This paper presents both algorithms and experimental results to solve a distributed rendezvous problem with shortest distance to convex regions. In a multiagent network, each agent is assigned to a certain convex region and has information about only its own region. All these regions might not have an intersection. Through local interaction with their neighbors, multiple agents collectively rendezvous at an optimal location that is a priori unknown to each agent and has the shortest total squared distance to these regions. First, a distributed time-varying algorithm is introduced, where a corresponding condition is given to guarantee that all agents rendezvous at the optimal location asymptotically for bounded convex regions. Then a distributed tracking algorithm combined with a distributed estimation algorithm is proposed. It is first shown that for general possibly unbounded convex regions, all agents rendezvous in finite time and then collectively slide to the optimal location asymptotically. Then it is shown that for convex regions with certain projection compressibility, all agents collectively rendezvous at the optimal location in finite time, even when the regions are time varying. The algorithms are experimentally implemented on multiple ground robots to illustrate the obtained theoretical results.

中文翻译：

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具有空交点的凸区域最短距离的多智能体交会：算法和实验


本文提出了解决距凸区域最短距离的分布式交会问题的算法和实验结果。在多智能体网络中，每个智能体都被分配到某个凸区域，并且仅拥有有关其自己区域的信息。所有这些区域可能没有交集。通过与邻居的本地交互，多个智能体集体在每个智能体事先未知的最佳位置会合，并且到这些区域的总平方距离最短。首先，引入分布式时变算法，给出相应的条件来保证所有智能体渐近地在有界凸区域的最佳位置会合。然后提出了一种与分布式估计算法相结合的分布式跟踪算法。首先表明，对于一般可能无界的凸区域，所有智能体在有限时间内会合，然后渐近地共同滑向最优位置。然后表明，对于具有一定投影压缩性的凸区域，即使区域随时间变化，所有智能体也会在有限时间内集体会合在最佳位置。该算法在多个地面机器人上进行了实验实施，以说明所获得的理论结果。