If faced with the choice of sending a swarm of full-sized, distinct robots to space, or a large crew of smaller robotic modules, you might want to enlist the latter. Modular robots, like those depicted in films such as "Big Hero 6," hold a special type of promise for their self-assembling and reconfiguring abilities. But for all of the ambitious desire for fast, reliable deployment in domains extending to space exploration, search and rescue, and shape-shifting, modular robots built to date are still a little clunky. They're typically built from a menagerie of large, expensive motors to facilitate movement, calling for a much-needed focus on more scalable architectures -- both up in quantity and down in size. Scientists from MIT's Computer Science and Artificial Intelligence Laboratory (CSAIL) called on electromagnetism -- electromagnetic fields generated by the movement of electric current -- to avoid the usual stuffing of bulky and expensive actuators into individual blocks.

Gridworlds have been long-utilised in AI research, particularly in reinforcement learning, as they provide simple yet scalable models for many real-world applications such as robot navigation, emergent behaviour, and operations research. We initiate a study of gridworlds using the mathematical framework of reconfigurable systems and state complexes due to Abrams, Ghrist & Peterson. State complexes represent all possible configurations of a system as a single geometric space, thus making them conducive to study using geometric, topological, or combinatorial methods. The main contribution of this work is a modification to the original Abrams, Ghrist & Peterson setup which we believe is more naturally-suited to the context of gridworlds. With this modification, the state complexes may exhibit geometric defects (failure of Gromov's Link Condition), however, we argue that these failures can indicate undesirable or dangerous states in the gridworld. Our results provide a novel method for seeking guaranteed safety limitations in discrete task environments with single or multiple agents, and offer potentially useful geometric and topological information for incorporation in or analysis of machine learning systems.

Complex electro-mechanical products, such as high-end printers and photocopiers, are designed as families, with reusable modules put together in different manufacturable configurations, and the ability to add new modules in the field. The modules are controlled locally by software that must take into account the entire configuration. This poses two problems for the manufacturer. This has become an accepted part of the practice of Xerox, and the control software is deployed in high-end Xerox printers.