提出控制方法的有效性.     

基于伸缩因子的代数曲线曲面变形方法

提出了一种基于伸缩因子的代数曲线曲面变形方法。首先构造了一种用于代数曲线曲面变形的伸缩因子,然后将所构造的伸缩因子分别作用于待变形的代数曲线与曲面,通过改变伸缩因子各参数的取值实现对代数曲线曲面的变形。实例表明,该方法操作方便,易于控制,可获得丰富的变形效果,是一种简单有效的代数曲线曲面变形方法。     

A bottom-up algorithm for finding principal curves with applications to image skeletonization

This paper proposes a new method for finding principal curves from data sets. Motivated by solving the problem of highly curved and self-intersecting curves, we present a bottom-up strategy to construct a graph called a principal graph for representing a principal curve. The method initializes a set of vertices based on principal oriented points introduced by Delicado, and then constructs the principal graph from these vertices through a two-layer iteration process. In inner iteration, the kernel smoother is used to smooth the positions of the vertices. In outer iteration, the principal graph is spanned by minimum spanning tree and is modified by detecting closed regions and intersectional regions, and then, new vertices are inserted into some edges in the principal graph. We tested the algorithm on simulated data sets and applied it to image skeletonization. Experimental results show the effectiveness of the proposed algorithm.     

基于SO(3)的多四旋翼无人机编队协同控制

针对多四旋翼无人机系统的编队飞行问题,提出了基于特殊正交群SO(3)的协同控制设计方法.在给出编队空间队形和通信拓扑描述后,建立了多四旋翼无人机系统SO(3)控制模型.由于SO(3)与传统俯仰/偏航/滚转三通道模型具有不同的结构,文中进一步研究了SO(3)中无人机之间相对误差的表示方法,设计了适用于多飞行器的SO(3)控制器实现对编队和姿态的协同控制.推力控制器用于调节无人机的位置与速度,并在此基础上构造旋转矩阵形式的姿态协同指令.文中相应设计了SO(3)姿态控制器用于实现指令跟踪,最后从理论上对协同稳定性进行了分析.提出的控制方法能够使得多四旋翼无人机形成期望的队形,并且保持姿态一致进行稳定飞行.仿真结果验证了本文方法的有效性.     

Circular Formation Flight Control for Unmanned Aerial Vehicles With Directed Network and External Disturbance

This paper proposes a new distributed formation flight protocol for unmanned aerial vehicles(UAVs)to perform coordinated circular tracking around a set of circles on a target sphere.Different from the previous results limited in bidirectional networks and disturbance-free motions,this paper handles the circular formation flight control problem with both directed network and spatiotemporal disturbance with the knowledge of its upper bound.Distinguishing from the design of a common Lyapunov fiunction for bidirectional cases,we separately design the control for the circular tracking subsystem and the formation keeping subsystem with the circular tracking error as input.Then the whole control system is regarded as a cascade connection of these two subsystems,which is proved to be stable by input-tostate stability(ISS)theory.For the purpose of encountering the external disturbance,the backstepping technology is introduced to design the control inputs of each UAV pointing to North and Down along the special sphere(say,the circular tracking control algorithm)with the help of the switching function.Meanwhile,the distributed linear consensus protocol integrated with anther switching anti-interference item is developed to construct the control input of each UAV pointing to east along the special sphere(say,the formation keeping control law)for formation keeping.The validity of the proposed control law is proved both in the rigorous theory and through numerical simulations.     

Representation of segment Voronoi diagram by Bezier curves

A new method for representing the Voronoi diagram of a set of line segments in a plane in the form of a flat straight-line graph is proposed. The graph is composed of control polygons of linear and quadratic Bezier curves. The radial function of the Voronoi diagram, which defines distance from the Voronoi edges to the generator sites, is described similarly with the help of the Bezier curves. The method allows one to construct an explicit medial representation of polygonal figures for the image shape analysis and transformation.

     

Bézier样条曲线的近似弧长参数化方法

提出了Bézier样条曲线近似弧长参数化的方法及相应的算法。通过求出曲线近似二分之一弧长的点及其相应的参数值,可将曲线分割为两条Bézier样条曲线。这两条曲线的弧长近似相等,因此让它们带有相同的权1。对新生成的Bézier样条曲线不断重复上述工作,最终得到一条由多条Bézier样条曲线所构成的新的曲线。将这多条Bézier样条曲线合并为一条Bézier样条曲线,进而通过节点插入技术将其转化为B样条形式的曲线以便得到全局参数,其中各段Bézier曲线在全局参数域中所占子区间的长度与它们所具有的权成比例,这样便得到一条近似弧长参数化曲线。     

增量极坐标编码的贝赛尔曲线智能优化算法

针对基于统计的隶属度函数确定方法进行了改进,使用贝塞尔曲线作为隶属度函数的上升或下降沿,使隶属度函数可以经过统计结果规定的任意中间点。使用新的增量极坐标编码对贝塞尔曲线控制点进行表达,解决了传统贝塞尔曲线优化中的控制点约束问题。采用差分进化算法对贝塞尔曲线控制点进行优化,可智能拟合经过任意点的最佳贝塞尔曲线。算法可扩展到任意阶贝塞尔曲线,所得隶属度函数较非贝塞尔曲线方法更为合理。     

