We describe the National Museum of Mathematics's Robot Swarm exhibit and our approach for achieving a reliable system for collision avoidance. The Robot Swarm exhibit allows visitors to program behaviors and interact with a “swarm” of small robots. The exhibit supports extended unattended run times, continuous interaction with the public and the demonstration of evocative group behaviors. The exhibit software includes a robust collision avoidance scheme that prevents collisions between robots and collisions between robots and static obstructions in the exhibit space. This system was achieved by building on the Optimal Reciprocal Collision Avoidance (ORCA) algorithm in a novel implementation: the Extended Velocity Obstacle validation system. This paper presents: 1) A collision avoidance algorithm that robustly and efficiently avoids collisions between many robots and static obstacles. 2) A unique hybrid ORCA collision avoidance approach that utilizes global state knowledge without subverting the behavioral independence of each robot. 3) A unique position filtering system which is tailored to an error model in which positions reads can be treated as “ground-truth” and a noise model that is highly discontinuous and non-linear. We present experiments and experimental data that demonstrate the efficacy of our approach.