概率机器人学：探索不确定性

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"Probabilistic Robotics" 是一本由Sebastian Thrun、Wolfram Burgard和Dieter Fox合著的专业书籍，被广泛认为是机器人学领域的经典之作，特别适合于研究和学习机器人技术的人群。Sebastian Thrun是谷歌无人车项目的重要创始人之一，因此这本书在自动驾驶和智能机器人领域具有极高的权威性。该书主要探讨了机器人在面对不确定性时如何运用概率方法进行决策和感知。在机器人学中，不确定性是一个普遍存在的问题，它来源于传感器数据的噪声、环境的复杂性和模型的不精确性。作者们引入了概率机器人学的概念，这是一种利用概率理论来处理这些不确定性的方法，使得机器人能够更准确地理解和预测周围环境。书中第1章介绍了不确定性在机器人学中的重要性以及概率机器人学的基本思想和影响。作者阐述了这本书的总体结构和内容概述，同时也提供了相关的文献参考。第2章深入讨论了递归状态估计，这是机器人定位和跟踪的关键技术。这一章涵盖了概率、状态、环境交互的基础概念，以及贝叶斯滤波器的原理和应用。通过数学推导，解释了贝叶斯滤波算法的工作机制，并对马尔科夫假设进行了讲解。此外，还探讨了表示和计算效率的问题，最后进行了总结并推荐了进一步阅读的资料。第3章则聚焦于高斯滤波器，特别是卡尔曼滤波器。卡尔曼滤波器是线性高斯系统中最常用的滤波算法，用于处理系统状态的估计问题。书中详细解释了线性高斯系统的特性，以及如何通过卡尔曼滤波算法实现对这些系统的最优估计。这部分内容为后续章节的高级滤波器理论奠定了基础。 "Probabilistic Robotics" 这本书是机器人学和人工智能领域的一本重要教材，它不仅提供了理论框架，还包含了大量的实例和数学推导，对于理解和实践概率方法在机器人中的应用至关重要。无论是初学者还是经验丰富的专业人士，都能从中获益匪浅，深化对机器人决策与感知过程的理解。

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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