Geometric problem solving with strings and pins

Humans solve spatial and abstract problems more easily if these can be visualized and/or physically manipulated. We analyze the domain of geometric problem solving from a cognitive perspective and identify several levels of domain abstraction that interact in the problem solving process. We discuss the roles of physical manifestations of spatial configurations, their manipulation, and their perception for understanding problem solving processes. We propose an extension of the classical problem solving repertoire of constructive geometry to approach certain problems more directly than under the compass-and-straightedge paradigm. Specifically, we introduce strings and pins as helpful metaphors for a generalization of the constructive geometry approach. We present classical problems from spatial problem solving to illustrate the ‘strings and pins’ paradigm. Three case studies are discussed: strings-and-pins solutions to (i) the ellipse construction problem; (ii) the shortest path problem; and (iii) the angle trisection problem. Comparisons to formal solutions are drawn. Differences and similarities between the compass-and-straightedge paradigm and the strings-and-pins paradigm are analyzed. Features and limitations of constructive and depictive geometry as well as implications for computational approaches are discussed. The strings-and-pins domain is shown to be more general and less restrictive than the compass-and-straightedge domain.     

目标跟踪多智能体一致控制

研究了二阶多智能体系统跟踪一致问题。针对相对速度信息未知的网络,分析了有时滞和无时滞情况下网络的稳定性,给出了系统能够实现跟踪一致的条件。最后,通过仿真表明所提协议比现有协议性能更好。     

大型伞绳帆和抽打现象连续模型及验证

文章主要推导了可用于描述大型降落伞绳帆和抽打现象的一般绳索三维动力学连续模型,及弦坐标系下可用于求解绳帆现象的两点边值问题(BVP)模型,并采用某型号大型降落伞的空投录像和杆件算例对模型进行验证对比,说明了模型的正确性,采用这一连续模型能够更直观地对大型伞的绳帆和抽打现象进行定性和定量分析。     

基于可满足性问题求解器的星上FPGA永久损伤容错技术研究

现代卫星广泛使用的FPGA在空间高能粒子的影响下,会产生门电路的永久性损伤。而传统的三模冗余等容错方法不但成倍增加了系统硬件开销,还存在因冗余器件耗尽而失效的风险。因此,提出一种利用FPGA自身冗余资源,修复永久性损伤的容错方案。该方案通过建立FPGA内部资源的功能模型,将容错问题转化为数学上的可满足性问题。并且利用经过改进的GSAT算法对该问题求解,可以获得在功能上与损伤前完全相同的电路结构,及其所对应的FPGA配置文件。将该文件重新下载到FPGA中,可以屏蔽损伤带来的影响,从而达到利用FPGA自身冗余资源容错的目的。通过实验和分析可以看出,本文方案具有对损伤修复成功率高、计算量小和需要内存空间少的特点,因此符合星上计算能力和硬件资源十分有限的实际情况。     

The feasibility of using an L1 positioned dust cloud as a method of space-based geoengineering

In this paper a method of geoengineering is proposed involving clouds of dust placed in the vicinity of the L₁ point as an alternative to the use of thin film reflectors. The aim of this scheme is to reduce the manufacturing requirement for space-based geoengineering. It has been concluded that the mass requirement for a cloud placed at the classical L₁ point, to create an average solar insolation reduction of 1.7%, is 7.60 × 10¹⁰ kg yr⁻¹ whilst a cloud placed at a displaced equilibrium point created by the inclusion of the effect of solar radiation pressure is 1.87 × 10¹⁰ kg yr⁻¹. These mass ejection rates are considerably less than the mass required in other unprocessed dust cloud methods proposed and are comparable to thin film reflector geoengineering requirements. Importantly, unprocessed dust sourced in-situ is seen as an attractive scheme compared to highly engineered thin film reflectors. It is envisaged that the required mass of dust can be extracted from captured near Earth asteroids, whilst stabilised in the required position using the impulse provided by solar collectors or mass drivers used to eject material from the asteroid surface.     

