机器人代写|SLAM代写机器人导航代考|FastSLAM with Unknown Data Association

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我们提供的SLAM及其相关学科的代写,服务范围广, 其中包括但不限于:

  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等概率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (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
机器人代写|SLAM代写机器人导航代考|FastSLAM with Unknown Data Association

机器人代写|SLAM代写机器人导航代考|FastSLAM with Unknown Data Association

The biggest limitation of the FastSLAM algorithm described thus far is the assumption that the data associations $n^{t}$ are known. In practice, this is rarely the case. This section extends the FastSLAM algorithm to domains in which the mapping between observations and landmarks is not known [57]. The classical solution to the data association problem in SLAM is to chose $n_{t}$ such that it maximizes the likelihood of the sensor measurement $z_{t}$ given all available data [18].
\hat{n}{t}=\underset{n{t}}{\operatorname{argmax}} p\left(z_{t} \mid n_{t}, \hat{n}^{t-1}, s^{t}, z^{t-1}, u^{t}\right)
The term $p\left(z_{t} \mid n_{t}, \hat{n}^{t-1}, s^{t}, z^{t-1}, u^{t}\right)$ is referred to as a likelihood, and this approach is an example of a maximum likelihood (ML) estimator. ML data association is also called “nearest neighbor” data association, interpreting the negative log likelihood as a distance function. For Gaussians, the negative log likelihood is Mahalanobis distance, and the estimator selects data associations by minimizing this Mahalanobis distance.

In the EKF-based SLAM approaches described in Chapter 2, a single data association is chosen for the entire filter. As a result, these algorithms tend to be brittle to failures in data association. A single data association error can induce significant errors in the map, which in turn cause new data association errors, often with fatal consequences. A better understanding of how uncertainty in the SLAM posterior generates data association ambiguity will demonstrate how simple data association heuristics often fail.

机器人代写|SLAM代写机器人导航代考|Data Association Uncertainty

Two factors contribute to uncertainty in the SLAM posterior: measurement noise and motion noise. As measurement noise increases, the distributions of possible observations of every landmark become more uncertain. If measurement noise is sufficiently high, the distributions of observations from nearby landmarks will begin to overlap substantially. This overlap leads to ambiguity

in the identity of the landmarks. We will refer to data association ambiguity caused by measurement noise as measurement ambiguity. An example of measurement ambiguity is shown in Figure 3.7. The two ellipses depict the range of probable observations from two different landmarks. The observation, shown as an black circle, plausibly could have come from either landmark.
Attributing an observation to the wrong landmark due to measurement ambiguity will increase the error of the map and robot pose, but its impact will be relatively minor. Since the observation could have been generated by either landmark with high probability, the effect of the observation on the landmark positions and the robot pose will be small. The covariance of one landmark will be slightly overestimated, while the covariance of the second will be slightly underestimated. If multiple observations are incorporated per control, a data association mistake due to measurement ambiguity of one observation will have relatively little impact on the data association decisions for the other observations.

Ambiguity in data association caused by motion noise can have much more severe consequences on estimation accuracy. Higher motion noise will lead to higher pose uncertainty after incorporating a control. If this pose uncertainty is high enough, assuming different robot poses in this distribution will imply drastically different ML data association hypotheses for the subsequent observations. This motion ambiguity, shown in Figure $3.8$, is easily induced if there is significant rotational error in the robot’s motion. Moreover, if multiple observations are incorporated per control, the pose of the robot will correlate the data association decisions of all of the observations. If the SLAM algorithm chooses the wrong data association for a single observation due to motion ambiguity, the rest of the data associations also will be wrong with high probability.

机器人代写|SLAM代写机器人导航代考|Per-Particle Data Association

Unlike most EKF-based SLAM algorithms, FastSLAM takes a multi-hypothesis approach to the data association problem. Each particle represents a different hypothesized path of the robot, so data association decisions can be made on a per-particle basis. Particles that pick the correct data association will receive high weights because they explain the observations well. Particles that pick wrong associations will receive low weights and be removed in a future resampling step.

Per-particle data association has several important advantages over standard ML data association. First, it factors robot pose uncertainty out of the data association problem. Since motion ambiguity is the more severe form of data association ambiguity, conditioning the data association decisions on hypothesized robot paths seems like a logical choice. Given the scenario in Figure 3.8, some of the particles would draw new robot poses consistent with data association hypothesis on the left, while others would draw poses consistent with the data association hypothesis on the right.

Doing data association on a per-particle basis also makes the data association problem easier. In the EKF, the uncertainty of a landmark position is due to both uncertainty in the pose of the robot and measurement error. In FastSLAM, uncertainty of the robot pose is represented by the entire particle set. The landmark filters in a single particle are not affected by motion noise because they are conditioned on a specific robot path. This is especially useful if the robot has noisy motion and an accurate sensor.

