Planning problems involve a state space that captures all possible situations that could arise. The state could, for example, represent the position and orientation of a robot, the locations of tiles in a puzzle, or the position and velocity of a helicopter. Both discrete (finite, or countably infinite) and continuous (uncountably infinite) state spaces will be allowed. One recurring theme is that the state space is usually represented implicitly by a planning algorithm. In most applications, the size of the state space (in terms of number of states or combinatorial complexity) is much too large to be explicitly represented. Nevertheless, the definition of the state space is an important component in the formulation of a planning problem and in the design and analysis of algorithms that solve it.

Steven M LaValle 2020-08-14