### robotics代写|寻路算法代写Path Planning Algorithms|Optical Imaging of Global Air Circulation

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## robotics代写|寻路算法代写Path Planning Algorithms|Optical Imaging of Global Air Circulation

Although complex mathematical/computational models for the global air circulation in the Earth’s atmosphere have been developed for weather prediction, the input data for these models are often derived from real-time optical imaging of the Earth’s atmosphere exhibited by cloud formation patterns. This task can be accomplished by implementing an observer system composed of cameras attached to a set of geosynchronous and low-orbit satellites. Since the cameras have finite viewing apertures, a basic problem is to determine the minimum number of cameras and their attitudes for complete coverage of Earth’s atmosphere. The satellites should be capable of communicating with each other to form a real-time global-circulation monitoring network.

An asteroid is usually a small irregularly-shaped solid body with nearly uniform mass density. When such an asteroid enters the spatial region where the Earth’s gravitational force becomes significant, it is of interest to predict its motion or path in the world or observation space, and to determine its surface and material properties. The second task can be accomplished by using one or more spacecraft equipped with cameras, radars and sensors moving in the vicinity of the asteroid. An important problem is to select the spacecraft motion so that the asteroid’s surface can be mapped out completely. In the case where the observation time duration is specified, the main task is to map out the asteroid’s surface as much as possible within the given observation time duration. For a single spacecraft, it is required to select a path/motion satisfying certain constraints such that maximum or complete visual coverage of the asteroid surface is attained (see Fig. 1.1). Here, the object under observation is a moving solid body in a three-dimensional world space. In this problem, a basic difficulty is that complete information about the asteroid surface is usually unavailable before launching of the spacecraft. Thus, one cannot preplan its observation path. The asteroid surface information must be acquired progressively as the spacecraft moves in the vicinity of the asteroid. We shall discuss practical methods for overcoming this difficulty later.

## robotics代写|寻路算法代写Path Planning Algorithms|Path Planning on Structured Network

By a structured network defined on a given terrain, we mean a set of specified fixed nodes interconnected by a set of well-defined bidirectional or unidirectional paths on the terrain. Given a pair of starting and terminal nodes, it is required to find a path connecting these nodes such that an observer (e.g. a mobile robot or rover equipped with camera) attains maximum visual coverage of the terrain. This is an optimal path planning problem. For example, a tourist bus guide wishes to find the shortest sightseeing route in a city such that maximum visual coverage of the attractions can be attained. When the observation time interval is specified, the tourist bus guide may wish to plan the bus motion such that similar objective is achieved over the given time interval. This is a visibility-based optimal motion planning problem.

## robotics代写|寻路算法代写Path Planning Algorithms|Objects Under Observation

Let the world space $\mathcal{W}$ be a specified subset of the $n$-dimensional Euclidean space $\mathbb{R}^{n}, n \in{2,3}$ in which a vector $x$ is an ordered n-tuple $\left(x_{1}, \ldots, x_{n}\right)$ of real numbers $x_{i}, i=1, \ldots, n$. The scaler product between two vectors $x$ and $x^{\prime}$ in $\mathbb{R}^{n}$ is denoted by $\left(x, x^{\prime}\right)$. The representation of a vector $x$ with respect to a given bases $B=\left{e_{1}, \ldots, e_{n}\right}$ for $\mathbb{R}^{n}$ is denoted by the column vector $[x]$. When ambiguity does not occur, the bracket notation [ -] is dropped for brevity. We assume that an object under observation $\mathcal{O}$ is a compact (closed and bounded) connected subset of $\mathcal{W}$ with boundary $\partial \mathcal{O}$. The observation of the object $\mathcal{O}$ is made from point-observers or observation points on an observation platform $\mathcal{P}$ corresponding to a given subset of $\mathcal{W}$. In what follows, we shall focus our attention mainly on the practically important case where $\mathcal{P} \subset \overline{\mathcal{O}^{c}}$ (the closure of the complement of $\mathcal{O}$ relative to $\mathcal{W}$ ). We assume that $\mathcal{P}$ is transparent in the sense that it can be penetrated by the line segment or an arc connecting an observation point in $\mathcal{P}$ and an observed point in $\mathcal{O}$. For opaque or non-transparent objects, only the boundary $\partial \mathcal{O}$ can be observed by point-observers in $\mathcal{P}$. The difficulty associated with the visibility problems to be considered generally depends on the dimensions and geometric properties of $\mathcal{O}$ and $\mathcal{P}$. A few cases of special interest are given in the sequel.
Case (i) $\mathcal{W}=\mathbb{R}^{2}$
(a) $\mathcal{O}$ is a plane curve which can be represented by $G_{f}=\left{(x, f(x)) \in \mathbb{R}^{2}: x \in \Omega\right}$, the graph of a real-valued $C_{m}$-function $f=f(x)$ defined on a compact interval $\Omega \subset \mathbb{R}$ (i.e. $f(\cdot) \in C_{m}(\mathbb{R} ; \Omega), m \geq 1$, the space of all real-valued functions having continuous derivatives on $\Omega$ up to the $m$ th order). The observations of the

