For autonomous robots, the ability to autonomously create maps of the environment may not, at first glance, seem like a requirement for many tasks. That is, it is sometimes assumed that a robot should be able to take for granted the a priori availability of a map. Unfortunately, this is rarely the case. Not only do architectural blueprints or related types of maps fail to be consistently reliable (since even during construction they are not always updated to reflect necessary alternations), but, furthermore, numerous aspects of an environment are not likely to appear on a map, such as tables, chairs, and transitory objects.

Perhaps equally important, maps usually represent structural elements in some abstract domain (perhaps with semantic labels), while a mobile robot must be able to relate its current location directly to its own perceptions regarding its environment. Maps made for people often depend upon the interpretative skills of the persons using the map and on their ability to make functional inferences, abilities often absent in computational systems.

The first edition of this book arose from a tutorial that was initially presented in 1993. It evolved over a number of years and finally appeared in 2000. Robotics is, of course, a rapidly changing field, and even as the first edition was appearing, it was apparent that it would become dated rather quickly. Thus in late 2002, the first steps were taken toward a second edition.

The field of mobile robotics continues to evolve, and this book has (we hope) evolved with the field. Topics that were in their infancy when the first edition was published – such as SLAM and multi-robot systems – have evolved into much more mature disciplines. The mathematical foundations of much of mobile robotics has also matured, and this too is reflected in this volume. In addition to updating the various algorithms and methods described in the first edition, the second edition is somewhat more self-contained. Specifically, various mathematical techniques that were assumed in the first edition are now introduced, albeit briefly, in appendices at the end of the text.

Anyone who has had to move about in the dark recognizes the importance of vision to human navigation. Tasks that are fraught with difficulty and danger in the dark become straightforward when the lights are on. Given that we seem to navigate effortlessly with vision, it seems natural to consider vision as a sensor for mobile robots. Visual sensing has many desirable potential features, including that facts that it is passive, has high resolution, and is long range.

Human vision relies on two eyes to transform information encoded in light into electrical signals transmitted by neurons. In the biological sciences, the fields of perception and cognition investigate how this neural information is processed to build internal representations of the environment and how humans reason about their environment using these representations. From a robotics point of view, the fields of computer vision and robot vision examine the task of building computer representations of the environment from light, and the study of artificial intelligence deals in part with the task of reasoning or planning based on the resulting environmental representation. Like the previous chapter, this chapter continues the exploration of how to build descriptions of the work from sensor data. In this chapter, we consider the issues involved in sensing using light and related media.

Vision is both strikingly powerful as a sensory medium and strikingly difficult to use in a robotics context.

Sensing is a key requirement for any but the simplest mobile behavior. In order for Robot to be able to warn the crew of Lost in Space that there is danger ahead, it must be able to sense and reason about its sensor responses. Sensing is a critical component of the fundamental tasks of pose estimation – determining where the robot is in its environment; pose maintenance – maintaining an ongoing estimate of the robot's pose; and map construction – building a representation of the robot's environment. This need for sensing is illustrated in Figure 4.1, which shows a time-lapse photograph of a simple robot executing repeated motion in a carpeted lab. As the wheels slip, the true position of the robot deviates from its commanded position. Without external measurements of the outside world this deviation quickly results in the robot becoming “lost.”

In this chapter and the next we consider a range of sensing technologies. The sensors most strongly associated with mobility are those that measure the distance that the vehicle has moved (e.g., the distance the wheels have travelled along the ground), those that measure inertial changes, and those that measure external structure in the environment. For a robot to know where it is or how it got there, or to be able to reason about where it has gone, sensors and sensing algorithms are required.

For numerous tasks a mobile robot needs to know “where it is” either on an ongoing basis or when specific events occur. A robot may need to know its location in order to be able to plan appropriate paths or to know if the current location is the appropriate place at which to perform some operation. Knowing “where the robot is” has many different connotations. In the strongest sense, “knowing where the robot is” involves estimating the location of the robot (in either qualitative or quantitative terms) with respect to some global representation of space: we refer to this as strong localization. The weak localization problem, in contrast, involves merely knowing if the current location has been visited before (this is known as the “have I been here before” problem). In certain cases, complete qualitative maps can be constructed simply from weak positioning information: thus, weak localization can be used to construct maps that can be used subsequently for strong localization. Between the extremes of the weak-localization and the strong-localization problems exists a continuum of different problem specifications that involve knowing where the robot is or estimating the robot's pose.

