Anisotropic shape-shifting robotic matter enabling versatile collective behaviors

Collective robotic systems can exhibit emergent behaviors through local interactions among individual robots, yet most existing platforms rely on sophisticated individuals or complex control strategies to achieve diverse functionalities. Here, we present TriHex, a minimalist robotic unit capable of shape-shifting between triangular and hexagonal shapes using single-motor actuation. Despite its simplicity, collectives of TriHex units display remarkable behavioral diversity through two control dimensions: system configuration and individual unit's shape-shifting phase. By adjusting these parameters, a static tessellated assembly's stiffness can be programmed. In discrete assemblies, the system transitions between solid-like and liquid-like states and achieves programmable viscosity. When arranged in cellular configurations with a pre-designed phase difference, the system realizes controllable porosity. Additionally, shape changes enable coordinated collective locomotion, reconfiguration and integrating capabilities of object gripping and transportation. Analytical models and numerical simulations are developed that successfully capture and predict the TriHex collective's behavior. This work demonstrates that complex collective behaviors can emerge from relatively simple individual units, offering insights for designing scalable and adaptive robotic matter.