Improved Techniques for Grid Mapping With Rao-Blackwellized Particle Filters全文翻译Gmapping

Improved Techniques for Grid Mapping With Rao-Blackwellized Particle Filters全文翻译Gmapping

Improved Techniques for Grid Mapping With Rao-Blackwellized Particle Filters

Abstract—Recently, Rao-Blackwellized particle filters (RBPF)have been introduced as an effective means to solve the simultaneous localization and mapping problem. This approach uses a particle filter in which each particle carries an individual map of the environment. Accordingly, a key question is how to reduce the number of particles. In this paper, we present adaptive techniques for reducing this number in a RBPF for learning grid maps. We propose an approach to compute an accurate proposal distribution, taking into account not only the movement of the robot, but also the most recent observation. This drastically decreases the uncertainty about the robot’s pose in the prediction step of the filter. Furthermore, we present an approach to selectively carry out resampling operations, which seriously reduces the problem of particle depletion. Experimental results carried out with real mobile robots in large-scale indoor, as well as outdoor, environments illustrate the advantages of our methods over previous approaches.
近年来，Rao-Blackwellized粒子滤波器（RBPF）被引入到解决同时定位和建图问题中。此方法使用粒子过滤器，其中每个粒子都携带环境的单个地图。因此，一个关键问题是如何减少粒子的数量。在这篇文章中，我们提出了在学习网格地图的RBPF中减少粒子数量的自适应技术。我们提出了一种计算精确建议分布的方法，不仅考虑了机器人的运动，而且还考虑了最近的观察。这大大降低了滤波器建议步骤中机器人姿态的不确定性。此外，我们还提出了一种选择性地执行重采样操作的方法，这大大减少了粒子耗尽的问题。在大型室内和室外环境中，用真实的移动机器人进行的实验结果说明了我们的方法比以前的方法的优势。
Index Terms—Adaptive resampling, improved proposal, motion model, Rao-Blackwellized particle filter (RBPF), simultaneous localization and mapping (SLAM).
索引项-自适应重采样、改进方案、运动模型、Rao-Blackwellized粒子滤波器（RBPF）、同步定位与建图（SLAM）。
I. INTRODUCTION
Building maps is one of the fundamental tasks of mobile robots. In the literature, the mobile-robot mapping problem is often referred to as the simultaneous localization and mapping (SLAM) problem [1]–[9]. It is considered to be a complex problem, because for localization, a robot needs a consistent map, and for acquiring a map, a robot requires a good estimate of its location. This mutual dependency between the pose and the map estimates makes the SLAM problem hard, and requires searching for a solution in a high-dimensional space.
地图绘制是移动机器人的基本任务之一。在文献中，移动机器人的建图问题通常被称为同时定位和映射（SLAM）问题[1]-[9]。这被认为是一个复杂的问题，因为对于定位，机器人需要一个一致的地图，而对于获取地图，机器人需要对其位置进行良好的估计。姿态估计和地图估计之间的这种相互依赖使得SLAM问题变得困难，需要在高维空间中寻找解决方案。
Murphy, Doucet, and colleagues [2], [8] introduced Rao-Blackwellized particle filters (RBPF) as an effective means to solve the SLAM problem. The main problem of the Rao-Blackwellized approaches is their complexity, measured in terms of the number of particles required to build an accurate map. Therefore, reducing this quantity is one of the major challenges for this family of algorithms. Additionally, the resampling step can potentially eliminate the correct particle.This effect is also known as the particle-depletion problem, or particle impoverishment [10].
Murphy，Doucet及其同事[2]，[8]介绍了Rao-Blackwellized粒子滤波器（RBPF）作为解决SLAM问题的有效方法。Rao-Blackwellized方法的主要问题是它们的复杂性，用建立精确地图所需的粒子数来衡量。因此，减少粒子数量是这类算法面临的主要挑战之一。此外，重采样步骤可以潜在地消除正确的粒子。这种效果也称为粒子耗尽问题，或粒子贫化[10]。
In this paper, we present two approaches to substantially increase the performance of RBPFs applied to solve the SLAM problem with grid maps:
•a proposal distribution that considers the accuracy of the robot’s sensors and allows us to draw particles in a highly accurate manner;
• an adaptive resampling technique which maintains a reasonable variety of particles, and in this way, enables the algorithm to learn an accurate map while reducing the risk of particle depletion.
在本文中，我们提出了两种方法来显著提高RBPFs的性能，并将其应用于解决栅格地图的SLAM问题：
•一种建议分布，不仅考虑到机器人传感器精度并允许我们以高精度方式绘制粒子；
•一种自适应重采样技术，它保持了粒子的合理多样性，并以这种方式使算法能够学习精确的映射，同时降低粒子耗尽的风险。
The proposal distribution is computed by evaluating the likelihood around a particle-dependent most-likely pose, obtained by a scan-matching procedure combined with odometry information. In this way, the most recent sensor observation is taken into account for creating the next generation of particles. This allows us to estimate the state of the robot according to a more informed (and thus, more accurate) model than the one obtained based only on the odometry information. The use of this refined model has two effects. The map is more accurate, since the current observation is incorporated into the individual maps after considering its effect on the pose of the robot. This significantly reduces the estimation error, so that fewer particles are required to represent the posterior. The second approach, the adaptive resampling strategy, allows us to perform a resampling step only when needed, and in this way, keeps a reasonable particle diversity. This results in a significantly reduced risk of particle depletion.
建议分布是通过评估与粒子相关的最可能姿态周围的可能性来计算的，该可能性是通过扫描匹配过程与里程信息相结合获得的。以这种方式，最新的传感器观测被考虑到创造下一代粒子。这使得我们能够根据一个比仅基于里程信息获得的模型更为富含信息（从而更为准确）的模型来估计机器人的状态。使用这种改进的模型有两个效果。考虑到当前的观测结果对机器人姿态的影响，该地图更加精确。这显著地减少了估计误差，因此需要更少的粒子来表示后验。第二种方法，自适应重采样策略，允许我们仅在需要时执行重采样步骤，这样，就保持了合理的粒子多样性。这将显著降低微粒耗尽的风险。
The work presented in this paper is an extension of our previous work [11], as it further optimizes the proposal distribution to even more accurately draw the next generation of particles.Furthermore, we added a complexity analysis, a formal description of the techniques used, and provide more detailed experiments in this paper. Our approach has been validated by a set of systematic experiments in large-scale indoor and outdoor environments. In all experiments, our approach generated highly accurate metric maps. Additionally, the number of the required particles is one order of magnitude lower than with previous approaches.
本文的工作是我们先前工作的扩展[11]，因为它进一步优化了建议分布，以更准确地绘制下一代粒子。此外，我们还添加了复杂性分析，对所使用的技术进行了形式化描述，并在本文中提供了更详细的实验。我们的方法已经在一系列大型室内外环境的系统实验中得到了验证。在所有实验中，我们的方法生成了高精度的度量地图。此外，所需粒子的数量比以前的方法低一个数量级。
This paper is organized as follows. After explaining how a Rao-Blackwellized filter can be used in general to solve the SLAM problem, we describe our approach in Section III. We then provide implementation details in Section IV. Experiments carried out on real robots are presented in Section VI. Finally,Section VII discusses related approaches.
本文的结构如下。在解释了如何使用Rao-Blackwellized滤波器来解决SLAM问题之后，我们在第三节描述了我们的方法。然后在第四节提供了实现细节。在第六节中介绍了在真实机器人上进行的实验。最后，第七节讨论了相关的方法。
II. MAPPING WITH RBPFS
According to Murphy [8], the key idea of the RBPF for SLAM is to estimate the joint posterior p(x_(1:t),m|z_(1:t),u_(1:t-1))about the map mand the trajectory x_(1:t)=x_1,…,x_tof the robot. This estimation is performed given the observations z_(1:t)=z_1,…,z_tand the odometry measurements u_(1:t-1)=u,…,u_(t-1)obtained by the mobile robot. The RBPF for SLAM makes use of the following factorization:
根据Murphy[8]，SLAM的RBPF的关键思想是估计地图上的联合后验概率p(x_(1:t),m|z_(1:t),u_(1:t-1))和机器人的轨迹x_(1:t)=x_1,…,x_t。在给定移动机器人获得的观测值z_(1:t)=z_1,…,z_t和里程测量值u_(1:t-1)=u,…,u_(t-1)的情况下，进行该估计。SLAM的RBPF使用以下因子分解：
p(x_(1:t),m|z_(1:t),u_(1:t-1))= p(m│x_(1:t),z_(1:t) )·p(x_(1:t)│z_(1:t),u_(1:t-1) ) (1)
This factorization allows us to first estimate only the trajectory of the robot, and then to compute the map given that trajectory. Since the map strongly depends on the pose estimate of the robot, this approach offers an efficient computation. This technique is often referred to as Rao-Blackwellization.
这个分解允许我们首先估计机器人的轨迹，然后计算给定轨迹的地图。由于地图高度依赖于机器人的姿态估计，这种方法提供了一种有效的计算方法。这种技术通常被称为Rao-Blackwellization。
Typically, (1) can be calculated efficiently, since the posterior over maps p(m│x_(1:t),z_(1:t) ) can be computed analytically using “mapping with known poses” [12], since x_(1:t)andz_(1:t) are known.
通常，（1）可以被有效地计算，因为x_(1:t)和z_(1:t) 是已经知道的。地图的概率密度函数可以通过已知位姿的建图方法“mapping with known poses”来计算。
To estimate the posterior over the potential trajectories, one can apply a particle filter. Each particle represents a potential trajectory of the robot. Furthermore, an individual map is associated with each sample. The maps are built from the observations, and the trajectory represented by the corresponding particle.
为了估计潜在轨迹上的后验概率p(x_(1:t)│z_(1:t),u_(1:t-1) )，可以应用粒子滤波器。每个粒子代表机器人的一个潜在轨迹。此外，一个单独的地图与每个样本相关联。这些地图是根据观测结果建立的，轨迹由相应的粒子表示。
One of the most common particle-filtering algorithms is the sampling importance resampling (SIR) filter. A Rao-Blackwellized SIR filter for mapping incrementally processes the sensor observations and the odometry readings as they are available. It updates the set of samples that represents the posterior about the map and the trajectory of the vehicle. The process can be summarized by the following four steps.
最常用的粒子滤波算法之一是（SIR）滤波器。用于建图的Rao-Blackwellized SIR滤波器，增量式地处理传感器观测值和里程计读数（当他们可获取的时候）。它更新代表地图和车辆轨迹的后验概率的样本集。这个过程可以概括为以下四个步骤。

