Universal Dancing by Luminous Robots Under Sequential Schedulers
摘要
The Dancing problem requires a swarm of n autonomous mobile robots to form a sequence of patterns, i.e., perform a choreography. Existing work has proven that some crucial restrictions on choreographies and initial configurations (e.g., on repetitions of patterns, periodicity, symmetries, contractions/expansions) must hold so that the Dancing problem can be solved under certain robot models. Here, we prove that these necessary constraints can be dropped by considering the \(\mathcal {LUMI}\) model (i.e., where robots are endowed with a light whose color can be chosen from a constant-size palette) under the quite unexplored sequential scheduler. We formalize the class of Universal Dancing problems which require a swarm of n robots starting from any initial configuration to perform a (periodic or finite) sequence of arbitrary patterns, only provided that each pattern consists of n vertices (including multiplicities). However, we prove that, to be solvable under \(\mathcal {LUMI}\) , the length of the feasible choreographies is bounded by the compositions of n into the number of colors available to the robots. We provide an algorithm solving Universal Dancing by exploiting the peculiar capability of sequential robots to implement a distributed counter. Even assuming non-rigid movements, our algorithm ensures spatial homogeneity of the performed choreography.