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

TL;DR

A distributed swarm controller for the trapezoid virtual tube without obstacles is proposed and a switching logic for obstacle avoidance is proposed by dividing the trapezoid virtual tube containing static obstacles into several subtrapezoid virtual tubes without obstacles.

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.

Figures (13)

• Figure 1: A trapezoid virtual tube with some static obstacles inside is used to guide multiple multicopters through a narrow opening.
• Figure 2: Trapezoid virtual tube.
• Figure 3: Three areas inside the trapezoid virtual tube. In plot (b), there exists $\mathcal{R}_\mathcal{T}=\varnothing$.
• Figure 4: Repulsive vector field of the extended tube boundary $\left[\mathbf{p}_{\text{eh},0},{\mathbf{p}}_{\text{h},1}\right]$.
• Figure 5: The introduction of $\theta_\text{h}$ and $\theta_\text{r}$.