Rao-Blackwellized粒子滤波提升Gmapping算法理解
需积分: 26 190 浏览量
更新于2024-09-04
收藏 1.16MB PDF 举报
本文主要探讨了"Improved Techniques for Grid Mapping With Rao-Blackwellized Particle Filters"，发表在2007年3月的IEEE Transactions on Robotics上。论文的作者包括Giorgio Grisetti、Cyrill Stachniss和Wolfram Burgard，他们均来自德国弗莱堡大学。文章的核心内容集中在Rao-Blackwellized粒子滤波（Rao-Blackwellized Particle Filters, RBPF）在网格地图构建（Grid Mapping）中的优化方法上。
Rao-Blackwellization是一种统计学上的概念，用于改进粒子滤波器的性能，特别是在处理高维状态空间时。粒子滤波是Simultaneous Localization and Mapping (SLAM)领域中的重要技术，它通过将传感器数据与机器人运动模型结合，实现对未知环境的建图和自身定位。传统的粒子滤波可能会因为维度膨胀问题而效率低下，Rao-Blackwellization通过将部分随机变量的后验分布分解出来，降低了计算复杂性，并提高了估计精度。
Gmapping算法是基于概率图模型的SLAM方法，它通常用于构建静态障碍物地图，利用激光雷达数据生成栅格地图。原始的Gmapping算法可能依赖大量粒子来保持地图的准确性，但Rao-Blackwellized粒子滤波的引入允许更有效地利用信息，减少了粒子数量，从而降低了内存消耗和计算需求。
文章讨论了如何将Rao-Blackwellization应用到Gmapping中，可能包括改进的采样策略、信息融合方法以及如何处理不确定性。此外，文中还可能涉及了实际的实验结果和性能评估，展示了RBPF在处理复杂环境和动态障碍物时的优越性。
除了技术层面的阐述，该文还提及了与之相关的项目，如SA-SHA（Unified Registration of Geometric Primitives）和EUROPA（欧洲项目），这表明作者们不仅关注理论研究，还在实际应用中探索和优化SLAM技术。
Wolfram Burgard作为合著者，他的研究兴趣和贡献对该领域的整体发展有着深远影响。文章上传者在2015年7月9日更新了内容，这可能反映了当时最新的研究成果和改进方向。
阅读这篇论文对于理解Gmapping算法的高级版本以及Rao-Blackwellized粒子滤波在其中的作用至关重要，特别是对于那些对SLAM技术有深入研究或希望在实际环境中应用这些方法的工程师和研究人员来说，无疑是一份宝贵的知识资源。
2
trajectory x
1:t
= x
1
, . . . , x
t
of the robot. This estimation is
performed given the observations z
1:t
= z
1
, . . . , z
t
and the
odometry measurements u
1:t−1
= u
1
, . . . , u
t−1
obtained by
the mobile robot. The Rao-Blackwellized particle filter for
SLAM makes use of the following factorization
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.
Typically, Eq. (1) can be calculated efficiently since the pos-
terior over maps p(m | x
1:t
, z
1:t
) can be computed analytically
using “mapping with known poses” [31] since x
1:t
and z
1:t
are known.
To estimate the posterior p(x
1:t
| z
1:t
, u
1:t−1
) over the po-
tential 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.
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:
1) Sampling: The next generation of particles {x
(i)
t
} is ob-
tained from the generation {x
(i)
t−1
} 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
(i)
t
is assigned to each particle according to the impor-
tance sampling principle
w
(i)
t
=
p(x
(i)
1:t
| z
1:t
, u
1:t−1
)
π(x
(i)
1:t
| z
1:t
, u
1:t−1
)
. (2)
The weights account for the fact that the proposal distri-
bution π is in general not equal to the target distribution
of successor states.
3) Resampling: Particles are drawn with replacement pro-
portional to their importance weight. This step is nec-
essary since only a finite number of particles is used to
approximate a continuous distribution. Furthermore, re-
sampling 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
(i)
1:t
, z
1:t
) is computed based on
the trajectory x
(i)
1:t
of that sample and the history of
observations z
1:t
.
The implementation of this schema requires to evaluate
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. [7], we obtain
a recursive formulation to compute the importance weights by
restricting the proposal π to fulfill the following assumption
π(x
1:t
| z
1:t
, u
1:t−1
) = π(x
t
| x
1:t−1
, z
1:t
, u
1:t−1
)
·π(x
1:t−1
| z
1:t−1
, u
1:t−2
). (3)
Based on Eq. (2) and (3), the weights are computed as
w
(i)
t
=
p(x
(i)
1:t
| z
1:t
, u
1:t−1
)
π(x
(i)
1:t
| z
1:t
, u
1:t−1
)
(4)
=
ηp(z
t
| x
(i)
1:t
, z
1:t−1
)p(x
(i)
t
| x
(i)
t−1
, u
t−1
)
π(x
(i)
t
| x
(i)
1:t−1
, z
1:t
, u
1:t−1
)
·
p(x
(i)
1:t−1
| z
1:t−1
, u
1:t−2
)
π(x
(i)
1:t−1
| z
1:t−1
, u
1:t−2
)
|
{z }
w
(i)
t−1
(5)
∝
p(z
t
| m
(i)
t−1
, x
(i)
t
)p(x
(i)
t
| x
(i)
t−1
, u
t−1
)
π(x
t
| x
(i)
1:t−1
, z
1:t
, u
1:t−1
)
· w
(i)
t−1
.(6)
Here η = 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.
Most of the existing particle filter applications rely on the
recursive structure of Eq. (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. Through-
out the remainder of this paper, we describe a technique that
computes an accurate proposal distribution and that adaptively
performs resampling.
III. RBPF WITH IMPROVED PROPOSALS AND ADAPTIVE
RESAMPLING
In the literature, several methods for computing improved
proposal distributions and for reducing the risk of particle
depletion have been proposed [7, 30, 35]. Our approach applies
two concepts that have previously been identified as key
pre-requisites for efficient particle filter implementations (see
Doucet et al. [7]), namely the computation of an improved
proposal distribution and an adaptive resampling technique.
A. On the Improved Proposal Distribution
As described in Section II, one needs to draw samples from
a proposal distribution π in the prediction step in order to ob-
tain the next generation of particles. Intuitively, the better the
proposal distribution approximates the target distribution, the
better is 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.
As a result, typical particle filter applications [3, 29] use
the odometry motion model as the proposal distribution. This
motion model has the advantage that it is easy to compute for
剩余12页未读，继续阅读
点击了解资源详情
点击了解资源详情
点击了解资源详情
2020-09-17 上传
2022-07-15 上传
2022-07-15 上传
2022-07-14 上传
2021-03-19 上传
2021-06-02 上传
Amanda1m
- 粉丝: 660
- 资源: 11
我的内容管理
展开