基于几何约束的三次代数曲线插值

尽管三次参数曲线在曲线曲面造型中扮演着主要角色,但是计算几何专家也一直没有放弃对三次代数曲线的性质及应用进行研究。该文首先综述了近年来有关三次代数曲线研究的最新进展,对各主要方法的优缺点进行了客观的评价。然后提出了一种基于几何约束的三次代数曲线的插值方法,该方法守完全通过几何量如控制顶点、切线和曲率来控制三次代数曲线的形状,使得对三次代数曲线的编辑与对三次B－样条曲线的编辑一样灵活方便。该文提出的代数曲线的结构有两种,一种是插值平面上四点及两端点切线的三次代数曲线;另一种是插值两端点、两切线及两曲率的三次代数曲线。在第二种情况下对曲率的情况进行了详细的分类。并且从理论上对曲线的连续性及保凸性进行了严格的证明。     

Decentralized sliding‐mode control for attitude synchronization in spacecraft formation

This paper addresses attitude synchronization and tracking problems in spacecraft formation in the presence of model uncertainties and external disturbances. A decentralized adaptive sliding mode control law is proposed using undirected interspacecraft communication topology and analyzed based on algebraic graph theory. A multispacecraft sliding manifold is derived, on which each spacecraft approaches desired time‐varying attitude and angular velocity while maintaining attitude synchronization with the other spacecraft in the formation. A control law is then developed to ensure convergence to the sliding manifold. The stability of the resulting closed‐loop system is proved by application of Barbalat's Lemma. Simulation results demonstrate the effectiveness of the proposed attitude synchronization and tracking methodology. Copyright © 2012 John Wiley & Sons, Ltd.     

Global set stabilisation of the spacecraft attitude using finite-time control technique

In this article, we revisit the classical problem of attitude stabilisation for a rigid spacecraft with external disturbances. A global set stabilisation method using finite-time control technique is proposed. In the absence of disturbances, the states of the closed loop system will be stabilised in finite time to a set consisting of two equilibria. In the presence of disturbances, the states will be stabilised to a neighbourhood of this set. By constructing a particular Lyapunov function, it is proved that the closed-loop system satisfies global set stability. The control method in this article is based on set control idea and thus is more natural and energy-efficient. Numerical simulation results show the effectiveness of the method.     

Calculation of dimensions of curves generated by subdivision schemes

Little attention has been paid to estimating dimensions of the curves generated by the subdivision algorithms. A unified method is proposed to estimate the dimension of curves generated by the arbitrary, stationary, linear subdivision schemes with given control points, based on a theorem about the Hausdorff dimension of iterated function systems. Several examples are given to demonstrate the implementation of the method, including the Koch curve, the uniform quadratic B-spline curve and the curves generated by the four-point binary and ternary interpolatory subdivision schemes with a free parameter. Compared with the method of the traditional iterated function system collage theorem, our algorithm overcomes the disadvantage of choosing points and collage, avoiding a large amount of calculation to find the contractive affine transformations and the contraction constants. Furthermore, we can calculate not only the dimension of the special curves with the geometric structure of self-similarity, but also the dimension of the curves generated by more general subdivision algorithms.     

考虑状态约束的航天器编队分布式姿态协同跟踪控制

针对有向通信拓扑结构下的航天器编队姿态协同控制问题,提出一种基于反步法的分布式姿态协同跟踪控制律.在仅有部分跟随航天器可以获取动态领航航天器信息的情况下,利用多层神经网络的逼近特性对系统的非线性不确定性进行估计.同时,考虑到航天器编队的姿态协同跟踪控制性能,构造Barrier Lyapunov函数,使得状态变量保持在预设的约束区间内,进而实现对姿态跟踪误差的约束.根据代数图论和Lyapunov理论,证明跟随航天器的姿态跟踪误差最终有界.仿真分析表明了所提出控制方法的有效性.     

一类三角Bézier曲线的形状特征

在几何造型的许多应用中,良好的曲线形状应该消除不必要的奇点和拐点,因此 往往需要预知与分析参数曲线的各种形状特征,以避免出现奇异形状的设计风险。为了快速确 定参数曲线的形状特征,利用锥面的齐次性简化了参数曲线的形状条件,得出了一类带 2 个形 状参数的二次三角 Bézier 曲线的尖点条件锥和 2 张重结点边界条件锥;3 张特征锥面及其切平 面将特征空间划分为不同的特征区域。曲线的形状特征完全由特征点在特征空间的分布区域决 定。用垂直于坐标轴的平面切割特征空间,可得到基于包络与拓扑映射方法的所有形状条件分 布图。进而讨论了形状参数变化对各特征区域的影响,相关结果可使设计者明确如何配置控制 顶点或者调节形状参数,使得生成曲线为全局凸或局部凸曲线,或具有所需要的奇点与拐点, 或将当前曲线形状调节为另一种所需的形状。     

