Higher‐Order Interaction Models for Real Robot Swarms: Bridging Theory and Practice With Physical and Operational Constraints

This work promotes traditional pair‐wise interaction (PWI) to higher‐order interaction (HOI) models in real robot swarms, aiming to faithfully represent complex phenomena such as the agile and stable turning manoeuvres observed in natural bird flocks. However, existing HOI models are typically based on idealised particle‐like assumptions, which are rarely applicable to real robot swarms due to physical and operational constraints. To address this gap, we propose an embodied framework for extending PWI to HOI in real robot swarms. Our framework explicitly accounts for physical dimensions and operational constraints by incorporating suitable potential functions and designing a velocity coordination component consistent with HOI principles. The proposed approach is evaluated through comprehensive simulations and physical experiments under two distinct scenarios: collective evasion and trajectory tracking. Results show that the extension to HOI models contributes to improvements of up to in overall performance, in responsiveness and in cohesion. Beyond deployment of HOI models in real robot swarms, our work paves a practical way for using robot swarms to investigate HOI topologies that underlie collective behaviours, such as bird flocking, fish schooling and mammal herding.