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

TL;DR

The paper addresses how to design homogeneous Modular Soft Robots (MSoRos) that can morph between planar and spherical configurations to optimize locomotion on varying terrains. It introduces a geometry-based design framework that uses a base platonic solid and a module-topology curve, with spherical topology obtained via inverse orthographic projection and planar topology via azimuthal projection, yielding scale-invariant topologies. Distortion-based metrics for intermodular and intramodular surfaces are defined to optimize reconfiguration and locomotion via a weighted objective, and cavity geometry is tuned to balance limb stiffness and curling ability. Experimental validation with a cube-based four-limb MSoRo demonstrates planar locomotion and spherical reconfiguration, supported by cavity design choices (outward trapezoid) and a central hub for actuation, pointing to future docking and multi-modal capabilities.

Abstract

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 them to maneuver variable terrains. The sphere-plane reconfiguration is equivalent to projecting a spherical shell onto a plane, an operation which is not possible without distortions. Fortunately, soft materials have potential to adapt to this disparity of the Gaussian curvatures. Modular Soft Robots (MSoRos) have promise of achieving dimensional change by exploiting their continuum and deformable nature. We present topology and morphology design of MSoRos capable of reconfiguring between spherical and planar configurations. Our approach is based in geometry, where a platonic solid determines the number of modules required for plane-to-sphere reconfiguration and the radius of the resulting sphere, e.g., four `tetrahedron-based' or six `cube-based' MSoRos are required for spherical reconfiguration. The methodology involves: (1)inverse orthographic projection of a `module-topology curve' onto the circumscribing sphere to generate the spherical topology,(2)azimuthal projection of the spherical topology onto a tangent plane at the center of the module resulting in the planar topology, and (3)adjusting the limb stiffness and curling ability by manipulating the geometry of cavities to realize a physical finite-width, Motor-Tendon Actuated MSoRo. The topology design is shown to be scale invariant, i.e., scaling of base platonic solid is reflected linearly in spherical and planar topologies. The module-topology curve is optimized for the reconfiguration and locomotion ability using a metric that quantifies sphere-to-plane distortion. The geometry of the cavity optimizes for the limb stiffness and curling ability without compromising the actuator's structural integrity.

Figures (13)

• Figure 1: Collective morphing by MSoRos between one dimension (caterpillar-like orientation), two (planar swarm) and three (sphere) dimensions. The three, four and five limb modules result from one of the five platonic solids.
• Figure 2: Projection of all the five platonic solids of edge length $a$ onto a circumscribing sphere of radius $R$. The number of faces $F$, edges per face $q$, and the dihedral angle $\theta$ correlate to the number of modules required for spherical reconfiguration, the number of limbs per module and the topology curve plane respectively.
• Figure 3: The design process is based in geometry where (a) the designer has choice of a platonic solid (cube as a visual example) and module-topology curve. (b) The module-topology curve is drawn along the polyhedron edge on a topology curve plane (blue). The normal to the plane (dotted line) is the vector joining the centers of the circumscribing sphere (red) and the edge of the platonic solid. The dihedral angle $\theta$ is the angle between adjacent faces.
• Figure 4: The topology curve plane (blue) and the tangent plane (green) for cube as the base platonic solid. The topology curve plane passes through the edge of the polyhedron with the normal vector along the line joining the centers of the circumscribing sphere (red) $O$ and the edge $A$. The tangent plane normal is along the vector joining $O$ and the center of the polyhedron face $B$.
• Figure 5: Summary of the sequential methodology for designing homogeneous, rotationally symmetric multi-limb MSoRos. The designer has choice of base platonic solid and the module-topology curve. The outcome is spherical and planar configurations of MSoRos.