The paper provides a method to determine and compare the reconfigurability of lattice systems. First it shows the difference that exists between the reconfigurability and self-reconfigurability features of a lattice system. Then a method using displacement groups is introduced to characterize these features. Based on this method, these features are then compared for some existing lattice systems.

We identify three fundamental properties of lattice robots such as (1) discreteness (2) translational symmetry and (3) composition, and explain the analogy of lattice robots kinematics and crystal symmetry described by space groups. Then we give the possible connectors symmetries and orientations compatible with space groups, and the possible sliding and hinge joints locations and orientations compatible with the displacements in such groups. We present a framework for the design of lattice robots by assembling compatible joints and connectors into a space group and give a 3D example.

This work presents some general considerations on self-reconfigurable robots design, and proposes an original design of mechatronic modules. Geometrical and kinematical features of these modules, offer the ability to be used as well as wheels to produce rolling motion, and as joints for building kinematic chains as legs, arms or snakes.