Recently, a class of mechanical lattices with reconfigurable, zero-stiffness structures has been proposed, called Totimorphic structures. In this work, we introduce a computational framework that allows continuous reprogramming of a Totimorphic lattice's effective properties, such as mechanical and optical properties, via continuous geometric changes alone. Our approach is differentiable and guarantees valid Totimorphic lattice configurations throughout the optimisation process, thus providing not only specific configurations with desired properties but also trajectories through configuration space connecting them. It enables re-programmable structures where actuators are controlled via automatic differentiation on an objective-dependent cost function, altering the lattice structure at all times to achieve a given objective - which is interchangeable to achieve different functionalities. Our main interest lies in deep space applications where harsh, extreme, and resource-constrained environments demand solutions that offer flexibility, resource efficiency, and autonomy. We illustrate our framework through two proofs of concept: a re-programmable metamaterial as well as a space telescope mirror with adjustable focal length, both made from Totimorphic structures. The introduced framework is easily adjustable to a variety of Totimorphic designs and objectives, providing a light-weight model for endowing physical prototypes of Totimorphic structures with autonomous self-configuration and self-repair capabilities.

翻译：近年来，一类具有可重构、零刚度结构的机械晶格被提出，称为全形结构。本文提出一种计算框架，该框架仅通过连续几何变化即可实现对全形晶格有效属性（如力学与光学特性）的连续重编程。我们的方法具备可微性，并在整个优化过程中保证全形晶格构型的有效性，从而不仅能提供具有目标属性的特定构型，还能给出连接这些构型的构型空间轨迹。该方法实现了可重编程结构，其中执行器通过目标相关代价函数的自动微分进行控制，持续改变晶格结构以实现给定目标——该目标可替换以实现不同功能。我们的主要兴趣在于深空应用领域，其严酷、极端且资源受限的环境要求解决方案具备灵活性、资源高效性和自主性。我们通过两个概念验证案例展示该框架：一个可重编程超材料以及一个焦距可调的空间望远镜反射镜，二者均由全形结构构成。所提出的框架可轻松适配多种全形结构设计与目标，为全形结构物理原型赋予自主自配置与自修复能力提供了一个轻量化模型。