概率机器人学：不确定性与贝叶斯滤波

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《概率机器人学》是一本由Sebastian Thrun、Wolfram Burgard和Dieter Fox合著的专业书籍，主要探讨了在机器人技术领域的不确定性处理和概率方法应用。书中强调了在机器人系统中，由于环境的复杂性和感知的不精确性，不确定性是无法避免的。作者从不确定性在机器人中的基本概念入手，深入阐述了如何通过概率论的原理来解决这些问题。在第1章"Introduction"中，作者介绍了不确定性在机器人操作中的核心地位，指出机器人必须能够处理各种形式的不确定性，包括传感器噪声、环境变化和动态模型的不完全性。接着，章节探讨了概率机器人学这一概念，它旨在将概率理论融入机器人设计，以更有效地处理这些不确定性。第2章"Recursive State Estimation"（递归状态估计）是本书的重点部分。该章节详细讲解了基本的概率概念，如状态、环境交互和概率生成律，这些都是构建机器人行为模型的基础。作者介绍了信念分布，这是一种用来表示对机器人状态不确定性量度的方式，通过贝叶斯滤波器（Bayes Filters）来更新和融合传感器数据。贝叶斯滤波器算法是关键，它利用贝叶斯定理在不断收到新信息时动态更新对机器人状态的估计，即使在非马尔可夫（non-Markovian）环境中也能保持准确性。章节中还通过实例和数学推导深入解析了贝叶斯滤波器的工作原理，特别是马尔可夫假设在简化计算中的作用。此外，还讨论了状态的表示和计算问题，以及如何将这些理论应用于实际的机器人系统中。第3章"Gaussian Filters"进一步深化了对线性高斯系统的理解，如卡尔曼滤波器（Kalman Filter），这是处理高维随机过程和线性系统的理想工具。这部分内容对控制和导航任务中的机器人定位与避障至关重要。总体来说，《概率机器人学》是一本深入浅出的指南，为读者展示了如何利用概率方法在机器人领域解决复杂问题，提供了一种强大的工具集，使机器人能够适应不断变化的环境，并实现智能决策。对于从事机器人技术研究、开发AGV（自动导引车）或其他依赖于高级感知和决策系统的工程师和研究人员来说，这本书是不可或缺的参考资料。

4 Chapter 1

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Figure 1.1 The basic idea of Markov localization: A mobile robot during global localiza-

tion.

Introduction 5

This example illustrates the probabilistic paradigm in the context of a speciﬁc per-

ceptual problem. Stated probabilistically, the robot perception problem is a state es-

timation problem, and our localization example uses an algorithm known as Bayes

ﬁlter for posterior estimation over the space of robot locations. Similarly, when select-

ing actions, probabilistic approaches considers the full uncertainty, not just the most

likely guess. By doing so, the probabilistic approach trades off information gathering

(exploration) and exploitation, and act optimally relative to the state of knowledge.

1.3 IMPLICATIONS

What are the advantages of programming robots probabilistically, when compared to

other approaches that do not represent uncertainty explicitly? Our central conjecture

is nothing less than the following:

A robot that carries a notion of its own uncertainty and that acts accordingly

is superior to one that does not.

In particular, probabilistic approaches are typically more robust in the face of sensor

limitations, sensor noise, environment dynamics, and so on. They often scale much

better to complex and unstructured environments, where the ability to handle uncer-

tainty is of even greater importance. In fact, certain probabilistic algorithms are cur-

rently the only known working solutions to hard robotic estimation problems, such as

the kidnapped robot problem, in which a mobile robot must recover from localization

failure; or the problem of building accurate maps of very large environments, in the

absence of a global positioning device such as GPS. Additionally, probabilistic algo-

rithms make much weaker requirements on the accuracy of models than many classical

planning algorithms do, thereby relieving the programmer from the unsurmountable

burden to come up with accurate models. Viewed probabilistically, the robot learning

problem is a long-term estimation problem. Thus, probabilistic algorithms provide a

sound methodology for many ﬂavors of robot learning. And ﬁnally, probabilistic al-

gorithms are broadly applicable to virtually every problem involving perception and

action in the real world.

However, these advantages come at a price. Traditionally, the two most frequently

cited limitations of probabilistic algorithms are computational inefﬁciency, and a

need to approximate. Probabilistic algorithms are inherently less efﬁcient than non-

probabilistic ones, due to the fact that they consider entire probability densities. The

need to approximate arises from the fact that most robot worlds are continuous. Com-

puting exact posterior distributions is typically infeasible, since distributions over the

6 Chapter 1

continuum possess inﬁnitely many dimensions. Sometimes, one is fortunate in that

the uncertainty can approximated tightly with a compact parametric model (e.g., dis-

crete distributions or Gaussians); in other cases, such approximations are too crude

and more complicated representations most be employed. Recent research has suc-

cessfully led to a range of are computationally efﬁcient probabilistic algorithms, for a

range of hard robotics problems—many of which are described in depth in this book.

1.4 ROAD MAP

This book attempts to provide a comprehensive and in-depth introduction into proba-

bilistic robotics. The choice of material is somewhat biased towards research carried

out at Carnegie Mellon University, the University of Bonn, and afﬁliated labs. How-

ever, we have attempted to include in-depth descriptions of other, important proba-

bilistic algorithms. The algorithms described here have been developed for mobile

robots; however, many of them are equally applicable to other types of robots. Thus,

the coverage of the material is by no means complete; probabilistic ideas have recently

become extremely popular in robotics, and a complete description of the ﬁeld would

simply not ﬁt into a single book. However, we believe that the choice of material is

representative for the existing body of literature.

