A non-cubic space-filling modular robot

TL;DR

This work roboticize a non-cubic space-filling shape: the rhombic dodecahedron, and introduces a strategy for genderless passive docking of cells that generalizes to any polyhedra with radially symmetrical faces.

Abstract

Space-filling building blocks of diverse shape permeate nature at all levels of organization, from atoms to honeycombs, and have proven useful in artificial systems, from molecular containers to clay bricks. But, despite the wide variety of space-filling polyhedra known to mathematics, only the cube has been explored in robotics. Thus, here we roboticize a non-cubic space-filling shape: the rhombic dodecahedron. This geometry offers an appealing alternative to cubes as it greatly simplifies rotational motion of one cell about the edge of another, and increases the number of neighbors each cell can communicate with and hold on to. To better understand the challenges and opportunities of these and other space-filling machines, we manufactured 48 rhombic dodecahedral cells and used them to build various superstructures. We report locomotive ability of some of the structures we built, and discuss the dis/advantages of the different designs we tested. We also introduce a strategy for genderless passive docking of cells that generalizes to any polyhedra with radially symmetrical faces. Future work will allow the cells to freely roll/rotate about one another so that they may realize the full potential of their unique shape.

Figures (5)

• Figure 1: Exploded view of internal components within an active cell. Active cells include: a hexagonal PCB (A) as a structural foundation and to create all electrical connections; an analog ON/OFF switch (B) for simple mode control; an eccentric rotating mass (ERM) motor (C) to provide mechanical energy to the morphological system; a 100 mAh LiPo battery cell (D) with high discharge capabilities; surface mounted light emitting diodes (LEDs; E) to indicate active cells' current states; a 3D printed PCB mount (F) to hold components in place and mount outer shells; M2 heat inserts (G) to mount the outer shells; two outer shell halves (H) with 48 face-embedded magnets; and M2 screws (I) to complete cell assembly.
• Figure 2: The potential for self reconfiguration in future work. (A and B:) The two kinds of rolling motions for cubes. (C:) 2D projection of rhombic dodecahedron rotation (hexagon).
• Figure 3: Genderless passive docking was achieved by arranging and embedding axially-poled neodymium magnets into the outer shell of the cells (A). The arrangement of north (N) and south (S) poled magnets takes advantage of the symmetry line that exists along the long axis of the rhombic faces. (B:) A jig was designed and 3D printed to simplify cell assembly. The jig consists of a base (B1) to hold and supply magnets, a slider base (B2) with identical magnet configurations as shown in A that automatically loads itself when slid through the base, and a slider top (B3) that can be removed to allow all four magnets in a cell face to be embedded simultaneously.
• Figure 4: Robotic crystals formed by various numbers (n) of space-filling unit cells.
• Figure 5: Locomotion. Behavior was tracked for four different designs (A-D). Across six independent trials, design's center of mass was tracked over an evaluation period of 1 min. The initial orientation for each trial--- the top-down view used for motion tracking--- as well as a side view of each morphology, is shown for each respective design. The origin of each trial is marked with a red triangle indicating the initial position and orientation of the robot. The robot's position over the trial period, along with the final position and orientation, are marked with grayscale lines and corresponding triangles. Active cells (white) were rotated into six different random orientations, one for each trial, to understand the influence of motor orientation on behavior. In smaller body plans (e.g. A), the orientation of active cells were found to have greater influence on behavior (e.g. the direction of rotation) when compared to larger bodies (e.g. C and D). Potential correlations between the type of surface contact for a given design were also identified. For example, point contacts seem to produce a high rate of rotation (A); edge contacts produced large, sweeping rotations (B and C); and face contact produced mostly translational motion (D).