Noise-Enabled Goal Attainment in Crowded Collectives

Departments of Physics, and Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138 In crowded environments, individuals must navigate around other occupants to reach their destinations. Understanding and controlling traffic flows in these spaces is relevant to coordinating robot swarms and designing infrastructure for dense populations. Here, we combine simulations, theory, and robotic experiments to study how noisy motion can disrupt traffic jams and enable flow as agents travel to individual goals. Above a critical noise level, large jams do not persist. From this observation, we analytically approximate the goal attainment rate as a function of the noise level, then solve for the optimal agent density and noise level that maximize the swarm's goal attainment rate. We perform robotic experiments to corroborate our simulated and theoretical results. Finally, we compare simple, local navigation approaches with a sophisticated but computationally costly central planner. A simple reactive scheme performs well up to moderate densities and is far more computationally efficient than a planner, suggesting lessons for real-world problems. Consider a robot team with a time-sensitive distributed task such as assembling a machine, fulfilling orders in a warehouse, or cleaning up hazardous debris. Robots must transport items to specific goal locations. When the space is relatively empty, adding robots is advantageous: several robots together work faster than a lone one. However, adding too many robots will lead to traffic that slows the entire team down. Emergent traffic patterns like jam formation, laning, and various transitions between ordered and disordered behavior have been studied in diverse settings spanning car traffic [1, 2], colloids and bacteria [3], robots [4, 5], ants [6, 7], and humans [8, 9]. In these systems, the simple constraint that two agents cannot occupy the same location at the same time, so that agents must stop or slow down in high-traffic regions, produces a set of rich and interesting phenomena. For instance, it is known that collectives of random walkers with exclusion constraints alone and no attraction can self-organize into large jams [3], and that ants or pedestrians following simple rules can self-organize into lanes [7, 9].