机器人网络中约束分布式代数连通性最大化
Constrained Distributed Algebraic Connectivity Maximization in Robotic Networks
AI总结：
针对移动机器人网络，通过分布式半定规划（SDP）优化机器人位置以最大化通信图的代数连通性，并基于局部可计算度量调整通信负载。
摘要：
我们考虑通过将移动机器人移动到适当位置来最大化其通信网络的代数连通性问题。我们将图的拉普拉斯矩阵定义为依赖于机器人之间的成对距离，并将问题近似为一系列半定规划（SDP）。我们提出了一种分布式解决方案，由仅使用附近邻居机器人信息的局部SDP组成。我们表明，由此产生的分布式优化框架导致可行的子问题，并通过重复执行，代数连通性单调增加。此外，我们描述了如何基于局部可计算度量调整机器人的通信负载。数值模拟显示了该算法相对于集中式解决方案的性能。
英文摘要：
We consider the problem of maximizing the algebraic connectivity of the communication graph in a network of mobile robots by moving them into appropriate positions. We define the Laplacian of the graph as dependent on the pairwise distance between the robots and we approximate the problem as a sequence of Semi-Definite Programs (SDP). We propose a distributed solution consisting of local SDP's which use information only from nearby neighboring robots. We show that the resulting distributed optimization framework leads to feasible subproblems and through its repeated execution, the algebraic connectivity increases monotonically. Moreover, we describe how to adjust the communication load of the robots based on locally computable measures. Numerical simulations show the performance of the algorithm with respect to the centralized solution.
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