A Probabilistic Measure of Multi-Robot Connectivity and Ergodic Optimal Control

This paper considers multi-robot trajectory planning for information gathering with intermittent connectivity maintenance.For information gathering, ergodic search provides a framework to inherently balance between exploration (visit all locations for information) and exploitation (greedily search high information regions), by planning trajectories such that the amount of time the robots spend in a region is proportional to the amount of information in that region.Although ergodic search was studied in different ways, most of them ignore or over-simplify the connectivity maintenance requirement among the robots, which is crucial for information exchange in missions without global communication.This paper introduces a novel probabilistic measure of inter-robot connectivity based on the time-averaged statistics of the robots' trajectories.Such a measure provides a new way to impose intermittent connectivity constraints during the ergodic search, which leads to an optimal control problem (OCP).We derive the theoretical condition for optimality based on the Pontryagin principle, and develop iLQR and augmented Lagrangian methods to numerically solve this OCP.Our experimental results validate the effectiveness of the proposed probabilistic measure and demonstrate that the ergodic search combined with this measure achieves better ergodic metrics compared to baseline approaches.We also demonstrate our planner on a multi-drone system. 1