  Voxel-based structures provide a modular, mechanically flexible periodic
lattice which can be used as a soft robot through internal deformations. To
engage these structures for robotic tasks, we use a finite element method to
characterize the motion caused by deforming single degrees of freedom and
develop a reduced kinematic model. We find that node translations propagate
periodically along geometric planes within the lattice, and briefly show that
translational modes dominate the energy usage of the actuators. The resulting
kinematic model frames the structural deformations in terms of user-defined
control and end effector nodes, which further reduces the model size. The
derived Planes of Motion (POM) model can be equivalently used for forward and
inverse kinematics, as demonstrated by the design of a tripod stable gait for a
locomotive voxel robot and validation of the quasi-static model through
physical experiments.
