### robotics代写|SLAM定位算法代写Simultaneous Localization and Mapping|Applications of SLAM

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## robotics代写|SLAM定位算法代写Simultaneous Localization and Mapping|Applications of SLAM

The problem of Simultaneous Localization and Mapping, or SLAM, has attracted immense attention in the robotics literature. SLAM addresses the problem of a mobile robot moving through an environment of which no map is available a priori. The robot makes relative observations of its ego-motion and of features in its environment, both corrupted by noise. The goal of SLAM is to reconstruct a map of the world and the path taken by the robot. SLAM is considered by many to be a key prerequisite to truly autonomous robots [85].
If the true map of the environment were available, estimating the path of the robot would be a straightforward localization problem [16]. Similarly, if the true path of the robot were known, building a map would be a relatively simple task $[63,86]$. However, when both the path of the robot and the map are unknown, localization and mapping must be considered concurrently-hence the name Simultaneous Localization and Mapping.

SLAM is an essential capability for mobile robots traveling in unknown environments where globally accurate position data (e.g. GPS) is not available. In particular, mobile robots have shown significant promise for remote exploration, going places that are too distant [34], too dangerous [88], or simply too costly to allow human access. If robots are to operate autonomously in extreme environments undersea, underground, and on the surfaces of other planets, they must be capable of building maps and navigating reliably according to these maps. Even in benign environments, such as the interiors of buildings, accurate, prior maps are often difficult to acquire. The capability to map an unknown environment allows a robot to be deployed with minimal infrastructure. This is especially important if the environment changes over time.

The maps produced by SLAM algorithms typically serve as the basis for motion planning and exploration. However, the maps often have value in their own right. In July of 2002 , nine miners in the Quecreek Mine in Sommerset, Pennsylvania were trapped underground for three and a half days after accidentally drilling into a nearby abandoned mine. A subsequent investigation attributed the cause of the accident to inaccurate maps [32]. Since the accident, mobile robots and SLAM have been investigated as possible technologies for acquiring accurate maps of abandoned mines. One such robot, shown in Figure $1.1(\mathrm{~b})$, is capable of building $3 \mathrm{D}$ reconstructions of the interior of abandoned mines using SLAM technology [88].

## robotics代写|SLAM定位算法代写Simultaneous Localization and Mapping|Joint Estimation

The chicken-or-egg relationship between localization and mapping is a consequence of how errors in the robot’s sensor readings are corrupted by error in the robot’s motion. As the robot moves, its pose estimate is corrupted by motion noise. The perceived locations of objects in the world are, in turn, corrupted by both measurement noise and the error in the estimated pose of the robot. Unlike measurement noise, however, error in the robot’s pose will have a systematic effect on the error in the map. In general, this effect can be stated more plainly; error in the robot’s path correlates errors in the map. As a result, the true map cannot be estimated without also estimating the true path of the robot. The relationship between localization and mapping was first identified by Smith and Cheeseman $[82]$ in their seminal paper on SLAM in $1986 .$

Figure $1.2$ shows a set of laser range scans collected by a mobile robot moving through a typical indoor environment. The robot generates estimates of its position using odometers attached to each of its wheels. In Figure 1.2(a), the laser scans are plotted with respect to the estimated position of the robot. Clearly, as error accumulates in the robot’s odometry, the map becomes increasingly inaccurate. Figure $1.2(\mathrm{~b})$ shows the laser readings plotted according to the path of the robot reconstructed by a SLAM algorithm.

Although the relationship between robot path error and map error does make the SLAM problem harder to solve in principle, one can exploit this relationship to factor the SLAM problem into a set of much smaller problems. Each of these smaller problems can be solved efficiently.

## robotics代写|SLAM定位算法代写Simultaneous Localization and Mapping|Posterior Estimation

Two types of information are available to the robot over time: controls and observations. Controls are noisy predictions of the robot’s motion, while observations are noisy measurements of features in the robot’s environment. Each control or observation, coupled with an appropriate noise model, can be thought of as a probabilistic constraint. Each control probabilistically constrains two successive poses of the robot. Observations, on the other hand, constrain the relative positions of the robot and objects in the map. When previously observed map features are revisited, the resulting constraints can be used to update not only the current map feature and robot pose, but also correct map features that were observed in the past. An example of a network of constraints imposed by controls and observations is shown in Figure 1.3.
Initially, the constraints imposed by controls and observations may be relatively weak. However, as map features are repeatedly observed, the constraints will become increasingly rigid. In the limit of an infinite number of observations and controls, the positions of all map features will become fully correlated [19]. The primary goal of SLAM is to estimate this true map and the true pose of the robot, given the currently available set of observations and controls.

