Decentralized Autonomous Navigation of Large-Scale Robotic Swarms with Control Barrier Functions

This paper addresses the shape formation problem for large-scale robotic swarms by proposing an optimization-based cooperative navigation method. First, the physical space is partitioned into multiple disjoint bins, and the stochastic evolution of robots is modelled using a Markov matrix. An optimal control problem is formulated to derive the optimal Markov sequence, navigating the swarm to converge toward the desired density distribution. In contrast to most existing shape formation methods for large-scale robotic swarms that lack explicit trajectory planning algorithms, we utilize inverse sampling techniques to determine the desired target points. By designing reasonable control Lyapunov functions and control barrier functions to construct a quadratic programming problem, robots are able to asymptotically converge to their targets while avoiding collisions. However, as the number of robots increases, control barrier function as a hard constraint may lead to deadlock. Therefore, we then propose a task-swapping mechanism to resolve this issue. Finally, simulation experiments demonstrate the stability and effectiveness of our approach.