Tensegrities synergistically combine tensile (cable) and rigid (link) elements to achieve structural integrity, making them lightweight, packable, and impact resistant. Consequently, they have high potential for locomotion in unstructured environments. This research presents geometric modeling of a Tensegrity eXploratory Robot (TeXploR) comprised of two semi-circular, curved links held together by 12 prestressed cables and actuated with an internal mass shifting along each link. This design allows for efficient rolling with stability (e.g., tip-over on an incline). However, the unique design poses static and dynamic modeling challenges given the discontinuous nature of the semi-circular, curved links, two changing points of contact with the surface plane, and instantaneous movement of the masses along the links. The robot is modeled using a geometric approach where the holonomic constraints confirm the experimentally observed four-state hybrid system, proving TeXploR rolls along one link while pivoting about the end of the other. It also identifies the quasi-static state transition boundaries that enable a continuous change in the robot states via internal mass shifting. This is the first time in literature a non-spherical two-point contact system is kinematically and geometrically modeled. Furthermore, the static solutions are closed-form and do not require numerical exploration of the solution. The MATLAB simulations are experimentally validated on a tetherless prototype with mean absolute error of 4.36{\deg}.

翻译：张拉整体结构通过协同结合拉伸（缆索）与刚性（连杆）元件实现结构完整性，使其具备轻量化、可折叠及抗冲击特性。因此，其在非结构化环境中的运动应用具有巨大潜力。本研究提出一种由两个半圆形曲线连杆构成的张拉整体探索机器人（TeXploR）的几何建模方法，该机器人通过12根预应力缆索连接，并借助沿各连杆移动的内部质量块驱动。此设计实现了高效且稳定的滚动（例如在斜坡上防倾覆）。然而，由于半圆形曲线连杆的非连续性、与接触平面的两个变化接触点以及质量块沿连杆的瞬时运动，其独特设计带来了静态与动态建模的挑战。本研究采用几何方法对机器人进行建模，其中完整约束条件证实了实验观测到的四状态混合系统，证明TeXploR沿一个连杆滚动时绕另一连杆端点旋转。研究同时确定了通过内部质量块移动实现机器人状态连续变化的准静态状态转换边界。这是文献中首次对非球形两点接触系统进行运动学与几何建模。此外，静态解为闭合形式，无需对解空间进行数值探索。MATLAB仿真结果在无缆原型机上得到实验验证，平均绝对误差为4.36°。