Distributed Predictive Flocking for a Swarm of Miniature Vibration-Driven Robots in a Confined Arena

Coordinating many miniature robots in a confined arena, with no leader, central planner, or global map, is a core challenge for swarm robotics. As the swarm grows denser, collision avoidance becomes the limiting factor, and the number of safely coexisting robots depends on the formulation of the inter-robot safety constraint. We present a distributed predictive flocking controller in which each robot solves its own nonlinear model predictive control (NMPC) problem, optimizing swarm cohesion and alignment costs, inter-robot and obstacle safety, and a task objective, while exchanging only predicted trajectories with local neighbors. Within this generalized controller architecture, solved in real time, we compare six barrier and control-barrier-function (CBF) safety formulations on a digital twin of an open-source vibration-driven bristlebot in a $0.64\,\mathrm{m^2}$ arena. A look-ahead discrete-time CBF performs best overall, with the fewest collisions and the widest inter-robot margins across nearly every swarm size tested. We deploy it on phototaxis, phototactic orbiting, and cohesion without a stimulus tasks, using swarm sizes starting from ten robots and up to the geometric packing limit. The swarm holds well: collisions stay low in small swarms, rising steeply as the packing limit approaches, while coordination and cohesion degrade gently rather than collapsing. The swarm is found not to trade safety for order, keeping both across the confined arena, with local alignment high at every swarm size.