含滚阻摩擦平面多体系统的建模和数值方法

针对含滚阻和摩擦的平面多体系统,给出了通用的力学模型,利用第一类Lagrange方程建立了系统的动力学方程,为便于约束力的计算,利用局部方法列写约束方程,并以矩阵形式给出了该系统滚阻力偶和摩擦力的广义力.该系统动力学方程是非光滑的,通过建立滚阻定律的互补条件以及光滑铰链约束力的互补条件,给出了具有约束稳定化的基于事件驱动法的数值算法,将非光滑约束力、铰链约束力的求解以及滚轮滑动与粘滞的判断问题统一转化为一个线性互补问题进行求解.对两个算例进行了数值仿真,算例数值结果表明了该方法的可行性和有效性.     

三体问题地面实验的相似性分析

研究了三体问题相似性的分析流程,给出了三体问题实验近似相似性程度的公式化度量方法。首先,明确了三体问题地面实验的构建原理与方法;其次,建立圆形限制性三体问题的动力学模型,并利用相似性分析方法建立三体问题的相似性度量函数;再次,建立存在各种干扰因素情况下实验系统动力学模型,并利用相似性度量函数衡量在干扰因素作用下实验满足相似性的程度;最后,利用数值仿真法进行仿真分析从统计的角度得出各种干扰对于三体问题实验相似性的影响大小,并给出各种干扰因素对于三体问题相似性的影响排序。仿真表明这种分析方法对于实验系统的提高与实验方案的选择具有指导意义。     

登月舱上升段最优轨迹设计

为了实现登月舱上升段轨迹的优化,建立了上升段登月舱动力学模型,用单位归一化技术建立了最优控制模型,并以燃料消耗为最优指标,利用Pontryagin极小值原理,将问题转化为时间自由的两点边值问题 TPBVP 。采用了一种基于初值预估方法和向前扫描法求解TPBVP,从而设计出登月舱上升段最优轨迹,并进行了数值仿真。仿真结果表明所设计的算法收敛速度快、可靠性高。     

基于布谷鸟搜索算法的一类变体飞行器容错控制

针对一类存在执行机构故障的分布式结构变体飞行器的控制分配问题,结合整数规划理论,提出一种基于布谷鸟搜索算法的容错控制方法。首先,设计虚拟控制指令,使得系统状态能够很好地跟踪参考模型;然后,将执行器概率性故障与饱和约束转换为整数规划问题中决策变量的约束,从而将执行器控制分配问题转化为一类整数规划问题;最后,采用改进的布谷鸟搜索算法进行求解,得到实际的执行器控制分配指令。仿真结果表明,在执行器存在概率性故障的情况下,该容错控制方法较无容错策略的情况能够有效提升系统的跟踪性能;与遗传算法相比,该算法得到的执行器控制分配结果更加精确。     

On tethered sample and mooring systems near irregular asteroids

A tethered asteroid sample and mooring system is investigated in this paper. In this system the spacecraft is moored to the surface of an irregular asteroid such as 216 Kleopatra by using a rocket-propelled anchor with a cable. The rocket-propelled anchor is a kind of space penetrator, which can inject into asteroids at high speeds generated by its own rocket engine. It can be used to explore the interior structure of asteroids, and it can also be used as a sample collector. When the sampling mission is done, the sample can be pulled back to the spacecraft with the anchor. Using this method, the spacecraft can be kept in a safe region in which it cannot be trapped by the gravitational field of the asteroid. This work is concerned with the dynamics of the tethered system near irregular asteroids. First, a shape model and gravitational field model of irregular asteroids are built. Then, the configuration and the stability of the tethered system are investigated, and the quasi-periodic motion near the equilibrium point of the tethered system is analyzed. Finally, the non-uniform density distribution of the asteroids is considered. The deployment process and the oscillation of the tethered system in the uncertain asteroid gravity field are simulated using the Monte Carlo method. The feasibility of the tethered asteroid sample and mooring system is proved.