Designing Modular Lattice Systems with Chiral Space Groups

We propose to use the concept of chiral space groups used by the crystallography science to define and design lattice robots. Chiral space groups are of great interest because they give all possible sets of discrete displacements having a group structure and a translational symmetry. We explain the analogy between lattice robot kinematics and crystal symmetry, and identify three fundamental properties of lattice robots such as (1) discreteness (2) translational symmetry and (3) composition. Then we give the possible connectors symmetries and orientations into a chiral space group, and the possible sliding and hinge joints locations and orientations compatible with the displacements in chiral space groups. We present a framework for the design of lattice robots by assembling compatible joints and connectors into a chiral space group. Several 2D and 3D examples of design are given to illustrate the framework. Moreover, we list the symmetries of the two chiral space groups P432 and P622 because they contain the symmetries of all the 65 chiral space groups and allow to design any lattice system.