On embeddability of modular robot designs

We address the problem of detecting embeddability of modular robots: namely, to decide automatically whether a given modular robot design can simulate the functionality of a seemingly different design. To that end, we introduce a novel graph representation for modular robots and formalize the notion of embedding through topological and kinematic conditions. Based on that, we develop an algorithm that decides embeddability when the two involved designs have tree topologies. Our algorithm performs two passes and involves dynamic programming and maximum cardinality matching. We demonstrate our approach on real modular robots and show that we can detect embeddability of complex designs efficiently.