Computational Principles of Mobile Robotics

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.