How should robots think about space?

A robot’s action are carried out over time through space. The computational mechanisms that the robot uses to choose and guide actions must therefore at some level reflect the structure of time and space. This essay discusses what ontology for space and time should be built into a robot. I argue that the designers of a robot generally need to have in mind explicit otologies of time and space, and that these will generally be the real line and three-dimensional Euclidean space, though it is often advantageous to project down to a lower-dimensional space, when possible. I then discuss which spatial or spatio-temporal regions should be considered "wellbehaved" and which should be excluded as "monsters." I propose some principles that the class of well-behaved regions should observe, and discuss some examples.