Reconfiguration Planning for Pivoting Cube Modular Robots

In this paper, we present algorithms for self-reconfiguration of modular robots that move by pivoting. The modules are cubes that can pivot about their edges along the x̂, ŷ, or ẑ axes to move on a 3-dimensional substrate. This is a different model from prior work, which usually considers modules that slide along their faces. We analyze the pivoting cube model and give sufficient conditions for reconfiguration to be feasible. In particular, we show that if an initial configuration does not contain any of three subconfigurations, which we call rules, then it can reconfigure into a line. We provide provably correct algorithms for reconfiguration for both 2-D and 3-D systems, and we verify our algorithms via simulation on randomly generated 2-D and 3-D configurations.