Recently, a class of mechanical lattices with reconfigurable, zero-stiffness structures has been proposed, called Totimorphic lattices. In this work, we introduce a computational framework that enables continuous reprogramming of a Totimorphic lattice's effective properties, such as mechanical and optical behaviour, through geometric changes alone, demonstrated using computer simulations. Our approach is differentiable and guarantees valid Totimorphic configurations throughout the optimisation process, providing not only target states with desired properties but also continuous trajectories in configuration space that connect them. This enables reprogrammable structures in which actuators are controlled via automatic differentiation on an objective-dependent cost function, continuously adapting the lattice to achieve a given goal. We focus on deep space applications, where harsh and resource-constrained environments demand solutions that combine flexibility, efficiency, and autonomy. As proof of concept, we present two scenarios: a reprogrammable disordered lattice material and a space telescope mirror with adjustable focal length. The introduced framework is adaptable to a wide range of Totimorphic designs and objectives, providing a lightweight model for endowing physical systems with autonomous self-configuration and self-repair capabilities.

翻译：近期，一类具有可重构、零刚度结构的机械晶格被提出，称为全形晶格。本文中，我们提出了一种计算框架，该框架能够仅通过几何变化实现对全形晶格有效性质（如力学与光学行为）的连续重编程，并通过计算机仿真进行了验证。我们的方法具有可微性，并在整个优化过程中保证生成有效的全形构型，不仅能够获得具有目标性质的终态，还能提供连接这些终态的构型空间中的连续轨迹。这使得可重编程结构能够通过基于目标相关成本函数的自动微分来控制执行器，从而连续调整晶格以实现特定目标。我们聚焦于深空应用领域，该领域严苛且资源受限的环境要求解决方案兼具灵活性、高效性与自主性。作为概念验证，我们展示了两个应用场景：一种可重编程的无序晶格材料，以及一个具有可调焦距的空间望远镜反射镜。所提出的框架可适用于广泛的全形设计与目标，为物理系统赋予自主自配置与自修复能力提供了一个轻量化模型。