A Navier-Stokes-Equations-Based Virtual Tube Planning and Control Method for Robotic Swarms in Complex Environments

Classical methods, including formation control, cooperative trajectory planning, and control-based methods, have been proposed to solve the passing-through control problem of robotic swarms in complex environments. However, these methods often suffer from communication dependency, high computational cost, deadlock, or low passing-through efficiency. To address these issues, virtual tubes are proposed in our previous work, which provide safe passages for the swarm. However, the virtual-tube-based method generates narrow passages or is unable to obtain a feasible solution sometimes. Fortunately, fluid-inspired approaches offer a novel perspective for solving passing-through problems. In this paper, we propose a novel Navier-Stokes-equations-based virtual tube planning and control method, which adaptively generates a single or multiple smoother tubes, and the swarm is controlled based on the solution of the Navier-Stokes (NS) equations. Extensive simulations show that our approach improves the safety and efficiency of the swarm. Experiments on omnidirectional mobile robots validate the practicality of the proposed method.