1. Sampling: The next generation of particles {x_t^((i) )} is obtained from the generation {x_(t-1)^((i) ) }by sampling from the proposal distribution π. Often, a probabilistic odometry motion model is used as the proposal distribution.
2. Importance Weighting: An individual importance weight{w_t^((i) )} is assigned to each particle, according to the importance sampling principle

The weights account for the fact that the proposal distribution is, in general, not equal to the target distribution of successor states.
3) Resampling: Particles are drawn with replacement proportional to their importance weight. This step is necessary,since only a finite number of particles is used to approximate a continuous distribution. Furthermore, resampling allows us to apply a particle filter in situations in which the target distribution differs from the proposal. After resampling, all the particles have the same weight.
4) Map Estimation: For each particle, the corresponding map estimate p(m^i |x_(1:t)^((i) ),z_(1:t)) is computed, based on the trajectory x_(1:t)^((i)) of that sample and the history of observations z_(1:t)。
1)采样：下一代粒子{x_t^((i) )}是从{x_(t-1)^((i) ) }一代中通过从建议分布π采样获得的。通常，建议分布使用概率里程运动模型。
2）重要性权重：根据重要性抽样原则，为每个粒子分配一个单独的重要性权重{w_t^((i) )}

这些权重说明了这样一个事实，即建议分布一般不等于继承状态的目标分布。
3） 重采样：根据权值的比例重新分布采样粒子。这一步是必要的，因为只有有限数量的粒子用于近似连续分布。此外，重采样允许我们在目标分布与建议分布不同的情况下应用粒子过滤器。重采样后，所有粒子具有相同的权重。
4） 地图估计：对于每个粒子，根据该样本的轨迹x_(1:t)^((i))和观测历史z_(1:t)，计算相应的Map估计 p(m^i |x_(1:t)^((i) ),z_(1:t))
The implementation of this schema requires evaluating the weights of the trajectories from scratch whenever a new observation is available. Since the length of the trajectory increases over time, this procedure would lead to an obviously inefficient algorithm. According to Doucet et al. [13], we obtain a recursive formulation to compute the importance weights by restricting the proposal to fulfill the following assumption:
这个方案的实现需要在获取新的观测时从头开始评估轨迹的权重。由于轨迹的长度随着时间的推移而增加，此过程将导致明显低效的算法。根据Doucet等人的说法。[13] ，通过限制建议分布满足以下假设，我们获得了计算重要性权重的递归公式：

Here μ=1⁄(p(z_t |z_(1:t-1),u_(1:t-1))) is a normalization factor resulting from Bayes’ rule that is equal for all particles.
这里μ=1⁄(p(z_t |z_(1:t-1),u_(1:t-1)))是由Bayes规则产生的标准化因子,对所有粒子来说是一样的。
Most of the existing particle filter applications rely on the recursive structure of (6). Whereas the generic algorithm specifies a framework that can be used for learning maps, it leaves open how the proposal distribution should be computed and when the resampling step should be carried out. Throughout the remainder of this paper, we describe a technique that computes an accurate proposal distribution, and that adaptively performs resampling.
现有的粒子滤波应用大多依赖于（6）的递归结构。尽管通用算法指定了一个可用于学习地图的框架，但它对如何计算建议分布以及何时执行重采样步骤仍有开放性。在本文的其余部分中，我们描述了一种计算精确建议分布并自适应执行重采样的技术。
III. RBPF WITH IMPROVED PROPOSALSAND ADAPTIVE RESAMPLING
In the literature, several methods for computing improved proposal distributions and for reducing the risk of particle depletion have been proposed [13]–[15]. Our approach applies two concepts that have previously been identified as key prerequisites for efficient particle-filter implementations (see Doucet et al. [13]), namely, the computation of an improved proposal distribution and an adaptive resampling technique.
在文献中，已经提出了几种计算改进的建议分布和降低粒子耗尽风险的方法[13]-[15]。我们的方法应用了两个概念，这两个概念以前被认为是高效粒子滤波器实现的关键先决条件（参见Doucet等人。[13] ，即计算改进的建议分布和自适应重采样技术。
A. On the Improved Proposal Distribution
As described in Section II, one needs to draw samples from a proposal distribution in the prediction step in order to obtain the next generation of particles. Intuitively, the better the proposal distribution approximates the target distribution, the better the performance of the filter. For instance, if we were able to directly draw samples from the target distribution, the importance weights would become equal for all particles, and the resampling step would no longer be needed. Unfortunately,in the context of SLAM, a closed form of this posterior is not available, in general.
如第二节所述，需要从建议步骤中的建议分布中提取样本，以获得下一代粒子。直观地说，建议分布越接近目标分布，滤波器的性能越好。例如，如果我们能够直接从目标分布中提取样本，那么所有粒子的重要性权重都将相等，并且不再需要重采样步骤。不幸的是，在SLAM的情况下，一般来说，这种后验的封闭形式是无法获得的。
As a result, typical particle filter applications [16], [7] use the odometry motion model as the proposal distribution. This motion model has the advantage that it is easy to compute for most types of robots. Furthermore, the importance weights are then computed according to the observation model p(z_t |m,x_t) .This becomes clear by replacing in (6) by the motion model p(x_t |x_(t-1),u_(t-1))
因此，典型的粒子滤波应用[16]，[7]使用里程运动模型作为建议分布。这种运动模型的优点是，对于大多数类型的机器人来说，它易于计算。此外，根据观测模型 p(z_t |m,x_t)计算重要性权重，用运动模型 p(x_t |x_(t-1),u_(t-1))代替（6）中的π就可以清楚了。

This proposal distribution, however, is suboptimal, especially when the sensor information is significantly more precise than the motion estimate of the robot based on the odometry, which is typically the case if a robot equipped with a laser range finder [e.g., with a SICK Laser Measurement Sensor (LMS)]. Fig. 1 illustrates a situation in which the meaningful area of the observation likelihood is substantially smaller than the meaningful area of the motion model. When using the odometry model as the proposal distribution in such a case, the importance weights of the individual samples can differ significantly from each other,since only a fraction of the drawn samples cover the regions of state space that have a high likelihood under the observation model (area in Fig. 1). As a result, one needs a comparably high number of samples to sufficiently cover the regions with high observation likelihood.
然而，这种建议分布是次优的，特别是当传感器信息明显比基于里程计的机器人运动估计更精确时，通常情况下，如果机器人配备激光测距仪[例如，配备SICK的激光测量传感器（LMS）]。图1示出了观测似然的有意义区域实质上小于运动模型的有意义区域的情况。在这种情况下，当使用odometry模型作为建议分布时，各个样本的重要性权重可以彼此显著不同，因为只有一小部分提取的样本覆盖了状态空间中在观测模型下具有高可能性的区域（图1中的区域）。因此，需要相当多的样本来充分覆盖具有高观测可能性的区域。

