Scale-free, programmable design of morphable chain loops of kilobots and colloidal motors

Micron-scale robots require systems that can morph into arbitrary target configurations controlled by external agents such as heat, light, electricity, and chemical environment. Achieving this behavior using conventional approaches is challenging because the available materials at these scales are not programmable like their macroscopic counterparts. To overcome this challenge, we propose a design strategy to make a robotic machine that is both programmable and compatible with colloidal-scale physics. Our strategy uses motors in the form of active colloidal particles that constantly propel forward. We sequence these motors end-to-end in a closed chain forming a two-dimensional loop that folds under its mechanical constraints. We encode the target loop shape and its motion by regulating six design parameters, each scale-invariant and achievable at the colloidal scale. We demonstrate the plausibility of our design strategy using centimeter-scale robots called kilobots. We use Brownian dynamics simulation to explore the large design space beyond that possible with kilobots, and present an analytical theory to aid the design process. Multiple loops can also be fused together to achieve several complex shapes and robotic behaviors, demonstrated by folding a letter shape "M," a dynamic gripper, and a dynamic pacman. The material-agnostic, scale-free, and programmable nature of our design enables building a variety of reconfigurable and autonomous robots at both colloidal scales and macroscales.