Planar max flow maps and determination of lanes with clearance

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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 present in this paper a GPU-based methodology which leads to practical methods for computing maximum flow maps in arbitrary two-dimensional polygonal domains. Once a flow map representation is obtained, lanes can be extracted and optimized in length while keeping constant the flow capacity achieved by the system of trajectories. This work extends our previous work on max flow maps by presenting a clearance-based flow generation method which takes into account the size of the agents at the flow generation phase. In this way we ensure that the maximum possible number of lanes with the needed clearance is always obtained, a property that was found to not be always obtained with our previous method. 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 utilizing the maximum flow capacity of a continuous description of the environment and eliminating bottlenecks.