Connectivity Maintenance for Multi-Robot Systems Under Motion and\n Sensing Uncertainties Using Distributed ADMM-based Trajectory Planning

Abstract

Inter-robot communication enables multi-robot systems to coordinate and\nexecute complex missions efficiently. Thus, maintaining connectivity of the\ncommunication network between robots is essential for many multi-robot systems.\nIn this paper, we present a trajectory planner for connectivity maintenance of\na multi-robot system. We first define a weighted undirected graph to represent\nthe connectivity of the system. Unlike previous connectivity maintenance works,\nwe explicitly account for robot motion and sensing uncertainties while\nformulating the graph edge weights. These uncertainties result in uncertain\nrobot positions which directly affect the connectivity of the system. Next, the\nalgebraic connectivity of the weighted undirected graph is maintained above a\nspecified lower limit using a trajectory planner based on a distributed\nalternating direction method of multipliers (ADMM) framework. Here we derive an\napproximation for the Hessian matrices required within the ADMM optimization\nstep to reduce the computational load. Finally, simulation results are\npresented to statistically validate the connectivity maintenance of our\ntrajectory planner.\n