Minimally Persistent Graph Generation and Formation Control for Multi-Robot Systems under Sensing Constraints

This paper presents a minimally persistent graph generation and formation control strategy for multi-robot systems with sensing constraints. Specifically, each robot has a limited field of view (FOV) and range sensing capability. To tackle this problem, one needs to construct an appropriate interaction topology, namely assign neighbors to each robot such that all their sensing constraints are satisfied. In addition, as a stringent yet reasonable guarantee for the visual constraints, it is also required that the prescribed neighbors always stay within its visual field during the formation evolution. To this end, given a set of feasible initial positions, we first present a depth-first-search (DFS)-based algorithm to generate a minimally persistent graph, which encodes the sensing constraints via its directed edges. Then, based on the resultant graph, by invoking the gradient-based control technique and control barrier function (CBF), we propose a class of distributed formation control laws, rendering not only the convergence to the desired formation but also the satisfaction of sensing constraints. Simulation and experimental results are presented to verify the effectiveness of the proposed approach.