Previous swarmalator models have uncovered diverse behaviors, but they have assumed that agents interact through a single internal phase variable and are point-like particles, but most natural and robot swarms consist of agents with multiple internal coupling states and have bodies that take up space. Here, we study swarmalators that are space-filling, exhibit an orientation, have multiple spatially separated internal phases, and exhibit asymmetric phase coupling. We focus on the simplest case, where agents couple through two internal phases and demonstrate that this can be used to mimic the behaviors of real-world Janus swarmalators, but demonstrate that the model extends to any number of phases and characterize the behaviors for three, four, and five-phase agents as well as explore how the behaviors change when the model is extended to 3D. We also consider the inverse problem and exploit the control barrier function method to enable global and local control strategies. These strategies enable desired spatial orientation and motion that allow collectives to automatically traverse a complex environment while avoiding obstacles. We characterize several unexpected emergent collective behaviors and demonstrate how a swarmalator collective might be controlled to safely navigate complex environments. Janus swarmalators exhibit complex behaviors through multiple internal phases and spatial coupling. Utilizing control barrier functions, the model enables desired collective motion and orientation, facilitating navigation in intricate environments while revealing diverse emergent dynamics across various parameter spaces.
Ceron et al. (2026) studied this question.