This chapter provides introductory concepts that serve as an entry point into other parts of the book. The planning problems considered here are the simplest to describe because the state space will be finite in most cases. When it is not finite, it will at least be countably infinite (i.e., a unique integer may be assigned to every state). Therefore, no geometric models or differential equations will be needed to characterize the discrete planning problems. Furthermore, no forms of uncertainty will be considered, which avoids complications such as probability theory. All models are completely known and predictable.

There are three main parts to this chapter. Sections 2.1 and 2.2 define and present search methods for feasible planning, in which the only concern is to reach a goal state. The search methods will be used throughout the book in numerous other contexts, including motion planning in continuous state spaces. Following feasible planning, Section 2.3 addresses the problem of optimal planning. The principle of optimality, or the dynamic programming principle, [86] provides a key insight that greatly reduces the computation effort in many planning algorithms. The value-iteration method of dynamic programming is the main focus of Section 2.3. The relationship between Dijkstra's algorithm and value iteration is also discussed. Finally, Sections 2.4 and 2.5 describe logic-based representations of planning and methods that exploit these representations to make the problem easier to solve; material from these sections is not needed in later chapters.