A common approach, especially in localization, is to use a smoothed likelihood function, which avoids particles close to the meaningful area getting a too-low importance weight. However, this approach discards useful information gathered by the sensor and, at least in our experience, often leads to less accurate maps in the SLAM context.
一种常见的方法，特别是在定位中，是使用平滑似然函数，避免靠近有意义的区域的粒子获得太低的重要性权重。然而，这种方法丢弃了传感器收集到的有用信息，并且，至少在我们的经验中，常常导致在SLAM环境中不太准确的地图。
To overcome this problem, one can consider the most recent sensor observation when generating the next generation of samples. By integrating into the proposal, one can focus the sampling on the meaningful regions of the observation likelihood. According to Doucet [17], the distribution is

the optimal proposal distribution with respect to the variance of the particle weights. Using that proposal, the computation of the weights turns into
为了解决这个问题，可以在生成下一代样本时考虑最近的传感器观测。通过整合到建议分布中，可以将采样集中在观测似然的有意义区域上。根据Doucet[17]，该分布是关于粒子权重方差的最优建议分布。利用这个建议，权重的计算变成

When modeling a mobile robot equipped with an accurate sensor like, e.g., a laser range finder, it is convenient to use such an improved proposal, since the accuracy of the laser range finder leads to extremely peaked likelihood functions. In the context of landmark-based SLAM, Montemerlo et al. [6]presented an RBPF that uses a Gaussian approximation of the improved proposal. This Gaussian is computed for each particle, using a Kalman filter that estimates the pose of the robot.This approach can be used when the map is represented by a set of features, and if the error affecting the feature detection is assumed to be Gaussian. In this paper, we transfer the idea of computing an improved proposal to the situation in which dense grid maps are used, instead of landmark-based representations.
当对一个安装了一个精确的传感器，例如一种激光测距仪，的移动机器人进行建模时，使用这种改进方案很方便，因为激光测距仪的精度会导致极大的峰值似然函数。在基于地标的SLAM的背景下，Montemerlo等人[6]提出了一种基于高斯近似的RBPF改进方案。这个高斯分布是为每个粒子计算的，使用一个卡尔曼滤波器来估计机器人位姿。这个当地图由一组特征表示时，如果影响特征检测的误差假设为高斯误差，则可以使用该方法。在本文中，我们将计算改进建议分布的思想转移到使用密集网格地图而不是基于地标的表示的情况。
B. Efficient Computation of the Improved Proposal
When modeling the environment with grid maps, a closed-form approximation of an informed proposal is not directly available, due to the unpredictable shape of the observation likelihood function.
当使用栅格地图对环境进行建模时，由于观测似然函数的形状不可预测，因此无法直接获得建议分布的闭合形式近似。
In theory, an approximated form of the informed proposal can be obtained using the adapted particle filter [15]. In this framework, the proposal for each particle is constructed by computing a sampled estimate of the optimal proposal given in (9). In the SLAM context, one would first have to sample a set of potential poses〖 x〗jof the robot from the motion modelp(x_t |x(t-1)^((i) ),u_(t-1)).In a second step, these samples need to be weighed by the observation likelihood to obtain an approximation of the optimal proposal. However, if the observation likelihood is peaked, the number of pose samples 〖 x〗j that has to be sampled from the motion model is high, since a dense sampling is needed for sufficiently capturing the typically small areas of high likelihood.This results in a similar problem to using the motion model as the proposal: a high number of samples is needed to sufficiently cover the meaningful region of the distribution.
理论上，可以使用自适应粒子滤波器获得建议分布的近似形式[15]。在这个框架中，通过计算（9）中给出的最优建议分布的抽样估计来构造每个粒子的建议分布。在SLAM环境下，首先要从运动模型中提取机器人的一组潜在姿态，然后用观测似然法对这些姿态进行加权，得到最优建议分布的近似。但是，如果观测可能性达到峰值，则必须从运动模型中采样的姿势样本的数量会很高，由于需要密集采样才能充分捕获典型的高似然小区域，这导致了与使用运动模型作为建议分布类似的问题：需要大量采样才能充分覆盖分布的有意义区域。
One of our observations is that in the majority of cases, the target distribution has only a limited number of maxima, and it mostly has only a single one. This allows us to sample positions 〖 x〗j covering only the area surrounding these maxima. Ignoring the less meaningful regions of the distribution saves a significant amount of computational resources, since it requires fewer samples. In the previous version of this paper [11], we approximated p(x_t |x(t-1)^((i) ),u(t-1)) by a constant k within the interval L^((i))(see also Fig. 1), given by

我们的观察结果之一是，在大多数情况下，目标分布只有有限个极大值，而且大多只有一个极大值。这使得我们可以只对这些最大值周围的区域进行采样。忽略分布中不太有意义的区域可以节省大量的计算资源，因为它需要更少的样本。在本文[11]的前一版本中，我们用区间内的一个常数来近似（见图1），由
In our current approach, we consider both components,the observation likelihood and the motion model within that interval L^((i)). We locally approximate the posterior p(x_t |〖m_(t-1)^{((i)),x〗_(t-1)}((i) ),〖z_t,u〗_(t-1))around the maximum of the likelihood function reported by a scan registration procedure.
在我们目前的方法中，我们同时考虑了这两个分量，观测似然和该区间内的运动模型。我们在扫描配准过程中得出的的似然函数的最大值附近局部逼近后验函数。
To efficiently draw the next generation of samples, we compute a Gaussian approximation N based on that data. The main differences from previous approaches is that we first use a scanmatcher to determine the meaningful area of the observation likelihood function. We then sample in that meaningful area and evaluate the sampled points based on the target distribution. For each particle i, the parameters μ_t^((i))and ∑▒█((i)@t)are determined individually for Ksampled points {x_j }in the interval〖 L〗^((i)) . Furthermore, we take into account the odometry information when computing the mean and the variance . We estimate the Gaussian parameters as
为了有效地得到下一代样本，我们基于该数据计算高斯近似。与以往方法的主要区别在于，我们首先使用扫描匹配器来确定观测似然函数的有意义区域。然后在有意义的区域进行采样，并根据目标分布对采样点进行评估。对于每个粒子，分别为间隔内的采样点确定参数μ_t^((i))and ∑▒█((i)@t)。此外，在计算均值μ^((i))和方差∑▒〖(i)〗时，我们还考虑了里程信息。我们估计高斯参数为

In this way, we obtain a closed-form approximation of the optimal proposal which enables us to efficiently obtain the next generation of particles. Using this proposal distribution, the weights can be computed as
通过这种方法，我们得到了最优分布的一个闭式近似，这使得我们能够有效地获得下一代粒子。使用这个建议分布，权重可以计算为

Note that〖 η〗^((i)) is the same normalization factor that is used in the computation of the Gaussian approximation of the proposal in(17).
请注意，“η”与（17）中提案的高斯近似计算中使用的归一化因子相同。
C. Discussion About the Improved Proposal
The computations presented in this section enable us to determine the parameters of a Gaussian proposal distribution for each particle individually. The proposal takes into account the most recent odometry reading and laser observation, while at the same time allowing us efficient sampling. The resulting densities have a much lower uncertainty, compared with situations in which the odometry motion model is used. To illustrate this fact,Fig. 2 depicts typical particle distributions obtained with our approach. In case of a straight featureless corridor, the samples are typically spread along the main direction of the corridor, as depicted in Fig. 2(a). Fig. 2(b) illustrates the robot reaching the end of such a corridor. As can be seen, the uncertainty in the direction of the corridor decreases, and all samples are centered around a single point. In contrast to that, Fig. 2© shows the resulting distribution when sampling from the raw motion model.
本节中的计算使我们能够分别确定每个粒子的高斯建议分布的参数。这个提议考虑到了最近的里程计读数和激光观测，同时允许我们进行有效的采样。与使用里程运动模型的情况相比，得到的密度具有更低的不确定性。为了说明这一事实，图2描绘了用我们的方法获得的典型粒子分布。对于无特征的直线走廊，如图2（a）所示，样品通常沿着走廊的主要方向分布。图2（b）示出了到达这种走廊末端的机器人。可以看出，走廊方向的不确定性降低，所有样本都围绕一个点居中。与此相反，图2（c）示出了从原始运动模型采样时的结果分布。