curve are made from points $z=(x, w) \in \mathcal{P} \subset$ Epi $_{f}{ }{\text {def }}^{=}\left{\left(x^{\prime}, w^{\prime}\right) \in \Omega \times \mathbb{R}: w^{\prime} \geq\right.$ $\left.f\left(x^{r}\right)\right}$, the epigraph of $f$ (See Fig. 2.1a). We may also consider observations from points below the curve $G{f}$, i.e. $z \in\left{\left(x^{\prime}, w^{\prime}\right) \in \Omega \times \mathbb{R}: w^{\prime}<f\left(x^{\prime}\right)\right}$.
(b) $\mathcal{O}$ is an opaque object represented by a compact connected subset of $\mathcal{W}$. It can be described by $\bigcap_{k \in{1, \ldots, K}}\left{x \in \mathcal{W}: g_{k}(x) \leq 0\right}$, and has interior points and a piecewise smooth boundary $\partial \mathcal{O}$, where the $g_{k}$ ‘s are specified functions in $C_{m}(\mathbb{R} ; \mathcal{W}), m \geq 1$. The point-observers or observation points lie in $\mathcal{O}^{c}$ (See Fig. 2.1b).
Case (ii) $\mathcal{W}=\mathbb{R}^{3}$
(a) $\mathcal{O}$ is an opaque smooth surface described by $G_{f}$, the graph of a real-valued $C_{m}{ }^{-}$ function $(m \geq 1) f=f(x), x=\left(x_{1}, x_{2}\right) \in \Omega$, a compact connected subset of $\mathbb{R}^{2}$ (See Fig. 2.2). The observation points $z=(x, w)$ are located in Epi $\mathrm{i}{f} \subset \mathbb{R}^{3}$. (b) $\mathcal{O}$ is an opaque solid body represented by a nonempty compact connected subset of $\mathbb{R}^{3}$ with interior points and a piecewise smooth boundary $\partial \mathcal{O}$ which may be expressed as a level set of a real-valued continuous function $g=g(x)$ defined on $\mathbb{R}^{3}$, i.e. $\mathcal{O}=\left{x \in \mathbb{R}^{3}: g(x)=\alpha\right}$ or $g^{-1}(\alpha)$, where $\alpha \in \mathbb{R}$. As in Case (i)(b), the object $\mathcal{O}$ may also be described by $\bigcap{k \in{1, \ldots . K}}\left{x \in \mathcal{W}: g_{k}(x) \leq 0\right}$, where the $g_{k}$ ‘s are specified functions in $C_{m}(\mathbb{R} ; \mathcal{W})$. The observation points lie in $\mathcal{O}^{\text {}}$.

## robotics代写|寻路算法代写Path Planning Algorithms|Objects Under Observation

（一种）这是一条平面曲线，可以表示为G_{f}=\left{(x, f(x)) \in \mathbb{R}^{2}: x \in \Omega\right}G_{f}=\left{(x, f(x)) \in \mathbb{R}^{2}: x \in \Omega\right}, 实值图C米-功能F=F(X)在紧区间上定义Ω⊂R（IEF(⋅)∈C米(R;Ω),米≥1, 所有具有连续导数的实值函数的空间Ω至米次订单）。的观察

(二)这是一个不透明的对象，由 的紧凑连接子集表示在. 可以描述为\bigcap_{k \in{1, \ldots, K}}\left{x \in \mathcal{W}: g_{k}(x) \leq 0\right}\bigcap_{k \in{1, \ldots, K}}\left{x \in \mathcal{W}: g_{k}(x) \leq 0\right}，并且具有内部点和分段平滑边界∂这, 其中Gķ是指定的函数C米(R;在),米≥1. 点观察者或观察点位于这C（见图 2.1b）。

（一种）这是一个不透明的光滑表面，由GF, 实值图C米−功能(米≥1)F=F(X),X=(X1,X2)∈Ω, 的紧连通子集R2（见图 2.2）。观察点和=(X,在)位于 Epi一世F⊂R3. (二)这是一个不透明的实体，由 的非空紧连接子集表示R3具有内部点和分段平滑边界∂这可以表示为实值连续函数的水平集G=G(X)定义于R3， IE\mathcal{O}=\left{x \in \mathbb{R}^{3}: g(x)=\alpha\right}\mathcal{O}=\left{x \in \mathbb{R}^{3}: g(x)=\alpha\right}或者G−1(一种)， 在哪里一种∈R. 与情况 (i)(b) 一样，对象这也可以描述为\bigcap{k \in{1, \ldots 。K}}\left{x \in \mathcal{W}: g_{k}(x) \leq 0\right}\bigcap{k \in{1, \ldots 。K}}\left{x \in \mathcal{W}: g_{k}(x) \leq 0\right}, 其中Gķ是指定的函数C米(R;在). 观测点位于这.

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。