Emergent States of Swarmalators and Their Insights for Robotics and Biological Systems

Swarming oscillators, or swarmalators, enable diverse collective behaviors because of the agents’ interdependent spatial and temporal coupling pairwise interactions. Spatial coupling involves the swarmalators aggregating or dispersing as a function of their relative phase interactions, and temporal coupling involves them synchronizing or anti-coupling their phases as a function of their relative distances or motions. Through our work, we exploit the swarmalator model to discover and design collective behaviors that are possible through natural and engineered swarms; on the one hand, we analyze and characterize the collective behaviors that emerge throughout the coupling parameter space, and on the other hand, we use control theory to optimize the coupling pairwise interactions to achieve a desired collective behavior. By studying the emergent behaviors, we find that the swarmalator model can be tuned to exhibit some of the collective behaviors exhibited by swarming systems like spermatozoa, Quincke rollers, magnetic microrobot collectives, and social amoebae. On the flip side, we have developed a method for optimizing the global and local control policies that will enable a group of swarmalators to move along a trajectory, self-organize into a specific shape, and move as a group through a complex environment while avoiding obstacles. Moreover, we demonstrate through physical platforms at the macro-scale and the micro-scale that swarmalators can be realized in the physical realm, and we study how the oscillatory pairwise interactions must change depending on the length scale of the individual robots. By studying swarmalators, both experimentally and computationally, we can introduce new versions of the model that might be more applicable to specific platforms or natural swarms, as well as use it as a method for designing the specific behaviors we would like our micro- or macro-scale robot swarms to exhibit.