As explained above, we use a scan-matcher to determine the mode of the meaningful area of the observation likelihood function. In this way, we focus the sampling on the important regions. Most existing scan-matching algorithms maximize the observation likelihood, given a map and an initial guess of the robot’s pose. When the likelihood function is multimodal,which can occur when, e.g., closing a loop, the scan-matcher returns for each particle the maximum which is closest to the initial guess. In general, it can happen that additional maxima in the likelihood function are missed, since only a single mode is reported. However, since we perform frequent filter updates (after each movement of 0.5 m or a rotation of 25 )and limit the search area of the scan-matcher, we consider that the distribution has only a single mode when sampling data points to compute the Gaussian proposal. Note that in situations like a loop closure, the filter is still able to keep multiple hypotheses, because the initial guess for the starting position of the scan-matcher when reentering a loop is different for each particle.
如上所述，我们使用扫描匹配器来确定观测似然函数有意义的区域。这样，我们就把抽样的重点放在重要的区域。现有的扫描匹配算法大多在给定地图和机器人姿态的初始猜测的情况下，最大化观测概率。当似然函数为多模函数时（例如，关闭循环时），扫描匹配器为每个粒子返回最接近初始猜测的最大值。一般来说，可能会出现似然函数中的附加最大值丢失的情况，因为只报告了一个模式。然而，由于我们执行频繁的滤波器更新（每次移动0.5 m或旋转25 °后）并限制扫描匹配器的搜索区域，因此我们认为在对数据点进行采样以计算高斯建议分布时，分布只有一个模式。注意，在像循环闭合这样的情况下，过滤器仍然能够保留多个假设，因为重新进入循环时扫描匹配器的起始位置的初始猜测对于每个粒子是不同的。
Nevertheless, there are situations in which the filter can, at least in theory, become overly confident. This might happen in extremely cluttered environments and when the odometry is highly affected by noise. A solution to this problem is to track the multiple modes of the scan-matcher and repeat the sampling process separately for each node. However, in our experiments, carried out using real robots, we never encountered such a situation.
然而，在某些情况下，至少在理论上，过滤器会变得过于自信。这可能发生在极为杂乱的环境中，并且当里程计受到噪音的严重影响时。解决这个问题的方法是跟踪扫描匹配器的多个模式，并对每个节点分别重复采样过程。然而，在我们使用真实机器人进行的实验中，我们从未遇到过这样的情况。
During filtering, it can happen that the scan-matching process fails because of poor observations or a too-small overlapping area between the current scan and the previously computed map. In this case, the raw motion model of the robot which is illustrated in Fig. 2© is used as a proposal. Note that such situations occur rarely in real datasets (see also Section VI-E).
在过滤过程中，可能会发生扫描匹配过程失败，原因是观察不好或当前扫描与先前计算的地图之间的重叠区域太小。在这种情况下，使用图2（c）所示的机器人的原始运动模型作为建议分布。注意，这种情况很少发生在真实的数据集中（另见第VI-E节）。
D. Adaptive Resampling
A further aspect that has a major influence on the performance of a particle filter is the resampling step. During resampling, particles with a low importance weight w^((i)) are typically replaced by samples with a high weight. On the one hand, resampling is necessary, since only a finite number of particles are used to approximate the target distribution. On the other hand, the resampling step can remove good samples from the filter, which can lead to particle impoverishment. Accordingly, it is important to find a criterion for deciding when to perform the resampling step. Liu [18] introduced the so-called effective sample size to estimate how well the current particle set represents the target posterior. In this paper, we compute this quantity according to the formulation of Doucet et al. [13] as
对粒子滤波器的性能有主要影响的另一方面是重采样步骤。在重采样期间，具有低重要性权重的粒子通常被具有高权重的样本替换。一方面，由于仅使用有限数量的粒子来近似目标分布，因此需要重新采样。另一方面，重采样步骤可能从滤波器中去除好的样本，从而导致粒子贫化。因此，重要的是找到判断何时执行重采样步骤的标准。Liu[18]引入了所谓的有效样本大小来估计当前粒子集代表目标后验的程度。本文根据Doucet等人的公式计算了这个量。[13] 作为

where w ̃^((i)) refers to the normalized weight of particle i.
其中w ̃^((i))是指粒子i的标准化权重。
The intuition behind N_eff is as follows. If the samples were drawn from the target distribution, their importance weights would be equal to each other, due to the importance-sampling principle. The worse the approximation of the target distribution, the higher the variance of the importance weights. Since N_eff can be regarded as a measure of the dispersion of the importance weights, it is a useful measure to evaluate how well the particle set approximates the target posterior. Our algorithm follows the approach proposed by Doucet et al. [13] to determine whether or not the resampling step should be carried out.We resample each time drops below the threshold of ,where is the number of particles. In extensive experiments,we found that this approach drastically reduces the risk of replacing good particles, because the number of resampling operations is reduced, and they are only performed when needed.
N_eff背后的含义如下。如果样本是从目标分布中抽取的，由于重要性抽样原则，它们的重要性权重将是相等的。目标分布的近似程度越差，重要性权重的方差越大。由于N_eff可以被视为重要性权重分散的度量，因此它是评估粒子集在多大程度上逼近目标后验的有用度量。我们的算法遵循Doucet等人提出的方法。[13] 为确定是否应执行重采样步骤，我们会在每次低于阈值（粒子数）时重新采样。在大量的实验中，我们发现这种方法大大降低了替换好粒子的风险，因为重采样操作的次数减少了，而且只在需要时执行。
Algorithm
The overall process is summarized in Algorithm 1. Each time a new measurement tuple(u_(t-1),z_t) is available, the proposal is computed for each particle individually, and is then used to update that particle. This results in the following steps.
算法1总结了整个过程。每次有新的度量元组(u_(t-1),z_t)可用时，分别计算每个粒子的建议分布，然后使用该建议分布更新该粒子。具体过程如以下步骤。
1）An initial guess x_t^{(’(i))=x_(t-1)}((i))⨁u_(t-1) for the robot’s pose,represented by the particle i, is obtained from the previous pose x_(t-1)^((i)) of that particle and the odometry measurements u_(t-1) collected since the last filter update. Here, the operator ⨁ corresponds to the standard pose compounding operator [19]
2)A scan-matching algorithm is executed based on the map m_(t-1)^((i)), starting from the initial guess x_t^(’(i)). The search performed by the scan-matcher is bounded to a limited region around x_t^(’(i)). If the scan-matching reports a failure,the pose and the weights are computed according to the motion model (and steps 3) and 4) are ignored).
3) A set of sampling points is selected in an interval around the pose x ̂_t^((i)) reported scan-matcher. Based on these points,the mean and the covariance matrix of the proposal are computed by pointwise evaluating the target distribution p(z_t |m_(t-1)^((i) ),x_j)p(x_j |x_(t-1)^((i) ),u_(t-1)) in the sampled positions . During this phase, the weighting factor is also computed, according to (17).
4)The new pose x_t^((i))of the particle i is drawn from the Gaussian approximation N(μ_t^((i) ),Σ_t^((i))) of the improved proposal distribution.
5)Update of the importance weights.
6) The map m^((i)) of particle i is updated according to the drawn pose x_t^((i)) and the observation z_t.
After computing the next generation of samples, a resampling step is carried out, depending on the value of N_eff.
1）由粒子i表示的机器人姿势的初始猜测x_t^{(’(i))=x_(t-1)}((i))⨁u_(t-1)，是从该粒子的先前姿势x_(t-1)^((i))和自上次过滤器更新以来收集的里程测量值u_(t-1)获得的。这里，运算符⨁对应于标准姿势复合运算符[19]。
2） 基于地图m_(t-1)^{((i))执行扫描匹配算法，从初始猜测x_t}(’(i))开始。扫描匹配器执行的搜索被限定在x_t^(’(i))周围的有限区域内。如果扫描匹配报告失败，则会忽略根据运动模型计算的姿势和权重（步骤3和4）。
3） 在由扫描匹配器器得到的姿势x ̂_t^((i))周围选择一组采样点。基于这些点，通过逐点评估采样位置中的目标分布(z_t |m_(t-1)^((i) ),x_j)p(x_j |x_(t-1)^((i) ),u_(t-1))来计算建议分布的均值和协方差矩阵。在此阶段，还根据（17）计算加权因子。
4） 粒子i的新位姿x_t^{((i))是由改进的提议分布的高斯近似N(μ_t}((i) ),Σ_t^((i)))得出的。
5） 更新重要性权重。
6） 粒子i的地图m^{((i))根据绘制的姿态x_t}((i))和观测z_t进行更新。
在计算下一代样本之后，根据N_eff的值执行重采样步骤。
IV. IMPLEMENTATION ISSUES
This section provides additional information about implementation details used in our current system. These issues are not required for the understanding of the general approach, but complete the precise description of our mapping system. In the following, we briefly explain the used scan-matching approach,the observation model, and how to pointwise evaluate the motion model.
本节提供有关当前系统中使用的实现详细信息的附加信息。这些问题不是理解一般方法所必需的，而是完成对我们的建图系统的精确描述。在下面，我们将简要介绍所使用的扫描匹配方法、观察模型以及如何逐点评估运动模型。
Our approach applies a scan-matching technique on a perparticle basis. In general, an arbitrary scan-matching technique can be used. In our implementation, we use the scan-matcher “vasco,” which is part of the Carnegie Mellon Robot Navigation Toolkit (CARMEN) [20], [21]. This scan-matcher aims to find the most likely pose by matching the current observation against the map constructed so far
我们的方法在每粒子的基础上应用扫描匹配技术。一般来说，可以使用任意扫描匹配技术。在我们的实现中，我们使用扫描匹配器“vasco”，它是卡内基梅隆机器人导航工具包（CARMEN）[20]，[21]的一部分。这个扫描匹配器的目标是通过将当前的观测值与目前构建的地图进行匹配来找到最可能的姿态

