Optimal collision avoidance in swarms of active Brownian particles

The effectiveness of collective navigation biological or artificial agents requires to accommodate for contrasting requirements, such as staying in a group while avoiding close encounters and at the same time limiting energy expenditure manoeuvring. Here, we address this problem by considering system active Brownian particles finite two-dimensional domain ask what is control that realizes optimal tradeoff between collision avoidance expenditure. We couch language stochastic theory means mean-field game approach derive an analytic solution, characterized second-order phase transition alignment order parameter. find version classical model motion based on interactions (Vicsek model) performs remarkably control. Our results substantiate view observed behaviors may be explained result optimizing multiple objectives offer theoretical ground biomimetic algorithms used agents.