Robots in fiction seem to be able to engage in complex planning tasks with little or no difficulty. For example, in the novel 2001: A Space Odyssey, HAL is capable of long-range plans and reasoning about the effects and consequences of his actions. It is indeed fortunate that fictional autonomous systems can be presented without having to specify how such devices represent and reason about their environment. Unfortunately, real autonomous systems must make explicit any internal representations and mechanisms for reasoning about them. This chapter considers some of the fundamental computational tasks that must be addressed by a mobile robot: how space should be represented, how to represent the robot itself, and how the robot can reason with respect to its representation of space. These are fundamental tasks for a mobile robot that must plan complex strategies and establish long-term plans.

Although the vast majority of mobile robotic systems involve a single robot operating alone in its environment, a growing number of researchers are considering the challenges and potential advantages of having a group of robots cooperate in order to complete some required task. For some specific robotic tasks, such as exploring an unknown planet, pushing objects, or cleaning up toxic waste, it has been suggested that rather than send one very complex robot to perform the task, it would more effective to send a number of smaller, simpler robots. Such a collection of robots is sometimes described as a swarm, a colony, or a collective, or the robots may be said to exhibit cooperative behavior. Using multiple robots rather than a single robot can have several advantages and leads to a variety of design tradeoffs. Collectives of simple robots may be simpler in terms of individual physical design than a larger, more complex robot, and thus the resulting system can be more economical, more scalable, and less susceptible to task failure.

Robot collectives build on a wide range of research results in distributed algorithms, sensor networks, and biology. As a consequence, the literature on robot collectives spans a wide range with a wide variety of assumptions and goals. One common theme, however, is the desire to develop technology that will enable a group of robots to solve a common problem.

If a mobile robot is to do anything within its environment, it must be able to move and it must be able to sense. The next three chapters consider exactly these problems.

Chapter 3 examines the problems involved in getting a robot to move. Although the vast majority of mobile robots are wheeled, technologies based on aquatic, limbed, or flying robots and even robots based on rocket propulsion exist. Regardless of the technology used to move the robot, two fundamental problems need to be addressed:

• Given the control inputs, how does the robot move? this is known as the forward kinematics problem if the solution does not consider the forces involved in moving the vehicle. If the solution involves an investigation of the forces, then this is known as the forward dynamics problem.

• Given a desired motion, which control inputs should be chosen? This is known as the inverse kinematics problem if the forces to be applied are ignored. If the solution involves an investigation of the forces to be applied, then this is known as the inverse dynamics problem.

These tasks are considered in some detail for wheeled and legged vehicles.

A general dynamic model for a rigid vehicle of constant mass is developed, and the model is applied to flying, swimming, and space robots.

Although many mobile robot systems are experimental in nature, systems devoted to specific practical applications are being developed and deployed. This chapter examines some of the tasks for which mobile robotic systems are beginning to appear and describes several existing experimental and production systems that have been developed. As noted in Chapter 1, tasks for which practical mobile robot systems exist are usually characterized by one or more of the following properties:

• The environment is inhospitable, and sending a human is either very costly or very dangerous. Such environments include nuclear, chemical, underwater, battlefield and outer-space environments.

• The environment is remote, so that sending a human operator is too difficult or takes too long. Extreme instances of this are those environments that are completely inaccessible to humans, such as microscopic environments. Many other environments, including mining, outer space, and forestry exhibit these properties.

• The task has a very demanding duty cycle or a very high fatigue factor.

• The task is highly disagreeable to a human.

In addition, domains where the use of a robot may improve efficiency, robustness, or safety are candidates for the development of experimental systems that may subsequently become practical.

Fundamentally, the decision to implement a robotic solution to a given task often comes down to a question of economics. If it is cheaper, more efficient, or simpler to use a person to accomplish a task, then economically it does not make much sense to design and use a robot.

A full treatment of Markov models is beyond the limit of space available here. A number of introductory texts and tutorials on Markov models are given at the end of this chapter. The tutorial provided here follows that given in [520].

Discrete Markov Process

Suppose that an autonomous agent moves about its environment in such a way that transitions from one location to another are as sketched in Figure C.1. The robot's environment has 13 distinct locations, and at any one time the robot is in one of these. Identify these N = 13 distinct locations (or states) as S1, S2, …, Sn. At each time step the robot can move from one state to another, including possibly remaining in the same location, according to a set of probabilities associated with each state. Then the robot's environment can be represented as a directed graph with the nodes of the graph corresponding to the distinct locations and the directed edges of the graph corresponding to possible transitions for each location. Let t denote the time instant associated with robot motions (state changes), and denote the actual location (state) of the robot at time t as qt. Suppose that the robot at time t was in location Sk, at time t − 1 the robot was in location Sj, …, and at time 1 the robot was in location Si; then what is the probability that the robot is in location Sl at time t + 1?