where x_t^(’(i)) is the initial guess. The scan-matching technique performs a gradient-descent search on the likelihood function of the current observation, given the grid map. Note that in our mapping approach, the scan-matcher is only used for finding the local maximum of the observation likelihood function. In practice, any scan-matching technique which is able to compute the best alignment between a reference map m_(t-1)^((i)) and the current scan z_tgiven an initial guess x_t^(’(i)) can be used.
其中x_t^(’(i))是初始猜测。扫描匹配技术在给定栅格地图的情况下，对当前观测值的似然函数进行梯度下降搜索。注意，在我们的建图方法中，扫描匹配器仅用于寻找观测似然函数的局部最大值。在实践中，可以使用任何能够计算出参考地图和给定初始猜测的当前扫描之间的最佳对齐的扫描匹配技术。
In order to solve (21), one applies Bayes’ rule and seeks for the pose with the highest observation likelihood .To compute the likelihood of an observation p(z_t |x,m), we use the so called “beam-endpoint model” [22]. In this model, the individual beams within a scan are considered to be independent.Furthermore, the likelihood of a beam is computed based on the distance between the endpoint of the beam and the closest obstacle from that point. To achieve a fast computation, one typically uses a convolved local grid map.
为了求解（21），我们应用Bayes规则，寻找观测概率最高的姿态，为了计算观测概率p(z_t |x,m)，我们使用了所谓的“波束端点模型”[22]。在这个模型中，扫描中的单个光束被认为是独立。此外，根据光束端点与距离该点最近的障碍物之间的距离计算光束的可能性。为了实现快速计算，通常使用卷积的局部栅格地图。
Additionally, the construction of our proposal requires evaluating p(z_t |m_(t-1)^((i) ),x_j)p(x_j |x_(t-1)^((i) ),u_(t-1)) at the sampled points x_j. We compute the first component according to the previously mentioned beam-endpoint model. To evaluate the second term, several closed-form solutions for the motion estimate are available. The different approaches mainly differ in the way the kinematics of the robot are modeled. In our current implementation, we compute p(x_j |x_(t-1),u_(t-1)) according to the Gaussian approximation of the odometry motion model described in [23]. We obtain this approximation through Taylor expansion in an extended Kalman filter (EKF)-style procedure. In general, there are more sophisticated techniques estimating the motion of the robot. However, we use that model to estimate a movement between two filter updates, which is performed after the robot traveled around 0.5 m. In this case, this approximation works well, and we did not observe a significant difference between the EKF-like model and the, in general, more accurate sample-based velocity motion model [23].
此外，我们建议分布的构建需要评估采样点x_j处的p(z_t |m_(t-1)^((i) ),x_j)p(x_j |x_(t-1)^((i) ),u_(t-1))。我们根据前面提到的波束端点模型计算第一个分量。为了计算第二项，有几种运动估计的闭式解。不同的建模方法在机器人运动学建模上有很大的不同。在我们目前的实现中，我们根据文献[23]中描述的里程运动模型的高斯近似计算p(x_j |x_(t-1),u_(t-1))。在扩展卡尔曼滤波器（EKF）型过程中，我们通过泰勒展开得到了这种近似。一般来说，有更复杂的技术来估计机器人的运动。然而，我们使用该模型来估计两个滤波器更新之间的移动，这是在机器人移动约0.5 m后执行的。在这种情况下，这种近似效果很好，我们没有观察到类似于EKF的模型和通常更精确的基于样本的速度运动模型之间的显著差异[23]。
V. COMPLEXITY
This section discusses the complexity of the presented approach to learn grid maps with an RBPF. Since our approach uses a sample set to represent the posterior about maps and poses, the number N of samples is the central quantity. To compute the proposal distribution, our approach samples around the most likely position reported by the scan-matcher. This sampling is done for each particle a constant number of times ( K), and there is no dependency between the particles when computing the proposal. Furthermore, the most recent observation z_t used to compute μ^((i)) and Σ^((i)) covers only an area of the map (bounded by the odometry error and the maximum range of the sensor), so the complexity depends only on the number N of particles. The same holds for the update of the individual maps associated with each of the particles.
本节讨论了用RBPF学习栅格地图的方法的复杂性。由于我们的方法使用一个样本集来表示关于地图和姿势的后验，因此样本数N是中心量。为了计算建议分布，我们的方法在扫描匹配器报告的最可能位置周围采样。这个采样是为每一个粒子恒定次数（K）进行的，并且在计算建议分布时粒子之间没有依赖关系。此外，用于计算μ^((i)) and Σ^((i))的最新观测z_t仅覆盖地图的一个区域（以里程计误差和传感器的最大范围为界），因此复杂性仅取决于粒子数N。与每个粒子相关联的单个贴图的更新也是如此。
During the resampling step, the information associated with a particle needs to be copied. In the worst case,N-1 samples are replaced by a single particle. In our current system,each particle stores and maintains its own grid map. To duplicate a particle, we therefore have to copy the whole map. As a result, a resampling action introduces a worst-case complexity of O(NM), where M is the size of the corresponding grid map.However, using the adaptive resampling technique, only a very few resampling steps are required during mapping.
在重采样步骤中，需要复制与粒子关联的信息。在最坏的情况下，N-1样本被单个粒子所代替。在我们当前的系统中，每个粒子都存储并维护自己的栅格贴图。为了复制一个粒子，我们必须复制整个地图。结果，重采样操作引入了O（NM）的最坏情况复杂性，其中M是对应网格的大小.然而，地图使用自适应重采样技术，在建图过程中只需要很少的重采样步骤。
To decide whether or not a resampling is needed, the effective sample size [see (20)] needs to be taken into account. Again, the computation of the quantity introduces a complexity of O(N).
为了确定是否需要重新采样，需要考虑有效样本大小[见（20）]。同样，数量的计算引入了O（N）的复杂性。
As a result, if no resampling operation is required, the overall complexity for integrating a single observation depends only linearly on the number of particles. If a resampling is required,the additional factor which represents the size of the map is introduced, and leads to a complexity of O(NM). The complexity of each individual operation is depicted in Table I.

因此，如果不需要重采样操作，则集成单个观测的总体复杂性仅取决于粒子数的线性关系。如果需要重采样，则引入表示地图大小的附加因子，并导致O（NM）的复杂性。每个单独操作的复杂性如表一所示。
Note that the complexity of the resampling step can be reduced by using a more intelligent map representation, as done in distributed particle (DP)-SLAM [3], for example. It can be shown that in this case, the complexity of a resampling step is reduced to O(AN²logN), where A is the area covered by the sensor. However, building an improved map representation is not the aim of this paper. We actually see our approach as orthogonal to DP-SLAM, because both techniques can be combined. Furthermore, in our experiments using real-world data sets, we figured out the resampling steps are not the dominant part, and they occur rarely, due to the adaptive-resampling strategy.
注意，重采样步骤的复杂性可以通过使用更智能的地图表示来降低，例如在分布式粒子（DP）-SLAM[3]中所做的。可以证明，在这种情况下，重采样步骤的复杂度降低到O（AN？logN），其中A是传感器覆盖的区域。然而，建立一个改进的地图表示并不是本文的目的。我们实际上认为我们的方法与DP-SLAM是正交的，因为这两种技术都可以组合。此外，在使用真实数据集的实验中，我们发现由于自适应重采样策略，重采样步骤不是主要部分，而且很少发生。
VI. EXPERIMENTS
The approach described above has been implemented and tested using real robots and datasets gathered with real robots.Our mapping approach runs online on several platforms like ActivMedia Pioneer2 AT, Pioneer 2 DX-8, and iRobot B21r robots equipped with SICK LMS and PLS laser range finders (see Fig. 3). The experiments have been carried out in a variety of environments, and showed the effectiveness of our approach in indoor and outdoor settings. Most of the maps generated by our approach can be magnified up to a resolution of 1 cm, without observing considerable inconsistencies. Even in big real-world datasets covering an area of approximately 250 m by 250 m, our approach never required more than 80 particles to build accurate maps. In the reminder of this section, we discuss the behavior of the filter in different datasets. Furthermore, we give a quantitative analysis of the performance of the presented approach.Highly accurate grid maps have been generated with our approach from several datasets. These maps, raw data files, and an efficient implementation of our mapping system are available on the web [24].
上面描述的方法已经用真实的机器人和来自真实机器人的数据集来实现和测试。我们的建图方法在几个平台上在线运行，如ActivMedia先锋2 AT、先锋2 DX-8和iRobot B21r机器人，这些机器人配备有SICK LMS和PLS激光测距仪（见图3）。实验在多种环境下进行，证明了该方法在室内外环境中的有效性。我们的方法生成的大多数地图可以放大到1厘米的分辨率，而不会观察到相当大的不一致。即使在面积约为250米乘250米的大型真实数据集中，我们的方法也从不需要超过80个粒子来构建精确的地图。在本节的提醒中，我们将讨论过滤器在不同数据集中的表现。此外，我们对所提出方法的性能进行了定量分析。我们的方法从几个数据集生成了高精度的网格地图。这些地图、原始数据文件以及我们地图系统的有效实现都可以在web上找到[24]。

A. Mapping Results
The datasets discussed here have been recorded at the Intel Research Lab in Seattle, WA, at the campus of the University of Freiburg, and at the Killian Court at MIT (Cambridge, MA).
The maps of these environments are depicted in Figs. 4–6.

