Continuous Design and Reprogramming of Totimorphic Structures for Space Applications

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.