The research problems and solutions discussed in this book leave many issues unresolved. Given the current state of mobile robotics, what can be considered essentially solved and what tasks remain? It is clear that for restrictive environments and for limited tasks, autonomous systems can be readily developed. Tasks such as parts delivery in a warehouse, materials transport in hospitals, limited autonomous driving, and so on can all be “solved” for tight definitions of the task and provided that restrictive assumptions can be made concerning the environment. If the environment can be populated with unique markers or if a guidewire can be buried in the floor and dynamic features (including people) can be removed, then most of the problems involved in point-to-point navigation can be completely solved.

Unfortunately, systems that require such engineering of the environment are fragile and prone to failure if the key landmarks fail or are somehow obscured. Perhaps more important, the inflexibility inherent in constraining the environment makes the use of robot systems less appealing for both financial and logistic reasons. In addition to imposing environmental constraints, the use of existing robot systems implies a restricted and well-defined task specification.

The ability to navigate purposefully is fundamental to most animals and to every intelligent organism. In this book we examine the computational issues specific to the creation of machines that move intelligently in their environment. From the earliest modern speculation regarding the creation of autonomous robots, it was recognized that regardless of the mechanisms used to move the robot around or the methods used to sense the environment, the computational principles that govern the robot are of paramount importance. As Powell and Donovan discovered in Isaac Asimov's story “Runaround,” subtle definitions within the programs that control a robot can lead to significant changes in the robot's overall behavior or action. Moreover, the interactions among multiple complex components can lead to large-scale emergent behaviors that may be hard to predict.

Probabililty

Probability finds application throughout many scientific fields, but finds particular use in robotics in the modelling of uncertainty in terms of a vehicle's pose, interpretating sensor data, and mapping. This appendix reviews some of the fundamental aspects of probability and relates these aspects to problems in the mobile robotics domain. Although this appendix attempts to be reasonably complete in this regard, it cannot hope to provide an exhaustive review of the subject. See the end of the appendix for additional readings.

One problem encountered when modelling real-world systems is that few systems exhibit constant behavior. Observations vary depending on what appears to be random or chance variations. Probability theory provides a general technique for describing these variations. Suppose there is an experiment whose outcome depends on chance. The outcome of the experiment is described as a random variable X. The sample space Ω is the space from which X can be drawn. If the sample space is finite or countably infinite, then the random variable and sample space are said to be discrete; otherwise they are said to be continuous.

Probability of Discrete Events

The discrete probability function P(X) scores evidence that a discrete event X, where X is drawn from sample space Ω, has occurred.

Robotic systems, and in particular mobile robotic systems, are the embodiment of a set of complex computational processes, mechanical systems, sensors, user interface, and communications infrastructure. The problems inherent in integrating these components into a working robot can be very challenging. Overall system control requires an approach that can properly handle the complexity of the system goals while dealing with poorly defined tasks and the existence of unplanned and unexpected events. This task is complicated by the non-standard nature of much robotic equipment. Often the hardware seems to have been built following a philosophy of “ease of design” rather that with an eye towards assisting with later system integration. For example, at the hardware level the robot's wheels rotate in encoder counts, sonar sensors return clock ticks to the first returned echo, and the hardware interfaces can be very specialized. Even if the devices provide “standard” interfaces such as through a standard system bus, serial connections, or via some other standard protocol, the actual command stream can be very device specific. These factors impede abstraction, portability, rapid prototyping, modularity, and pedagogy. Software developers must write layers of code to divorce the low-level device interface from higher-level software functions.

Before delving into the harsh realities of real robots, it is worthwhile exploring some of the computational tasks that are associated with an autonomous system. This chapter provides a taste (an amuse bouche, if you will) of some of the computational problems that will be considered in later chapters. Here these problems are considered in their simplest form, and many of the realities of autonomous systems are ignored. Rest assured, the full complexity of the problems are considered in later chapters.

Perhaps the simplest theoretical abstraction of an autonomous robot is the point robot. A point robot abstracts the robot as a single point operating in some environment, typically a continuous Cartesian plane. Within this formalism, the robot can be represented as a point (x, y) ∈ ℝ2. The domain of operation of the robot is the plane. The point (x, y) fully describes the state of the robot and is also known as the robot's pose or configuration.

Moving the robot involves changing its state from one value (a, b) to another (c, d). The robot operates on a plane, but not all of this domain is necessarily available to the robot. The set of valid poses of the robot are known as its free space. Some states are not valid; rather, they correspond to obstacles or other states that the robot cannot occupy.