机器人学状态估计：矩阵李群方法

需积分: 2 201 浏览量更新于2024-07-17 1 收藏 4.37MB PDF 举报

"《机器人学的状态估计》是一本详尽阐述状态估计理论的书籍，特别适合于机器人学领域的SLAM（Simultaneous Localization And Mapping，同时定位与建图）学习者。作者Timothy D. Barfoot采用矩阵-李群的方法来探讨这一主题，书中的内容覆盖了概率理论、高斯概率密度函数等核心概念，对于理解和应用机器人状态估计至关重要。" 本书首先介绍了状态估计的历史背景，以及传感器、测量和问题定义的基本概念。它强调了在机器人学中，如何利用传感器数据来估计机器人自身的状态（如位置、速度和姿态）以及环境的信息。接着，书中详细阐述了书的组织结构和与其他相关书籍的关系，以便读者了解其独特之处和学习路径。 Part I“Estimation Machinery”深入探讨了状态估计的基础。第一章介绍了概率论的基础，包括概率密度函数（PDF）的定义、贝叶斯规则、矩、样本均值和协方差、统计独立性、无关联性、熵和互信息，以及Cramér-Rao下界和费舍尔信息。这些概念是理解估计和推断过程的关键。第二章则专门讨论高斯概率密度函数，这是在机器人状态估计中常见的分布类型。这里涵盖了高斯分布的定义、Isserlis定理、联合高斯PDF及其因子、统计独立性和无关联性、线性变量变换、高斯分布的乘积，以及Sherman-Morrison-Woodbury公式等。这些内容为处理含有不确定性数据的线性和非线性估计问题提供了理论工具。这本书不仅适合初学者，也适合希望深入理解状态估计理论的高级读者。通过学习，读者将能够运用矩阵-李群的方法解决实际的机器人定位和感知问题，从而在SLAM等领域取得进展。

4 Introduction

ter (measures angular rate). Typical exteroceptive sensors are the cam-

era (measures range/bearing to a landmark or landmarks), time-of-

ﬂight transmitter/receivers (e.g., laser rangeﬁnder, pseudolites, GPS

transmitter/receiver, and well, the tape measure). Roughly speaking,

we can think of exteroceptive measurements as being of the position

and orientation of a vehicle while interoceptive ones are of a vehicle’s

velocity or acceleration. In most cases, the best state estimation con-

cepts make use of both interoceptive and exteroceptive measurements.

For example, the combination of a GPS receiver (exteroceptive) and

an inertial measurement unit (3 linear accelerometers and 3 rate gy-

ros; interoceptive) is a popular means of estimating a vehicle’s po-

sition/velocity on Earth. And, the combination of a sun/star sensor

(exteroceptive) and three rate gyros (interoceptive) is commonly used

to carry out pose determination on satellites.

Now that we understand a little bit about sensors, we are prepared

to deﬁne the problem that will be investigated in this book:

Estimation is the problem of reconstructing the underlying state of a system given a

sequence of measurements as well as a prior model of the system.

There are many speciﬁc versions of this problem and just as many

solutions. The goal will be to understand which methods work well in

which situations, in order to pick the best tool for the job.

1.3 How This Book is Organized

The book is broken into three main parts:

I: Estimation Machinery

II: Three-Dimensional Machinery

III: Applications

The ﬁrst part, Estimation Machinery, presents classic and state-of-the-

art estimation tools, without the complication of dealing with things

that live in three-dimensional space (and therefore translate and ro-

tate); the state to be estimated is assumed to be a generic vector.

For those not interested in the details of working in three-dimensional

space, this ﬁrst part can be read in a standalone manner. It covers

both recursive state estimation techniques as well as batch methods

(less common in classic estimation books). It contrasts (full) Bayesian

methods with maximum-a-posterior methods, and attempts to make

clear the diﬀerence between these when faced with nonlinear problems.

It also connects continuous-time estimation with Gaussian-process re-

gression from the machine-learning world. Finally, it touches on some

practical issues such as robust estimation and biases.

1.4 Relationship to Other Books 5

The second part, Three-Dimensional Machinery, provides a basic

primer on three-dimensional geometry and gives a detailed but accessi-

ble introduction to matrix Lie groups. To represent an object in three-

dimensional space, we need to talk about that object’s translation and

rotation. The rotational part turns out to be a problem for our estima-

tion tools because rotations are not vectors in the usual sense and so

we cannot naively apply the methods from Part I to three-dimensional

robotics problems involving rotations. Part II, therefore, examines the

geometry, kinematics, and probability/statistics of rotations and poses

(translation plus rotation).

Finally, in the third part, Applications, the ﬁrst two parts of the book

are brought together. We look at a number of classic three-dimensional

estimation problems involving objects translating and rotating in three-

dimensional space. We show how to adapt the methods from Part I

based on the knowledge gained in Part II. The result is a suite of

easy-to-implement methods for three-dimensional state estimation. The

spirit of these examples can also hopefully be adapted to create other

novel techniques moving forwards.

1.4 Relationship to Other Books

There are many other good books on state estimation and robotics,

but very few that cover both topics simultaneously. We brieﬂy describe

a few recent works that do cover both topics and their relationships to

this book.

Probabilistic Robotics by Thrun et al. (2006) is a great introduction

to mobile robotics, with a large focus on state estimation in relation to

mapping and localization. It covers the probabilistic paradigm that is

dominant in much of robotics today. It mainly describes robots operat-

ing in the two-dimensional, horizontal plane. The probabilistic methods

described are not necessarily limited to the two-dimensional case, but

the details of extending to three dimensions are not provided.

Computational Principles of Mobile Robotics by Dudek and Jenkin

(2010) is a great overview book on mobile robotics that touches on state

estimation, again in relation to localization and mapping methods. It

does not work out the details of performing state estimation in three

dimensions.

Mobile Robotics: Mathematics, Models, and Methods by Kelly (2013)

is another excellent book on mobile robotics and covers state estimation

extensively. Three-dimensional situations are covered, particularly in

relation to satellite-based and inertial navigation. As the book covers

all aspects of robotics, it does not delve deeply into how to handle

rotational variables within three-dimensional state estimation.

Robotics, Vision, and Control by Corke (2011) is another great and

comprehensive book that covers state estimation for robotics, including

剩余367页未读，继续阅读

kaiwangtao

粉丝: 1
资源: 5

机器人学状态估计：矩阵李群方法

state estimation for robotics

STATE ESTIMATION FOR ROBOTICS pdf

State Estimation for Robotics20181128

state estimation for Robotics

STATE ESTIMATION FOR ROBOTICS 2017

State estimation for Robotics.pdf

State Estimation for Robotics_20180512

STATE ESTIMATION FOR ROBOTICS.pdf

YOLOv3-训练-修剪.zip

毕业设计&课设_智能算法中台管理系统.zip

最新资源