An Efficient Real-Time Planning Method for Swarm Robotics Based on an Optimal Virtual Tube

TL;DR

Addresses real-time trajectory planning for swarm robotics in unknown obstacle environments under limited onboard compute. Introduces an optimal virtual tube framework that centralizes planning on a host robot and uses multi-parametric programming to generate affine, real-time trajectories with complexity $O(n_t)$. Combines centralized planning with distributed control to enable fast replanning and safe swarming, validated by simulations, hardware-in-the-loop, and real-world drone experiments showing improved speed and safety. This work advances real-time swarm navigation in unknown environments with significant implications for search-and-rescue and environmental monitoring.

Abstract

Swarm robotics navigating through unknown obstacle environments is an emerging research area that faces challenges. Performing tasks in such environments requires swarms to achieve autonomous localization, perception, decision-making, control, and planning. The limited computational resources of onboard platforms present significant challenges for planning and control. Reactive planners offer low computational demands and high re-planning frequencies but lack predictive capabilities, often resulting in local minima. Long-horizon planners, on the other hand, can perform multi-step predictions to reduce deadlocks but cost much computation, leading to lower re-planning frequencies. This paper proposes a real-time optimal virtual tube planning method for swarm robotics in unknown environments, which generates approximate solutions for optimal trajectories through affine functions. As a result, the computational complexity of approximate solutions is $O(n_t)$, where $n_t$ is the number of parameters in the trajectory, thereby significantly reducing the overall computational burden. By integrating reactive methods, the proposed method enables low-computation, safe swarm motion in unknown environments. The effectiveness of the proposed method is validated through several simulations and experiments.

Figures (21)

• Figure 1: Trajectory overlap of swarm robots navigating through an unknown obstacle environment using the proposed method.
• Figure 2: An example of a virtual tube. The purple and blue polyhedrons are terminals. The shaded polyhedrons are cross sections ${\mathcal{C}}_t$. The black curve is a trajectory that is from ${\bf q}_{0}$ in terminal $\mathcal{C}_0$ to ${\bf q}_{m}$ in terminal $\mathcal{C}_1$. The gray area is the virtual tube. mao2023optimal
• