This section describes the methods used to implement the deliberative autonomy layer that was initially described in Chapter 1. Planning concerns the question of deciding what to do, of which deciding where to go is a special case. Central to planning is the predictive model, which maps candidate actions onto their associated consequences. Equally as important is the mechanism of search because there tend to be many alternative actions to be assessed at any point in time.

Planners think about the future, employing some degree of look ahead and there is a central trade-off between the computational cost of look ahead and the cognitive performance of the system. In addition to perception, planning is where most of what impresses us about robots is located. Given a sufficiently accurate model of the environment, planning technology today can solve, in a comparative instant, problems that we humans would find quite daunting.

Introduction

Planning refers to processes that deliberate, predict, and often optimize. Respectively these actions will mean:

• Deliberate: Consider many possible sequences of future actions.

• Predict: Predict the outcomes for each sequence.

• Optimize: Pick one, perhaps based on some sense of relative merit.

Although robot arms that spot weld our cars together have been around for some time, a new class of robots, the mobile robot, has been quietly growing in significance and ability. For several decades now, behind the scenes in research laboratories throughout the world, robots have been evolving to move automatically from place to place. Mobility enables a new capacity to interact with humans while relieving us from jobs we would rather not do anyway.

Mobile robots have recently entered the public consciousness as a result of the spectacular success of the Mars rovers, television shows such as Battlebots, and the increasingly robotic toys that are becoming popular at this time.

Mobility of a robot changes everything. The mobile robot faces a different local environment every time it moves. It has the capacity to influence, and be influenced by, a much larger neighborhood than a stationary robot. More important, the world is a dangerous place, and it often cannot be engineered to suit the limitations of the robot, so mobility raises the needed intelligence level. Successfully coping with the different demands and risks of each place and each situation is a significant challenge for even biological systems.

Preface

Robotics can be a very challenging and very satisfying way to spend your time. A profound moment in the history of most roboticists is the first moment a robot performed a task under the influence of his or her software or electronics. Although a productive pursuit of the study of robotics involves aspects of engineering, mathematics, and physics, its elements do not convey the magic we all feel when interacting with a responsive semi-intelligent device of our own creation.

This book introduces the science and engineering of a particularly interesting class of robots – mobile robots. Although there are many analogs to the field of robot manipulators, mobile robots are sufficiently different to justify their treatment in an entirely separate text. Although the book concentrates on wheeled mobile robots, most of its content is independent of the specific locomotion subsystem used.

The field of mobile robots is changing rapidly. Many specialties are evolving in both the research and the commercial sectors. Any textbook offered in such an evolving field will represent only a snapshot of the field as it was understood at the time of publication. However, the rapid growth of the field, its several decades of history, and its pervasive popular appeal suggest that the time is now right to produce an early text that attempts to codify some of the fundamental ideas in a more accessible manner.

A large number of problems in mobile robotics can be reduced to a few basic problem formulations. Most problems reduce to some mixture of optimizing something, solving simultaneous linear or nonlinear equations, or integrating differential equations. Well-known numerical methods exist for all of these problems and all are accessible as black boxes in both software applications and general purpose toolboxes. Of course offline toolboxes cannot be used to control a system in real time and almost any solution benefits from exploiting the nature of the problem, so it is still very common to implement numerical algorithms from scratch for many real time systems.

The techniques described in this section will be referenced in many future places in the text. These techniques will be used to compute wheel velocities, invert dynamic models, generate trajectories, track features in an image, construct globally consistent maps, identify dynamic models, calibrate cameras, and so on.

Linearization and Optimization of Functions of Vectors

Perhaps paradoxically, linearization is the fundamental process that enables us to deal with nonlinear functions. The topics of linearization and optimization are closely linked because a local optimum of a function coincides with special properties of its linear approximation.

The equations that describe the motion of wheeled mobile robots (WMRs) are very different from those that describe manipulators because they are differential rather than algebraic, and often underactuated and constrained. Unlike manipulators, the simplest models of how mobile robots move are nonlinear differential equations. Much of the relative difficulty of mobile robot modelling can be traced to this fact.

This section explores dynamics in two different senses of the term. Dynamics in mechanics refers to the particular models of mechanical systems that are used in that discipline. These tend to be second-order equations involving forces, mass properties, and accelerations. In control theory, dynamics refers to any differential equations that describe the system of interest.

Moving Coordinate Systems

The fact that mobile robot sensors are fixed to the robot and move with them has profound implications. On the one hand, it is the source of nonlinear models in Kalman filters. On the other, it is the source of nonholonomic wheel constraints. This section concentrates on a third effect – the fact that the derivatives of many vector quantities of interest depend on the motion of the robot.

Control is the process of converting intentions into actions. We use control to move the robot with respect to the environment but also to articulate sensor heads, arms, grippers, tools, and implements. Dynamic models are useful in control for purposes of analysis but they are also used explicitly in refined implementations.

Classical Control

The main objective of a control system is to provide the inputs necessary at the hardware level that will generate the desired motions. This section describes the methods used to implement the reactive autonomy layer that was initially described in Chapter 1.

Introduction

There are many motivations for the use of controllers on mobile robots:

• Real hardware ultimately responds to forces, energy, power, etc, whereas we are usually concerned with positions and velocities etc. Controllers map between the two.

• Measurements can be used to measure what the system is doing, thereby reject disturbances, and even alter the dynamics of the system in some favorable manner.

• Models of the system can be used to elaborate a terse description of the desired motion into the details necessary to make it happen.

Perception and localization often depend on each other. When building a map, a model of the environment is being constructed and perception and localization cooperate in order to put pieces of the map in the right place relative to each other. When using a map to localize, the robot is determining its location based on matching what it sees to what it expects to see and, in this case, localization depends on perception. More sophisticated approaches can construct a map and localize from it at the same time.

This section will present many aspects of both making and using maps of the environment. Many mobile robots need some kind of map in order to function effectively. Maps are needed when accurate absolute pose is needed. Accurate pose is needed when the robot is told to go to the coordinates of a specific place or when the robot wants to use information of any kind that is located by its position in a second map.

If localization is imperfect, it may be advisable to register data generated at different times and places. This is a more fundamental operation than either localization or mapping. It achieves both the goal of making the map consistent and the goal of refining the estimate of the intervening motion. For this reason, all three topics of mapping, registration, and ego-motion are presented together here.