For guiding the UAV swarm to pass through narrow openings, a trapezoid virtual tube is designed in our previous work. In this paper, we generalize its application range to the condition that there exist obstacles inside the trapezoid virtual tube and UAVs have strict speed constraints. First, a distributed vector field controller is proposed for the trapezoid virtual tube with no obstacle inside. The relationship between the trapezoid virtual tube and the speed constraints is also presented. Then, a switching logic for the obstacle avoidance is put forward. The key point is to divide the trapezoid virtual tube containing obstacles into several sub trapezoid virtual tubes with no obstacle inside. Formal analyses and proofs are made to show that all UAVs are able to pass through the trapezoid virtual tube safely. Besides, the effectiveness of the proposed method is validated by numerical simulations and real experiments.

In order to guide the multi-agent system in a cluttered environment, a connected quadrangle virtual tube is designed for all agents to keep moving within it, whose basis is called the single trapezoid virtual tube. There is no obstacle inside the tube, namely the area inside the tube can be seen as a safety zone. Then, a distributed swarm controller is proposed for the single trapezoid virtual tube passing problem. This issue is resolved by a gradient vector field method with no local minima. Formal analyses and proofs are made to show that all agents are able to pass the single trapezoid virtual tube. Finally, a modified controller is put forward for convenience in practical use. For the connected quadrangle virtual tube, a modified switching logic is proposed to avoid the deadlock and prevent agents from moving outside the virtual tube. Finally, the effectiveness of the proposed method is validated by numerical simulations and real experiments.