Continuous Design and Reprogramming of Totimorphic Structures for Space Applications

Abstract: 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.