This text addresses qualitative (as opposed to quantitative) spatial reasoning. Qualitative spatial reasoning and planning is considered by the authors to be a representation and methodology that is complementary to more traditional qualitative spatial reasoning/planning approaches. The underlying assumption of the quantitative approach is that, by eschewing the quantitative nature of more traditional approaches, solutions may be found to complex planning problems that are difficult or expensive to conduct using traditional (quantitative) approaches. The text is limited to the development of qualitative spatial reasoning for objects in the plane, and examines fundamental tasks in qualitative reasoning, including: mapping quantitative problem specifications to a qualitative representation, path planning as a qualitative task, and qualitative path planning subject to velocity (and other) constraints.

The book begins by providing formal definitions for qualitative relations relating to space, location, distance, and direction. These definitions are then used as the foundation of qualitative algorithms for a variety of “standard” quantitative spatial reasoning tasks, including forward kinematics (chapter 5), path planning (chapters 6 through 8), and map construction (chapter 9).

There is significant variation in the details of each of the algorithms presented, however, in general, each algorithm consists of three major steps. First, an instance of the problem, specified in a quantitative manner, is converted to its qualitative counterpart. Second, the qualitative version is solved qualitatively, and, finally, the qualitative solution is mapped back into the original quantitative representation, so that the task can be executed by a real, or (in the case of the examples in the text) a simulated machine. Each of these steps can be quite complex. Consider the case of mobile robot path planning, for example: converting a mobile robot path planning problem into a qualitative representation may require the construction of a topological representation of its environment. Qualitative path planning may be expressed as a hill-climbing operation within the qualitative representation. Finally, converting the qualitative path to a quantitative representation, so that it can be executed, is expressed as a simulated annealing search problem in a configuration-space representation of the environment.

The book presents a coherent, alternative approach to addressing classic spatial reasoning problems in a qualitative way. The text provides a coherent, unified approach to the problem, and I would certainly recommend the book to researchers interested in qualitative spatial representation and planning. That being said, the text does not provide much of a review of other approaches to qualitative representations. Such a review would have placed this work within the context of other qualitative approaches. Second, although the individual algorithms developed in the text are given in sufficient detail, little detail is provided in terms of the completeness (or lack of it) of specific steps. Finally, it would have been desirable to have seen more detailed comparisons of the qualitative approach with the performance of traditional quantitative algorithms, especially when applied to real devices, rather than just on software simulations.