Imagine a swarm of terrestrial robots that can explore an environment, and, on completion of this task, reconfigure into a spherical ball and roll out. This dimensional change alters the dynamics of locomotion and can assist them in maneuvering variable terrains. The sphere-plane reconfiguration is equivalent to projecting a spherical shell onto a plane, an operation that is not possible without distortions. Fortunately, soft materials have the 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. However, the design of such soft robots has remained unexplored thus far. Here, for the first time, we present the topology and morphology design of MSoRos that are 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, for example, 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 that can actuate between the sphere-plane configurations. The topology design is shown to be scale invariant, that is, the 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 an intramodular distortion 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.

中文翻译：

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球形可重构同质模块化软机器人的拓扑和形态设计

想象一下，一群可以探索环境的地面机器人，在完成这项任务后，重新配置成一个球体并滚出。这种尺寸变化改变了运动的动力学，可以帮助他们操纵多变的地形。球面重构等效于将球壳投影到平面上，如果不发生变形，则无法进行此操作。幸运的是，软材料有可能适应高斯曲率的这种差异。模块化软机器人 (MSoRos) 有望通过利用其连续性和可变形性来实现尺寸变化。然而，迄今为止，此类软体机器人的设计仍未得到探索。在这里，第一次，我们介绍了能够在球形和平面配置之间重新配置的 MSoRos 的拓扑和形态设计。我们的方法基于几何学，其中柏拉图式固体决定了平面到球体重新配置所需的模块数量和所得球体的半径，例如，四个“基于四面体”或六个“基于立方体”的 MSoRos 是需要进行球形重构。该方法包括：(1) 将“模块拓扑曲线”逆正交投影到外接球体上以生成球形拓扑；(2) 球形拓扑在模块中心的切平面上的方位角投影导致平面拓扑；(3) 通过操纵空腔的几何形状来调整肢体刚度和卷曲能力，以实现物理有限宽度、电机-肌腱驱动的 MSoRo可以在球面配置之间启动。拓扑设计显示为尺度不变，即基础柏拉图立体的尺度在球形和平面拓扑中线性反映。模块拓扑曲线针对重新配置和运动能力进行了优化，使用量化球面到平面失真的模块内失真度量。空腔的几何形状优化了肢体刚度和卷曲能力，而不会影响致动器的结构完整性。