Distributed Control within a Trapezoid Virtual Tube Containing Obstacles for Robotic Swarms Subject to Speed Constraints

Abstract: In our previous work, we design a trapezoid virtual tube to guide robotic swarms through narrow openings. This paper extends the application of the trapezoid virtual tube to the situations where there are static obstacles inside and robots have strict speed constraints. We first propose a distributed swarm controller for the trapezoid virtual tube without obstacles and present the relationship between the trapezoid virtual tube and speed constraints. Then a switching logic for obstacle avoidance is proposed by dividing the trapezoid virtual tube containing static obstacles into several sub trapezoid virtual tubes without obstacles. Formal analyses and proofs are presented to demonstrate that all robots can pass through the trapezoid virtual tube safely. Besides, we validate the effectiveness of our method through numerical simulations and real experiments.