<p>Field-based reactive control provides a minimalist, decentralized route to guiding robots that lack onboard computation. Such schemes are well suited to resource-limited machines like microrobots, yet implementation artifacts, limited behaviors, and the frequent lack of formal guarantees blunt adoption. Here, we address these challenges with a new geometric approach called artificial spacetimes. We show that reactive robots navigating control fields obey the same dynamics as light rays in general relativity. This surprising connection allows us to adopt techniques from relativity and optics for constructing and analyzing control fields. When implemented, artificial spacetimes guide robots around structured environments, simultaneously avoiding boundaries and executing tasks like rallying or navigation, even when the field itself is static. We augment these capabilities with formal tools for analyzing what robots will do and provide experimental validation with silicon-based microrobots. Combined, this work provides a new framework for generating composed robot behaviors with minimal overhead.</p>