1. Intel Research Lab: The Intel Research Lab is depicted in the left image of Fig. 4 and has a size of 28 m by 28 m.The dataset has been recorded with a Pioneer II robot equipped with a SICK sensor. To successfully correct this dataset, our algorithm needed only 15 particles. As can be seen in the right image of Fig. 4, the quality of the final map is so high that the map can be magnified up to 1-cm resolution without showing any significant errors.
2. Freiburg Campus: The second dataset has been recorded outdoors at the Freiburg campus. Our system needed only 30 particles to produce a good quality map, such as the one shown in Fig. 5. Note that this environment partly violates the assumptions that the environment is planar. Additionally, there were objects like bushes and grass, as well as moving objects like cars and people. Despite the resulting spurious measurements,our algorithm was able to generate an accurate map.
3. MIT Killian Court: The third experiment was performed with a dataset acquired at the MIT Killian court1 and the resulting map is depicted in Fig.6. This dataset is extremely challenging, since it contains several nested loops, which can cause an RBPF to fail due to particle depletion. Using this dataset, the selective resampling procedure turned out to be important. A consistent and topologically correct map can be generated with 60 particles. However, the resulting maps sometimes show artificial double walls. By employing 80 particles, it is possible to achieve high-quality maps.
   这里讨论的数据集已经在华盛顿州西雅图的英特尔研究实验室、弗赖堡大学校园和麻省理工学院的基里安法庭（马萨诸塞州剑桥）进行了记录。这些环境的地图如图4-6所示。
   1） 英特尔研究实验室：英特尔研究实验室如图4的左图所示，尺寸为28米乘28米。数据集是由配备有SICK传感器的Pioneer II机器人记录的。为了成功地修正这个数据集，我们的算法只需要15个粒子。如图4的右图所示，最终地图的质量非常高，可以将地图放大到1cm的分辨率，而不显示任何明显的误差。
   2） 弗赖堡校区：第二个数据集已经在弗赖堡校区的室外进行了记录。我们的系统只需要30个粒子就可以生成一个高质量的地图，如图5所示。请注意，此环境在一定程度上违反了环境是平面的假设。此外，还有像灌木丛和草地这样的物体，还有像汽车和人这样的移动物体。尽管产生了虚假的测量结果，我们的算法还是能够生成一个精确的地图。
   3） 麻省理工学院基利安法庭：第三个实验是在麻省理工学院基利安法庭1采集的数据集上进行的，结果地图如图6所示。这个数据集非常具有挑战性，因为它包含几个嵌套循环，这可能会导致RBPF由于粒子耗尽而失败。 ；使用这个数据集，选择性重采样过程变得非常重要。一个一致和拓扑正确的地图可以生成60个粒子。然而，生成的地图有时会显示人造的双层墙。通过使用80个粒子，可以获得高质量的地图。
   B. Quantitative Results
   In order to measure the improvement in terms of the number of particles, we compared the performance of our system using the informed proposal distribution with the approach done byHähnel et al. [5]. Table II summarizes the number of particles needed by an RBPF for providing a topologically correct map in at least 60% of all applications of our algorithm.
   It turns out that in all of the cases, the number of particles required by our approach was approximately one order of magnitude smaller than the one required by the other approach. Moreover, the resulting maps are better, due to our improved sampling process that takes the last reading into account.
   Fig. 7 summarizes results about the success ratio of our algorithm in the environments considered here. The plots show the percentage of correctly generated maps, depending on the number of particles used. The question of whether a map is consistent or not has been evaluated by visual inspection in a blind fashion (the inspectors were not the authors). As a measure of success, we used the topological correctness.
   为了衡量粒子数量的改进，我们将使用信息建议分布的系统的性能与hähnel[5]等人所做的方法进行了比较。表二总结了在我们算法的所有应用中至少60%的RBPF提供拓扑正确建图所需的粒子数。
   结果表明，在所有情况下，我们的方法所需的粒子数大约比另一种方法所需的粒子数小一个数量级。此外，由于我们改进了采样过程，并考虑了最后一次读数，因此得到的地图更好。
   图7总结了我们的算法在这里所考虑的环境中的成功率的结果。这些图显示了正确生成的贴图的百分比，具体取决于使用的粒子数。地图是否一致的问题是通过盲目的视觉检查来评估的（检查员不是作者）。为了衡量成功与否，我们使用了拓扑正确性。

C. Effects of Improved Proposals and Adaptive Resampling
The increased performance of our approach is due to the interplay of two factors, namely, the improved proposal distribution,which allows us to generate samples with a high likelihood, and the adaptive resampling controlled by monitoring N_eff. For proposals that do not consider the whole input history, it has been proven that N_effcan only decrease (stochastically) over time [13]. Only after a resampling operation, N_eff recovers its maximum value. It is important to notice that the behavior of N_eff depends on the proposal: the worse the proposal, the faster N_eff drops.
We found that the evolution of N_eff using our proposal distribution shows three different behaviors, depending on the information obtained from the robot’s sensors. Fig. 8 illustrates the evolution of N_(eff )during an experiment. Whenever the robot moves through unknown terrain, N_efftypically drops slowly.This is because the proposal distribution becomes less peaked,and the likelihoods of observations often differ slightly. The second behavior can be observed when the robot moves through a known area. In this case, each particle keeps localized within its own map, due to the improved proposal distribution, and the weights are more or less equal. This results in a more or less constant behavior of N_eff. Finally, when closing a loop, some particles are correctly aligned with their map, while others are not. The correct particles have a high weight, while the wrong ones have a low weight. Thus, the variance of the importance weights increases, and N_eff substantially drops.
Accordingly, the threshold criterion applied on N_eff typically forces a resampling action when the robot is closing a loop. In all other cases, the resampling is avoided, and in this way, the filter keeps a variety of samples in the particle set. As a result, the risk of the particle-depletion problem is seriously reduced.To analyze this, we performed an experiment in which we compared the success rate of our algorithm with that of a particle filter which resamples at every step. As Fig. 7 illustrates, our approach more often converged to the correct solution (MIT curve) for the MIT dataset, compared with the particle filter with the same number of particles and a fixed resampling strategy(MIT-2 curve).
To give a more detailed impression about the accuracy of our new mapping technique, Fig. 9 depicts maps learned from wellknown and freely available [25] real robot datasets recorded at the University of Texas, at the University of Washington, at Belgioioso, and at the University of Freiburg. Each map was built using 30 particles to represent the posterior about maps and poses.
我们的方法的性能提高是由于两个因素的相互作用，即改进的建议分布，它允许我们生成具有高可能性的样本，以及通过监测N_eff控制的自适应重采样。对于不考虑整个输入历史的建议分布，已经证明N_eff只会随着时间的推移而减少（随机地）。只有在重新采样操作之后，N_eff才能恢复其最大值。重要的是要注意到N_eff的行为取决于建议分布：建议分布越差，N_eff下降越快。
我们发现，根据从机器人传感器获得的信息，使用我们的建议分布的N_eff的演化显示出三种不同的行为。图8示出了N_eff在实验期间的演变。当机器人在未知的地形中移动时，N_eff通常会下降慢慢地。这个是因为建议分布变得不那么高峰，而且观察结果的可能性往往略有不同。当机器人通过一个已知区域时，可以观察到第二种行为。在这种情况下，由于改进了建议分布，每个粒子都在其自身的地图内保持局部化，并且权重或多或少相等。这会导致N_eff或多或少的恒定行为。最后，当关闭循环时，一些粒子与它们的地图正确对齐，而其他粒子则不对齐。正确的粒子有很高的重量，而错误的粒子有很低的重量。因此，重要性权重的方差增加，N_eff显著下降。

因此，当机器人正在闭合回路时，应用于N_eff的阈值标准通常强制执行重采样动作。在所有其他情况下，都会避免重采样，这样，过滤器会在粒子集中保留各种采样。因此，微粒耗尽问题的风险严重减少，我们进行了一个实验，我们比较了我们的算法和粒子滤波器的成功率，后者在每一步都重新采样。如图7所示，与具有相同数量粒子和固定重采样策略（MIT-2曲线）的粒子滤波器相比，我们的方法更经常收敛到MIT数据集的正确解（MIT曲线）。
为了更详细地了解我们新的建图技术的准确性，图9描绘了从德州大学、华盛顿大学、贝尔吉奥西奥大学和弗赖堡大学记录的知名和免费的[25]真实机器人数据集中学习到的地图。每个地图都是用30个粒子来表示地图和姿势的后延。

