Tube-RRT*: Efficient Homotopic Path Planning for Swarm Robotics Passing-Through Large-Scale Obstacle Environments

Recently, the concept of optimal virtual tube has emerged as a novel solution to the challenging task of navigating obstacle-dense environments for swarm robotics, offering a wide ranging of applications. However, it lacks an efficient homotopic path planning method in obstacle-dense environments. This paper introduces Tube-RRT*, an innovative homotopic path planning method that builds upon and improves the Rapidly-exploring Random Tree (RRT) algorithm. Tube-RRT* is specifically designed to generate homotopic paths for the trajectories in the virtual tube, strategically considering opening volume and tube length to mitigate swarm congestion and ensure agile navigation. Through comprehensive comparative simulations conducted within complex, large-scale obstacle environments, we demonstrate the effectiveness of Tube-RRT*.

Optimal Virtual Tube Planning and Control for Swarm Robotics

This paper presents a novel method for efficiently solving trajectory planning problems for swarm robotics in cluttered environments. While recent research has demonstrated high success rates in real-time local trajectory planning for swarm robotics in cluttered environments, optimizing every trajectory for each robot is computationally expensive, with a computational complexity of $O\left(n^2\right)$ to $ O\left(n^3\right)$. To address this issue, we first propose the concept of the \emph{optimal virtual tube}, which includes infinite optimal trajectories. Under certain conditions, any optimal trajectory in the optimal virtual tube can be expressed as a convex combination of a finite number of optimal trajectories, with a computational complexity of $O\left(1\right)$. Afterward, a planning method of \emph{the optimal virtual tube} is proposed. In simulations and experiments, we show that the proposed method efficiently reduces calculation and is validated by comparison with traditional methods.