Collective motion, such as milling, flocking, and collective turning, is a common and captivating phenomenon in nature, which arises in a group of many self-propelled individuals using local interaction mechanisms. Recently, vision-based mechanisms, which establish the relationship between visual inputs and motion decisions, have been applied to model and better understand the emergence of collective motion. However, previous studies often characterize the visual input as a transient Boolean-like sensory stream, which makes it challenging to capture the salient movements of neighbors. This further hinders the onset of the collective response in vision-based mechanisms and increases demands on visual sensing devices in robotic swarms. An explicit and context-related visual cue serving as the sensory input for decision-making in vision-based mechanisms is still lacking. Here, we hypothesize that body orientation change (BOC) is a significant visual cue characterizing the motion salience of neighbors, facilitating the emergence of the collective response. To test our hypothesis, we reveal the significant role of BOC during collective U-turn behaviors in fish schools by reconstructing scenes from the view of individual fish. We find that an individual with the larger BOC often takes on the leading role during U-turns. To further explore this empirical finding, we build a pairwise interaction mechanism on the basis of the BOC. Then, we conduct experiments of collective spin and collective turn with a real-time physics simulator to investigate the dynamics of information transfer in BOC-based interaction and further validate its effectiveness on 50 real miniature swarm robots. The experimental results show that BOC-based interaction not only facilitates the directional information transfer within the group but also leads to scale-free correlation within the swarm. Our study highlights the practicability of interaction governed by the neighbor’s body orientation change in swarm robotics and the effect of scale-free correlation in enhancing collective response.

A widely mentioned but not experimentally confirmed view (known as the ‘criticality hypothesis’) argues that biological swarm systems gain optimal responsiveness to perturbations and information processing capabilities by operating near the critical state where an ordered-to-disordered state transition occurs. However, various factors can induce the ordered–disordered transition, and the explicit relationship between these factors and the criticality is still unclear. Here, we present an experimental validation for the criticality hypothesis by employing real programmable swarm-robotic systems (up to 50 robots) governed by Vicsek-like interactions, subject to time-varying stimulus-response and hazard avoidance. We find that (i) not all ordered–disordered motion transitions correspond to the functional advantages for groups; (ii) collective response of groups is maximized near the critical state induced by alignment weight or scale rather than noise and other non-alignment factors; and (iii) those non-alignment factors act to highlight the functional advantages of alignment-induced criticality. These results suggest that the adjustability of velocity or directional coupling between individuals plays an essential role in the acquisition of maximizing collective response by criticality. Our results contribute to understanding the adjustment strategies of animal interactions from a perspective of criticality and provide insights into the design and control of swarm robotics.

Plenty of local interaction mechanisms have been proposed to achieve collective behaviors in swarm robotics. However, these mechanisms require robots to explicitly obtain the velocity of their neighbors as the sensory input to make motion decisions. This further poses great challenges in real-world applications of swarm robotics. In this letter, inspired by the chasing behavior in large-scale migrating locusts, we propose a visual attention-based swarm model to achieve collective behaviors with positional interaction. Through numerical simulations, we find the emergence of three typical collective behaviors: flocking, milling and swarming. To gain deep insights into the new proposed model, we investigate the impact of group size and sensory blindness on the emergence of collective behaviors. Moreover, by using the mean field analysis framework, we present the theoretical proof of the emergence of flocking and milling behavior. Furthermore, to validate the feasibility of our proposed model, we reproduce the flocking and milling behavior with up to 50 physical robots. Robotic experiments demonstrate the promising ability of the new proposed model to achieve collective behaviors with the absence of velocity alignment.

Survival in dynamic and complex environments requires groups to exhibit a high level of responsiveness to rapidly changing circumstances. Recent studies have shown the role of selective social interactions in driving responsive collective behavior at the individual-level decision making. However, much less effort has been devoted to understanding how structures of interaction networks shape collective responses. Here we show that the highly nested structures enhance responsiveness in schooling fish and swarm robotics. First, analysis of trajectories from schooling Hemigrammus rhodostomus reveals that the high nestedness, quantified through the nestedness metric based on overlap and decreasing fill (NODF), emerges as a key interaction structure feature in maneuverable movements. Using a general contagion model, we then show that the perfectly nested interaction network (PNIN) achieves the optimal information transfer efficiency. Furthermore, we integrate the PNIN into the self-propelled system and demonstrate the advantages of PNIN in facilitating efficient and robust collective responses through semi-physical simulations and 50 real robots. Our study provides a modeling perspective to elucidate collective responses through structural arrangements of interaction networks.

This letter presents a novel density-based control framework for shape formation in swarm robotic systems, operating exclusively on local perception without requiring communication or identity recognition among robots and targets. Inspired by Smoothed Particle Hydrodynamics (SPH), each robot estimates a local spatial density using kernel functions and regulates its motion based on the gradient of a constructed target density field. Unlike existing methods that depend on global coordination or explicit target assignments, the proposed approach enables fully distributed shape formation through local density regulation alone. By adjusting the reference density, the system supports autonomous scaling in both the number of robots and the geometric size of the target shape, seamlessly transitioning among shape-surrounding, double-layer contour, and boundary-conformal formations. A composite control law integrates density-driven forces, repulsive interactions for collision avoidance, and damping for dynamic stability. The effectiveness and robustness of the method are validated through extensive simulations and physical experiments with 50 robots under a motion capture laboratory setup. Results demonstrate the scalability, resilience, and practicality of the approach for decentralized swarm shape formation.

Swarm robotics exhibits scalable and adaptive collective behaviors, providing an effective solution for complex tasks in real-world applications. However, reliance on velocity and global positioning information of neighbors limits the practical deployment of swarm robots. In this letter, we propose a sensorimotor-based swarm model that directly maps first-person visual perception to motion decisions through probabilistic decision-making. Based on numerical simulations, we find the emergence of flocking, milling, and swarming behaviors without explicit velocity alignment and positional interactions. In addition, we investigate the effectiveness of the proposed swarm model under non-omniscient perception. Moreover, we show that probabilistic motion decision-making enhances the resilience of group coordination under sensory noise. Finally, we achieve flocking, milling and swarming behaviors in a swarm of 50 real robots under motion noise disturbance and simulated visual constraints, highlighting the potential of the proposed swarm model in real-world tasks.