D. The Influence of the Odometry on the Proposal
This experiment is designed to show the advantage of the proposal distribution, which takes into account the odometry information to draw particles. In most cases, the purely laser-based proposal, like the one presented in our previous approach [11]is well-suited to predict the motion of the particles. However, in a few situations, the knowledge about the odometry information can be important to focus the proposal distribution. This is the case if only very poor features are available in the laser data that was used to compute the parameters of the Gaussian proposal approximation. For example, an open free space without any obstacles or a long featureless corridor can lead to high variances in the computed proposal that is only based on laser range-finder data. Fig. 10 illustrates this effect based on simulated laser data.
In a further experiment, we simulated a short-range laser scanner (like, e.g., the Hokuyo URG scanner). Due to the maximum range of 4 m, the robot was unable to see the end of the corridor in most cases. This results in a high pose uncertainty in the direction of the corridor. We recorded several trajectories in this environment, and used them to learn maps with and without considering the odometry when computing the proposal distribution. In this experiment, the approach considering the odometry succeeded in 100% of cases to learn a topologically correct map. Contrast to that our previous approach, which does not take into account the odometry, and succeeded only in 50% of cases. This experiment indicates the importance of the improved proposal distribution. Fig. 11 depicts typical maps obtained with the different proposal distributions during this experiment. The left map contains alignment errors caused by the high pose uncertainty in the direction of the corridor. In contrast to that, a robot that also takes into account the odometry was able to maintain the correct pose hypotheses. A typical example is depicted in the right image.
Note that by increasing the number of particles, both approaches are able to map the environment correctly in 100% of cases, but since each particle carries its own map, it is of utmost importance to keep the number of particles as low as possible.Therefore, this improved proposal is a means to limit the number of particles during mapping with RBPFs.
本实验的目的是展示提议分布的优点，它考虑了里程信息来绘制粒子。在大多数情况下，纯粹基于激光的提议，就像我们在前面的方法[11]中提出的提议，非常适合预测粒子的运动。然而，在一些情况下，关于里程信息的知识对于关注建议分布是很重要的。如果用于计算高斯建议近似参数的激光数据中只有非常差的特征可用，则会出现这种情况。例如，没有任何障碍物的开放自由空间或长的无特征走廊可能导致仅基于激光测距仪数据的计算方案中的高方差。图10示出了基于模拟激光数据的这种效果。

在进一步的实验中，我们模拟了短程激光扫描器（例如，Hokuyo-URG扫描器）。由于最大射程为4米，机器人在大多数情况下都看不到走廊的尽头。这将导致走廊方向的高姿态不确定性。我们在这个环境中记录了几个轨迹，并在计算建议分布时使用它们来学习有或没有考虑里程的地图。在这个实验中，考虑里程计的方法在100%的情况下成功地学习了拓扑正确的地图。与我们之前的方法不同，我们之前的方法没有考虑里程计，并且只在50%的情况下成功。实验表明了改进建议分布的重要性。图11描绘了在该实验期间用不同的建议分布获得的典型地图。左侧地图包含由于道路方向上的高姿态不确定性而导致的路线误差。与此相反，一个同时考虑了里程计的机器人能够保持正确的姿势假设。典型的例子如右图所示。

请注意，通过增加粒子数，两种方法都能在100%的情况下正确地对环境进行建图，但是由于每个粒子都有自己的地图，因此将粒子数尽可能保持在低数量。因此, 该改进建议分布是一种在RBPFs建图过程中限制粒子数量的方法。
E. Situations in Which the Scan-Matcher Fails
As reported in Section III, it can happen that the scan-matcher is unable to find a good pose estimate based on the laser range data. In this case, we sample from the raw odometry model to obtain the next generation of particles. In most tested indoor datasets, however, such a situation never occurred at all. In the MIT dataset, this effect was observed once, due to a person walking directly in front of the robot while the robot was moving though a corridor that mainly consists of glass panes.
In outdoor datasets, such a situation can occur if the robot moves through large open spaces, because in this case, the laser range finder mainly reports maximum-range readings. While mapping the Freiburg campus, the scan-matcher also reported such an error at one point. In this particular situation, the robot entered the parking area (in the upper part of the map, compare Fig. 5). On that day, all cars were removed from the parking area due to construction work. As a result, no cars or other objects caused reflections of the laser beams, and most parts of the scan consisted of maximum-range readings. In such a situation, the odometry information provides the best pose estimate, and this information is used by our mapping system to predict the motion of the vehicle.
如第三节所述，扫描匹配器可能无法根据激光测距数据找到良好的姿态估计。在这种情况下，我们从原始的里程模型中取样以获得下一代粒子。然而，在大多数测试的室内数据集中，这种情况从未发生过。在麻省理工学院（MIT）的数据集中，有一次观察到了这种效果，这是因为一个人在机器人正前方行走，而机器人正穿过一条主要由玻璃窗组成的走廊。
在室外数据集中，如果机器人通过大的开放空间移动，可能会出现这种情况，因为在这种情况下，激光测距仪主要报告最大距离读数。在绘制弗赖堡校区地图时，扫描匹配器也曾报告过这样一个错误。在这种特殊情况下，机器人进入停车区（在地图的上部，比较图5）。当天，由于施工，所有车辆都被从停车场移走。结果，没有汽车或其他物体引起激光束的反射，扫描的大部分由最大范围读数组成。在这种情况下，里程信息提供了最佳的姿态估计，我们的地图系统使用此信息来预测车辆的运动。
F. Runtime Analysis
In this last experiment, we analyze the memory and computational resources needed by our mapping system. We used a standard PC with a 2.8-GHz processor. We recorded the average memory usage and execution time, using the default parameters that allows our algorithm to learn correct maps for nearly all real-world datasets provided to us. In this setting, 30 particles are used to represent the posterior about maps and poses,and a new observation, consisting of a full laser range scan, is integrated whenever the robot moved more than 0.5 m or rotated more than 25 . The Intel Research Lab dataset (see Fig. 4) contains odometry and laser range readings which have been recorded over 45 min. Our implementation required 150 MB of memory to store all the data, using maps with a size of approximately 40 m by 40 m and a grid resolution of 5 cm. The overall time to correct the log file using our software was less than 30 min. This means that the time to record a log file is around 1.5 times longer than the time to correct the log file.Table III depicts the average execution time for the individual operations.

