GPU-Based Max Flow Maps in the Plane

One main challenge in multi-agent navigation is to generate trajectories minimizing bottlenecks in environments cluttered with obstacles. In this paper we approach this problem globally by taking into account the maximum flow capacity of a given polygonal environment. Given the difficulty in solving the continuous maximum flow of a planar environment, we introduce in this paper a GPU-based methodology which leads to a practical method for computing maximum flow maps in arbitrary two-dimensional polygonal domains. Once the flow is computed, we then propose a method to extract lane trajectories according to the size of the agents and to optimize the trajectories in length while keeping constant the maximum flow achieved by the system of trajectories. As a result we are able to generate trajectories of maximum flow from source to sink edges across a generic set of polygonal obstacles, enabling the deployment of large numbers of agents optimally with respect to the maximum flow capacity of the environment. Our approach eliminates bottlenecks by producing trajectories which are globally-optimal with respect to the flow capacity and locally-optimal with respect to the total length of the system of trajectories.