The goal of the book is to provide a systematic introduction into the probabilistic

paradigm, from the underlying mathematical framework to implementation. For each

major algorithm, this book provides

a complete mathematical derivation,

pseudo-code in a C-like language,

discussions of implementation details and potential pitfalls, and

empirical results obtained in ﬁelded systems.

We believe that all four items are essential for obtaining a deep understanding of the

probabilistic paradigm. At the end of each chapter, the book also provides biblio-

graphical notes and a list of questions and exercises.

The book has been written with researchers, graduate students or advanced undergrad-

uate students in mind, specializing in robotics or applied statistics. We have attempted

to present the material in a way that requires a minimum of background knowledge.

Introduction 7

However, basic knowledge of probability theory will almost certainly help in under-

standing the material. The various mathematical derivations can easily be skipped at

ﬁrst reading. However, we strongly recommend to take the time and study the mathe-

matical derivations, as a profound mathematical understanding is will almost certainly

lead to deep and important insights into the working of the probabilistic approach to

robotics.

If used in the classroom, each chapter should be covered in one or two lectures; how-

ever, we recommend that the study of the book be accompanied by practical, hands-on

experimentation as directed by the questions and exercises at the end of each chapter.

This book is organized in four major parts.

The ﬁrst part, Chapters 2 through 5, discuss the basic mathematical framework

that underlies all of the algorithms described in this book. Chapters 2 through 4

introduce the basic probabilistic notation and describes a collection of ﬁlters for

probabilistic state estimation. Chapter 5 discusses speciﬁc probabilistic models

that characterize mobile robot perception and motion.

The second part, which comprised Chapters 7 to ??, describes a range of per-

ceptual algorithms, which map sensor measurements into internal robot beliefs.

In particular, Chapter 7 describes algorihtms for mobile robot localization, fol-

lowed by algorithms for map acquisition described in Chapters ??. This part also

contains a chapter on learning models.

The third part, in Chapters ?? to ??, introduces probabilistic planning and action

selection algorihtms.

Finally, Chapter ?? describes two robot systems that were controlled by proba-

bilistic algorithms. These robots were deployed in museums as interactive tour-

guide robots, where they managed to navigate reliably without the need to modify

the museums in any way.

The book is best read in order, from the beginning to the end. However, we have

attempted to make each individual chapter self-explanatory.

1.5 BIBLIOGRAPHICAL REMARKS

The term “robot” was invented in 1921 by the Czech novelist Karel

Capek [42], to describe a willing,

intelligent and human-like machines that make life pleasant by doing the type work we don’t like to do. In

the Fourties, Asimov coined the term “robotics” and postulated the famous three laws of robotics [1, 2],

8 Chapter 1

Robotics, as a scientiﬁc discipline has been an active ﬁeld of research foer several decades. In the early

years, most of the research focused on

Major trends in robotics:

Seventies: classical (deliberate) approach, accurate models, no uncertainty, no sensing. Still: very

hard problem. Reif: planning problem NP hard, but only doubly exponential algorithms known.

Canny: ﬁrst single exponential planning algorithm. Latombe: Many impressive randomized planning

algorithms. Important difference: randomization used for search, not for representing uncertainty.

Planning algorithm for special topologies: Schwartz, and Sharir. Some take sensor data into account.

Koditschek navigation function for feedback control, generalizes Khatib’s potential ﬁelds, which suf-

fer from local minima (navigation functions don’t).

Mid-Eighties: reactive approach, rejection of models, pure reliance on sensors, uncertainty (if any)

handled by feedback control. Relies on sensor data carrying sufﬁcient information for action selec-

tion, therefore uncertainty not an issue. Typically conﬁned to small environments, where everything

of importance can be perceived by the sensors. Nevertheless, some impressive results for control of

legged robots. Brooks, Mataric, Steels, Connell, and many others. Biologically inspired robotics.

Smithers.

Mid-Nineties: Hybrid approaches, reactive at low level (fast decision cycle), deliberate at higher

levels. Uses sensing mostly at low level, and models at high level. Gat, Arkins, Balch, Firby, Simmons

and many others. harvests best of both worlds: robust through reaction, but can do more powerful

tasks due to deliberation.

Late Ninties: Probabilistic robotics, different way to integrate models and sensor data.

Probabilistic robotics can be traced back to Sixties to advent of Kalman ﬁlters, which has been used exten-

sively in robotics. First serious advance is Smith and Cheeseman in mid-80s, who proppose an algorithm for

concurrent mapping and localization based on Kalman ﬁlters that is now in widespread use. Durrant-Whyte,

Leonard, Castellanos, and many others.

Main activity in past ﬁve years. Main advances: more ﬂexible representations (beyond Kalman ﬁlters),

more efﬁcient algorithms. Statistical approaches for solving hard correspondence problems.

What is new in probabilistic robotics, relative to approaches above?

seamlessly blends models and perception in a novel way

sound mathematical theory, clear assumptions, therefore it’s easier to predict failure modes

applies to all levels: lowest to highest, since uncertainty arises everywhere

currently the best known solutions in a range of hard robotics problems

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