VII. RELATED WORK
Mapping techniques for mobile robots can be roughly classified according to the map representation and the underlying estimation technique. One popular map representation is the occupancy grid [12]. Whereas such grid-based approaches are computationally expensive and typically require a huge amount of memory, they are able to represent arbitrary objects. Feature-based representations are attractive because of their compactness. However, they rely on predefined feature extractors,which assumes that some structures in the environments are known in advance.
移动机器人的地图绘制技术可以根据地图表示和基本估计技术进行大致分类。一个流行的地图表示是占用网格[12]。尽管这种基于网格的方法在计算上很昂贵，而且通常需要大量内存，但它们能够表示任意对象。基于特征的表示方法由于其紧凑性而备受关注。但是，它们依赖于预定义的特征提取程序，该程序假定环境中的某些结构是预先已知的。
The estimation algorithms can be roughly classified according to their underlying basic principle. The most popular approaches are EKFs, maximum-likelihood (ML) techniques, sparse extended information filters (SEIFs), smoothing techniques, and RBPFs. The effectiveness of the EKF approaches comes from the fact that they estimate a fully correlated posterior over landmark maps and robot poses [26], [27]. Their weakness lies in the strong assumptions that have to be made on both the robot motion model and the sensor noise. Moreover,the landmarks are assumed to be uniquely identifiable. There exist techniques [28] to deal with unknown data association in the SLAM context; however, if these assumptions are violated,the filter is likely to diverge [29]. Similar observations have been reported by Julier et al. [30], as well as by Uhlmann [31].The unscented Kalman filter described in [30] is one way of better dealing with the nonlinearities in the motion model of the vehicle.
估计算法可以根据其基本原理大致分类。最流行的方法是EKFs、最大似然（ML）技术、稀疏扩展信息滤波器（seif）、平滑技术和RBPFs。EKF方法的有效性来自于这样一个事实：它们估计了一个完全相关的后验过地标地图和机器人姿势[26]，[27]。它们的弱点在于必须对机器人的运动模型和传感器噪声做出强有力的假设。此外，地标被认为是唯一可识别的。存在处理SLAM上下文中未知数据关联的技术[28]；但是，如果违反了这些假设，过滤器可能会发散[29]。Julier等人也报告了类似的观察结果。[30]和Uhlmann[31]所述的[30]中的无迹卡尔曼滤波器是更好地处理车辆运动模型中非线性的一种方法。
A popular ML algorithm computes the most likely map, given the history of sensor readings, by constructing a network of relations that represents the spatial constraints between the poses of the robot [4], [19], [32], [33]. Gutmann et al. [4] proposed an effective way for constructing such a network and for detecting loop closures, while running an incremental ML algorithm. When a loop closure is detected, a global optimization on the network of relation is performed. Recently, Hähnel et al.[34], proposed an approach which is able to track several map hypotheses using an association tree. However, the necessary expansions of this tree can prevent the approach from being feasible for real-time operation.
一种流行的ML算法通过构造一个关系网络来计算给定传感器读数历史的最可能地图，该网络表示机器人姿态之间的空间约束[4]、[19]、[32]、[33]。Gutmann等人。[4] 提出了一种在运行增量ML算法的同时，构造此类网络和检测环路闭合的有效方法。当检测到环路闭合时，对关系网络进行全局优化。最近，Hähnel等人[34]提出了一种利用关联树跟踪多个地图假设的方法。然而，对该树进行必要的扩展可以防止该方法对实时操作的可行性。
Thrun et al. [35] proposed a method to correct the poses of robots based on the inverse of the covariance matrix. The advantage of the SEIFs is that they make use of the approximative sparsity of the information matrix, and in this way, can perform predictions and updates in constant time. Eustice et al. [36] presented a technique to make use of exactly sparse information matrices in a delayed-state framework. Paskin [37] presented a solution to the SLAM problem using thin junction trees. In this way, he is able to reduce the complexity compared with the EKF approaches, since thinned junction trees provide a linear-time filtering operation.
Thrun等人。[35]提出了一种基于协方差逆矩阵的机器人姿态校正方法。seif的优点是利用了信息矩阵的近似稀疏性，可以在恒定时间内进行预测和更新。Eustice等人。[36]提出了一种在延迟状态框架中使用精确稀疏信息矩阵的技术。Paskin[37]提出了一种利用细连接树解决SLAM问题的方法。与EKF方法相比，这种方法能够降低复杂度，因为细化的连接树提供线性时间滤波操作。
Folkessen et al. [38] proposed an effective approach for dealing with symmetries and invariants that can be found in landmark-based representation. This is achieved by representing each feature in a low-dimensional space (measurement subspace) and in the metric space. The measurement subspace captures an invariant of the landmark, while the metric space represents the dense information about the feature. A mapping between the measurement subspace and the metric space is dynamically evaluated and refined as new observations are acquired. Such a mapping can take into account spatial constraints between different features. This allows the authors to consider these relations for updating the map estimate.
Folkessen等人。[38]提出了一种处理基于地标的表示中对称性和不变量的有效方法。这是通过在低维空间（测量子空间）和度量空间中表示每个特征来实现的。测量子空间捕捉地标的一个不变量，而度量空间表示关于特征的密集信息。测量子空间和度量空间之间的映射在获取新的观测值时被动态地评估和细化。这种建图可以考虑不同特征之间的空间约束。这使得作者可以考虑这些关系来更新地图估计。
Very recently, Dellaert proposed a smoothing method called square-root smoothing and mapping [39]. It has several advantages compared with EKF, since it better covers the nonlinearities and is faster to compute. In contrast to SEIFs, it furthermore provides an exactly sparse factorization of the information matrix.
最近，Dellaert提出了一种称为平方根平滑和建图的平滑方法[39]。与EKF相比，它具有较好的非线性覆盖能力和计算速度。与seif相比，它还提供了信息矩阵的精确稀疏分解。
In work by Murphy, Doucet, and colleagues [2], [8], RBPF have been introduced as an effective means to solve the SLAM problem. Each particle in an RBPF represents a possible robot trajectory and a map. The framework has been subsequently extended by Montemerlo et al. [7], [40] for approaching the SLAM problem with landmark maps. To learn accurate grid maps, RBPFs have been used by Eliazar and Parr [3] and Hähnel et al. [5]. Whereas the first work describes an efficient map representation, the second presents an improved motion model that reduces the number of required particles. Based on the approach of Hähnel et al., Howard presented an approach to learn grid maps with multiple robots [41]. The focus of this work lies in how to merge the information obtained by the individual robots, and not in how to compute better proposal distributions.
在Murphy，Doucet和他的同事的工作中[2]，[8]，RBPF被引入作为解决SLAM问题的有效手段。RBPF中的每个粒子代表一个可能的机器人轨迹和一个地图。Montemerlo等人随后对该框架进行了扩展。[7] ，[40]用地标地图解决了SLAM问题。为了学习精确的栅格地图，Eliazar和Parr[3]以及Hähnel等人使用了RBPFs。[5] 是的。第一个工作描述了一个有效的地图表示，第二个工作提出了一个改进的运动模型，减少了所需的粒子数量。基于Hähnel等人的方法，Howard提出了一种多机器人学习网格地图的方法[41]。这项工作的重点在于如何合并各个机器人获得的信息，而不是如何计算更好的建议分布。
Bosse et al. [42] describe a generic framework for SLAM in large-scale environments. They use a graph structure of local maps with relative coordinate frames, and always represent the uncertainty with respect to a local frame. In this way, they are able to reduce the complexity of the overall problem. In this context, Modayil et al. [43] presented a technique which combines metrical SLAM with topological SLAM. The topology is used to solve the loop-closing problem, whereas metric information is used to build up local structures. Similar ideas have been realized by Lisien et al. [44], which introduce a hierarchical map in the context of SLAM.
Bosse等人。[42]描述大规模环境中SLAM的通用框架。它们使用具有相对坐标框架的局部地图的图形结构，并且总是表示相对于局部框架的不确定性。这样，他们就能降低整个问题的复杂性。在这方面，Modayil等人。[43]提出了一种度量SLAM和拓扑SLAM相结合的方法。拓扑结构用于解决闭环问题，而度量信息用于建立局部结构。Lisien等人也实现了类似的想法。[44]，它引入了SLAM上下文中的层次图。
The work described in this paper is an improvement of the algorithm proposed by Hähnel et al. [5]. Instead of using a fixed proposal distribution, our algorithm computes an improved proposal distribution on a per-particle basis on the fly. This allows us to directly use the information obtained from the sensors while evolving the particles. The work presented here is also an extension of our previous approach [11], which lacks the ability to incorporate the odometry information into the proposal. Especially, in critical situations in which only poor laser features for localization are available, our current approach performs better than our previous one.
本文的工作是对Hähnel等人提出的算法的改进。[5] 是的。我们的算法不使用固定的建议分布，而是根据每个粒子动态计算一个改进的建议分布。这使得我们可以在进化粒子的同时直接使用从传感器获得的信息。本文提出的工作也是我们先前方法[11]的一个扩展，该方法缺乏将里程计信息纳入建议分布的能力。特别是，在只有较差的激光定位功能可用的关键情况下，我们目前的方法比我们以前的方法表现更好。
The computation of the proposal distribution is done in a similar way as in FastSLAM-2, presented by Montemerlo et al. [6].In contrast to FastSLAM-2, our approach does not rely on predefined landmarks, and uses raw laser range-finder data to acquire accurate grid maps. Particle filters using proposal distributions that take into account the most recent observation are also called look-ahead particle filters. Moralez-Menéndez et al. [14]proposed such a method to more reliably estimate the state of a dynamic system where accurate sensors are available.
建议分布的计算方法与Montemerlo等人在FastSLAM-2中提出的方法类似[6] 。与FastSLAM-2相比，我们的方法不依赖预先定义的地标，而是使用原始的激光测距数据来获取精确的栅格地图。使用考虑到最新观测的建议分布的粒子过滤器也称为前瞻粒子过滤器。Moralez Mennendez等人。[14] 提出了一种更可靠地估计有精确传感器的动态系统状态的方法。
The advantage of our approach is twofold. First, our algorithm draws the particles in a more effective way. Second, the highly accurate proposal distribution allows us to use the effective sample size as a robust indicator to decide whether or not a resampling has to be carried out. This further reduces the risk of particle depletion.
我们的方法有两个优点。首先，我们的算法以更有效的方式绘制粒子。其次，高精度的建议分布允许我们使用有效样本量作为稳健的指标来决定是否必须进行重新采样。这进一步降低了粒子耗散的风险。
VIII. CONCLUSIONS
In this paper, we presented an improved approach to learning grid maps with RBPFs. Our approach computes a highly accurate proposal distribution based on the observation likelihood of the most recent sensor information, the odometry, and a scanmatching process. This allows us to draw particles in a more accurate manner, which seriously reduces the number of required samples. Additionally, we apply a selective resampling strategy based on the effective sample size. This approach reduces the number of unnecessary resampling actions in the particle filter,and thus substantially reduces the risk of particle depletion.
本文提出了一种改进的RBPFs学习网格地图的方法。我们的方法基于最新传感器信息、里程计和扫描匹配过程的观测可能性计算高精度的建议分布。这使我们能够以更精确的方式绘制粒子，从而大大减少所需样本的数量。此外，我们应用基于有效样本量的选择性重采样策略。这种方法减少了粒子过滤器中不必要的重采样操作的数量，从而大大降低了粒子耗尽的风险。
Our approach has been implemented and evaluated on data acquired with different mobile robots equipped with laser range scanners. Tests performed with our algorithm in different largescale environments have demonstrated its robustness and ability to generate high-quality maps. In these experiments, the number of particles needed by our approach often was one order of magnitude smaller, compared with previous approaches.
我们的方法已经在不同的移动机器人配备激光测距仪的数据采集上得到了实现和评估。该算法在不同的大尺度环境下进行了实验，证明了其鲁棒性和生成高质量地图的能力。在这些实验中，我们的方法所需的粒子数通常比以前的方法小一个数量级。