Complete reconfiguration algorithm for sliding cube-shaped modular robots with only sliding motion primitive

This paper presents a reconfiguration algorithm for a robot composed of sliding cube modules with a limited motion primitive. We assume that a cube module is not allowed to make convex motions around other modules but is allowed to slide across other modules' surfaces. Such a motion primitive limitation complicates the development of the reconfiguration algorithm; however, it simplifies the design of module hardware and reduces the size and manufacturing costs of modules. The algorithm uses a three-dimensional 2 × 2 × 2 meta-module to guarantee the existence of mobile modules and maintain the connectivity of the robot structure during the reconfiguration process. The transition of the meta-module is executed by the tunneling of cube modules. The tunneling movement is efficiently controlled by focusing on the motion of voids that are invoked through the transition of meta-modules. We show that the algorithm is complete for a connected robot structure with more than a certain number of meta-modules and that the reconfiguration in an environment with obstacles is executed in quadratic operating time cost.