  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.
