利用分布的基于ADMMD的轨迹规划,移动和遥感不确定性下多机器人系统的连接维护 (Connectivity Maintenance for Multi-Robot Systems Under Motion and Sensing Uncertainties Using Distributed ADMM-based Trajectory Planning)

Inter-robot communication enables multi-robot systems to coordinate and execute complex missions efficiently. Thus, maintaining connectivity of the communication network between robots is essential for many multi-robot systems. In this paper, we present a trajectory planner for connectivity maintenance of a multi-robot system. We first define a weighted undirected graph to represent the connectivity of the system. Unlike previous connectivity maintenance works, we explicitly account for robot motion and sensing uncertainties while formulating the graph edge weights. These uncertainties result in uncertain robot positions which directly affect the connectivity of the system. Next, the algebraic connectivity of the weighted undirected graph is maintained above a specified lower limit using a trajectory planner based on a distributed alternating direction method of multipliers (ADMM) framework. Here we derive an approximation for the Hessian matrices required within the ADMM optimization step to reduce the computational load. Finally, simulation results are presented to statistically validate the connectivity maintenance of our trajectory planner.

翻译：机器人间通信使多机器人系统能够有效地协调和执行复杂任务。因此, 维护机器人之间通信网络的连通性对于许多多机器人系统至关重要。在本文件中, 我们为多机器人系统的连通性维护提供了一个轨迹规划器。我们首先定义了一个加权非定向图表, 以代表系统的连通性。与先前的连通性维护工作不同, 我们在绘制图形边缘重量时, 明确核算机器人运动和感测不确定性。这些不确定性导致机器人位置不确定, 直接影响系统的连通性。其次, 加权非定向图形的代数连通性使用基于分布式交替式倍数(ADMMM)框架的轨迹规划器, 维持在规定的下限之上。在这里, 我们为ADMM 优化步骤内所需的赫森矩阵的近似值, 以减少计算负荷。最后, 模拟结果在统计上验证了我们轨迹规划器的连通性维护。