Another consequence of per-particle data association is implicit, delayeddecision making. At any given time, some fraction of the particles will receive plausible, yet wrong, data associations. In the future, the robot may receive a new observation that clearly refutes these previous assignments. At this point, the particles with wrong data associations will receive low weight and likely be removed from the filter. As a result of this process, the effect of a wrong data association decision made in the past can be removed from the filter. Moreover, no heuristics are needed in order to remove incorrect old associations from the filter. This is done in a statistically valid manner, simply as a consequence of the resampling step.

机器人代写|SLAM代写机器人导航代考|FastSLAM with Unknown Data Association


机器人代写|SLAM代写机器人导航代考|FastSLAM with Unknown Data Association

迄今为止描述的 FastSLAM 算法的最大限制是假设数据关联n吨是已知的。在实践中,这种情况很少见。本节将 FastSLAM 算法扩展到观察值和地标之间的映射未知的领域 [57]。SLAM中数据关联问题的经典解决方案是选择n吨使其最大化传感器测量的可能性和吨给定所有可用数据[18]。
术语p(和吨∣n吨,n^吨−1,s吨,和吨−1,在吨)被称为似然性,这种方法是最大似然(ML)估计器的一个例子。ML 数据关联也称为“最近邻”数据关联,将负对数似然解释为距离函数。对于高斯,负对数似然是马氏距离,估计器通过最小化这个马氏距离来选择数据关联。

在第 2 章描述的基于 EKF 的 SLAM 方法中,为整个过滤器选择单个数据关联。因此,这些算法往往会因数据关联失败而变得脆弱。单个数据关联错误可能会在地图中引发重大错误,进而导致新的数据关联错误,通常会带来致命的后果。更好地理解 SLAM 后验中的不确定性如何产生数据关联模糊性将证明简单的数据关联启发式方法经常失败。

机器人代写|SLAM代写机器人导航代考|Data Association Uncertainty

有两个因素会导致 SLAM 后验的不确定性:测量噪声和运动噪声。随着测量噪声的增加,每个地标的可能观测值的分布变得更加不确定。如果测量噪声足够高,来自附近地标的观测分布将开始大量重叠。这种重叠导致歧义

在地标的身份中。我们将由测量噪声引起的数据关联模糊度称为测量模糊度。图 3.7 显示了测量模糊度的一个示例。这两个椭圆描绘了来自两个不同地标的可能观测值的范围。显示为黑色圆圈的观察结果很可能来自任一地标。

由运动噪声引起的数据关联模糊会对估计精度产生更严重的影响。结合控制后,更高的运动噪声将导致更高的姿势不确定性。如果此姿势不确定性足够高,则假设此分布中的不同机器人姿势将意味着后续观察的 ML 数据关联假设大不相同。这种运动模糊,如图3.8, 如果机器人运动中存在明显的旋转误差,则很容易引起。此外,如果每个控件包含多个观测值,机器人的姿势将关联所有观测值的数据关联决策。如果 SLAM 算法由于运动模糊而为单个观察选择了错误的数据关联,那么其余数据关联也很有可能是错误的。

机器人代写|SLAM代写机器人导航代考|Per-Particle Data Association

与大多数基于 EKF 的 SLAM 算法不同,FastSLAM 对数据关联问题采用多假设方法。每个粒子代表机器人的不同假设路径,因此可以在每个粒子的基础上做出数据关联决策。选择正确数据关联的粒子将获得高权重,因为它们很好地解释了观察结果。选择错误关联的粒子将获得较低的权重,并在未来的重采样步骤中被移除。

与标准 ML 数据关联相比,每粒子数据关联具有几个重要优势。首先,它将机器人姿态不确定性排除在数据关联问题之外。由于运动模糊是数据关联模糊的更严重形式,因此根据假设的机器人路径调整数据关联决策似乎是一个合乎逻辑的选择。给定图 3.8 中的场景,一些粒子将绘制与左侧数据关联假设一致的新机器人姿态,而其他粒子将绘制与右侧数据关联假设一致的姿态。

在每个粒子的基础上进行数据关联也使数据关联问题更容易。在 EKF 中,地标位置的不确定性是由于机器人位姿的不确定性和测量误差造成的。在 FastSLAM 中,机器人姿态的不确定性由整个粒子集表示。单个粒子中的界标滤波器不受运动噪声的影响,因为它们以特定的机器人路径为条件。如果机器人有嘈杂的运动和准确的传感器,这将特别有用。


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