球形可重构同质模块化软体机器人（MSoRos）的拓扑与形态设计
Topology and morphology design of spherically reconfigurable homogeneous Modular Soft Robots (MSoRos)
AI总结：
针对软体机器人维度变化需求，提出基于柏拉图立体的MSoRos球形-平面重构拓扑与形态设计方法，通过几何投影和腔体优化实现尺度不变的重构与运动能力。
摘要：
想象一群陆地机器人，它们可以探索环境，并在完成此任务后重新配置成一个球形并滚离。这种维度变化改变了运动的动力学，并可以帮助它们穿越多变的地形。球面-平面重构等价于将球壳投影到平面上，这一操作在没有变形的情况下是不可能的。幸运的是，软材料有潜力适应这种高斯曲率的差异。模块化软体机器人（MSoRos）有望通过利用其连续体和可变形特性来实现维度变化。我们提出了能够在球形和平面构型之间重构的MSoRos的拓扑和形态设计。我们的方法基于几何学，其中柏拉图立体决定了平面到球面重构所需的模块数量以及所得球体的半径，例如，四个“基于四面体”或六个“基于立方体”的MSoRos是球形重构所必需的。该方法包括：（1）将“模块拓扑曲线”逆正交投影到外接球面上以生成球形拓扑，（2）将球形拓扑方位角投影到模块中心的切平面上，从而得到平面拓扑，以及（3）通过操纵腔体的几何形状来调整肢体刚度和卷曲能力，以实现物理上有限宽度的、电机-肌腱驱动的MSoRo。拓扑设计被证明是尺度不变的，即基础柏拉图立体的缩放线性地反映在球形和平面拓扑中。模块拓扑曲线通过量化球面到平面变形的度量进行优化，以提高重构和运动能力。腔体的几何形状在不妨碍执行器结构完整性的前提下优化了肢体刚度和卷曲能力。
英文摘要：
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.
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