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Imagine a swarm of terrestrial robots that can explore an environment, and,upon completion of this task, reconfigure into a spherical ball and roll out.This dimensional change alters the dynamics of locomotion and can assist themto maneuver variable terrains. The sphere-plane reconfiguration is equivalentto projecting a spherical shell onto a plane, an operation which is notpossible without distortions. Fortunately, soft materials have potential toadapt to this disparity of the Gaussian curvatures. Modular Soft Robots(MSoRos) have promise of achieving dimensional change by exploiting theircontinuum and deformable nature. We present topology and morphology design ofMSoRos capable of reconfiguring between spherical and planar configurations.Our approach is based in geometry, where a platonic solid determines the numberof modules required for plane-to-sphere reconfiguration and the radius of theresulting sphere, e.g., four `tetrahedron-based' or six `cube-based' MSoRos arerequired for spherical reconfiguration. The methodology involves: (1)inverseorthographic projection of a `module-topology curve' onto the circumscribingsphere to generate the spherical topology,(2)azimuthal projection of thespherical topology onto a tangent plane at the center of the module resultingin the planar topology, and (3)adjusting the limb stiffness and curling abilityby manipulating the geometry of cavities to realize a physical finite-width,Motor-Tendon Actuated MSoRo. The topology design is shown to be scaleinvariant, i.e., scaling of base platonic solid is reflected linearly inspherical and planar topologies. The module-topology curve is optimized for thereconfiguration and locomotion ability using a metric that quantifiessphere-to-plane distortion. The geometry of the cavity optimizes for the limbstiffness and curling ability without compromising the actuator's structuralintegrity.

Topology and morphology design of spherically reconfigurable homogeneous Modular Soft Robots (MSoRos)