One approach to the SLAM problem would be to estimate the most likely robot pose and map using a batch estimation algorithm similar to those used in the Structure From Motion literature $[43,91]$. While extremely powerful, these techniques operate on the complete set of observations and controls, which grows without bound over time. As a consequence, these algorithms are not appropriate for online operation. Furthermore, these algorithms generally do not estimate the certainty with which different sections of the map are known, an important consideration for a robot exploring an unknown environment.

The most popular online solutions to the SLAM problem attempt to estimate the posterior probability distribution over all possible maps $\Theta$ and robot poses $s_{t}$ conditioned on the full set of controls $u^{t}$ and observations $z^{t}$ at time $t$. The observation at time $t$ will be written as $z_{t}$, while the set of all observations up to time $t$ will be written $z^{t}$. Similarly, the control at time $t$ will be written $u_{t}$, and the set of all controls up to time $t$ will be written $u^{t}$.
Using this notation, the joint posterior distribution over maps and robot poses can be written as:
$$p\left(s_{t}, \Theta \mid z^{t}, u^{t}\right)$$
This distribution is referred to as the SLAM posterior. At first glace, posterior estimation may seem even less feasible than the batch estimation approach. However, by making judicious assumptions about how the state of the world evolves, the SLAM posterior can be computed efficiently. Posterior estimation has several advantages over solutions that consider only the most likely state of the world. First, considering a distribution of possible solutions leads to more robust algorithms in noisy environments. Second, uncertainty can be used to compare the information conveyed by different components of the solution. One section of the map may be very uncertain, while other parts of the map are well known.

Any parameterized model can be chosen for the map $\Theta$, however it is typically represented as a set of point features, or “landmarks” [19]. In a real implementation, landmarks may correspond to the locations of features extracted from sensors, such as cameras, sonars, or laser range-finder s. Throughout most of this book we assume the point landmark model, though other representations can be used. Higher order geometric features, such as line segments [70], have also been used to represent maps in SLAM.

## robotics代写|SLAM定位算法代写Simultaneous Localization and Mapping|Applications of SLAM

SLAM 是移动机器人在无法获得全球准确位置数据（例如 GPS）的未知环境中行驶的基本能力。特别是，移动机器人在远程探索、去太远的地方 [34]、太危险的地方 [88] 或太昂贵而无法让人类进入的地方已经显示出巨大的希望。如果机器人要在海底、地下和其他行星表面的极端环境中自主运行，它们必须能够构建地图并根据这些地图可靠地导航。即使在良性环境中，例如建筑物内部，通常也很难获得准确的先验地图。映射未知环境的能力允许以最少的基础设施部署机器人。如果环境随时间发生变化，这一点尤其重要。

SLAM 算法生成的地图通常用作运动规划和探索的基础。然而，这些地图往往本身就具有价值。2002 年 7 月，宾夕法尼亚州萨默塞特的 Quecreek 矿区的 9 名矿工在意外钻入附近废弃矿井后被困在地下三天半。随后的调查将事故原因归咎于地图不准确[32]。自事故发生以来，移动机器人和 SLAM 已被研究作为获取废弃矿山准确地图的可能技术。一种这样的机器人，如图所示1.1( b), 能够建造3D使用 SLAM 技术重建废弃矿井内部 [88]。

## robotics代写|SLAM定位算法代写Simultaneous Localization and Mapping|Posterior Estimation

SLAM 问题最流行的在线解决方案试图估计所有可能地图的后验概率分布θ和机器人姿势s吨以全套控制为条件在吨和观察和吨有时吨. 当时的观察吨将被写为和吨, 而到时间的所有观测值的集合吨会写和吨. 同样，控制时间吨会写在吨, 以及截至时间的所有控件的集合吨会写在吨.

p(s吨,θ∣和吨,在吨)

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