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.

中文翻译：

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平面最大流量图和带间隙的车道确定

多主体导航中的主要挑战之一是生成轨迹，以使在充满障碍物的环境中的瓶颈最小化。在本文中，我们通过考虑给定多边形环境的最大流量来全局解决此问题。考虑到解决平面环境连续最大流量的困难，我们在本文中介绍了一种基于GPU的方法，该方法导致了在任意二维多边形域中计算最大流量图的实用方法。一旦获得流图表示，就可以提取车道并优化长度，同时保持由轨迹系统实现的恒定流量。这项工作通过提出一种基于间隙的流量生成方法，扩展了我们先前在最大流量图上的工作，该方法考虑了流量生成阶段中代理的大小。这样，我们确保始终获得具有所需间隙的最大可能车道数，这是我们以前的方法无法始终获得的属性。结果，我们能够跨一组通用的多边形障碍生成从源到汇边缘的最大流量轨迹，从而能够利用环境的连续描述的最大流量来部署大量代理，并消除瓶颈。发现以前的方法并不总是可以获得的属性。结果，我们能够跨一组通用的多边形障碍生成从源到汇边缘的最大流量轨迹，从而能够利用环境的连续描述的最大流量来部署大量代理，并消除瓶颈。发现以前的方法并不总是可以获得的属性。结果，我们能够跨一组通用的多边形障碍生成从源到汇边缘的最大流量轨迹，从而能够利用环境的连续描述的最大流量来部署大量代理，并消除瓶颈。