一种多非完整移动机器人分布式编队控制方法

本文研究了多非完整移动机器人编队控制算法。在该算法中,参考轨迹被视为虚拟领导者,只有部分机器人可以接收到领导者信息,机器人之间只能进行局部信息交互。利用坐标变换将机器人系统的编队问题转化为变换后系统的一致性问题,在持续激励的条件下,设计了一种分布式控制算法,通过图论与Lyapunov 理论证明了该分布式控制算法可以使移动机器人队伍指数收敛于期望队形,并使队形的几何中心指数收敛到参考轨迹。最后,数值仿真验证了该控制算法的有效性。     

基于势函数的多机器人系统的编队控制

提出了一种基于势函数的、能够有效地对多机器人系统的编队队形进行稳定性分析和分布控制的方法．文章通过选择适当的、与目标和结构相关的势函数,利用图论知识和李亚普诺夫稳定理论,设计了一种新颖的能够稳定机器人编队队形并有效跟踪目标的分布控制律,并给出了多机器人系统编队队形稳定及控制问题有解的充分条件．算例仿真说明了这种控制方法的有效性．     

Progressive surface modelling scheme from unorganised curves

This paper presents a novel surface modelling scheme to construct a freeform surface progressively from unorganised curves representing the boundary and interior characteristic curves. The approach can construct a base surface model from four ordinary or composite boundary curves and support incremental surface updating from interior characteristic curves, some of which may not be on the final surface. The base surface is first constructed as a regular Coons surface and upon receiving an interior curve sketch, it is updated. With this progressive modelling scheme, a final surface with multiple sub-surfaces can be obtained from a set of unorganised curves and transferred to commercial surface modelling software for detailed modification. The approach has been tested with examples based on 3D motion sketches; it is capable of dealing with unorganised design curves for surface modelling in conceptual design. Its limitations have been discussed.     

Tool-path generation of planar NURBS curves

It has been widely used in CAD field for many years and gradually applied in CAM area with the prevalence of NURBS interpolator equipped in CNC controllers. But few of them provide the tool radius compensation function. In order to achieve the goal of generating tool-path, an algorithm was presented to offset NURBS curves by an optimum process for CAD/CAM systems in this paper. NURBS format is ideal for HSM applications, but not all NURBS outputs are equal and standard. Basically, there are two different ways to generate NURBS tool-paths; one is to fit a NURBS curve to the conventional tool-path output, the other one is to generate a NURBS tool-path from the start. The main targets for the tool-path of this paper are: (1) To keep a constant distance d between progenitor curve C(t) and offset curve C_d(t) on the normal direction of C(t); (2) to alternate the order k of the basis function in offset curve C_d(t); (3) to oscillate the number of control points of offset curve C_d(t) and compare it with progenitor curve C(t). In order to meet the tolerance requirements as specified by the design, this study offsets the NURBS curves by a pre-described distance d. The principle procedure consists of the following steps: (1) construct an evaluating bound error function; (2) sample offset point-sequenced curves based on first derivatives; (3) give the order of NURBS curve and number of control points to compute all initial conditions and (4) optimize the control points by a path searching algorithm.     

Bézier曲线的同次扩展及其参数选择

目的 本文旨在构造一种含形状参数的Bézier曲线,要求该曲线定义在代数多项式空间上,其基函数的次数与相同数量控制顶点所需Bernstein基函数的次数相同,对基函数以及相应曲线的计算要尽可能简单,并且要给出常见设计要求下曲线中形状参数的选取方案。方法 以三次Bézier曲线为初始研究对象,依据由可调控制顶点定义可调曲线的思想,在两个内控制顶点中引入参数,与Bernstein基函数作线性组合生成形状可调曲线,再将曲线表达式改写成固定控制顶点与含参数的调配函数的线性组合,从而得出三次Bernstein基函数的含参数扩展基,借助递推公式得出更高次的含参数扩展基,然后观察基函数表达式的规律,给出所有含参数扩展基统一的显示表达式,分析了扩展基的性质,并由之定义含参数的曲线,分析了曲线的性质,给出了曲线的几何作图法以及光滑拼接条件,以曲线拉伸能量、弯曲能量、扭曲能量近似最小为目标,推导了曲线中形状参数的计算公式,再通过曲线图和曲率图对比分析了不同能量目标所得曲线的差异。结果 由于所给含参数的扩展基并未提升Bernstein基函数的次数,且具有统一的显示表达式,因此本文方法在赋予Bézier曲线形状调整能力的同时并未增加计算量,由于提供了可以直接使用的形状参数的计算公式,因此在使用该方法时,符合设计要求的形状参数的确定变得简单,数值实例直观显示了所给曲线造型方法以及曲线中形状参数选取方案的正确性与有效性,体现了本文方法较文献中类似方法的优越之处。结论 所给含参数扩展基的构造方法以及形状参数的选取方法具有一般性,该方法可以推广至构造含形状参数的三角域Bézier曲面。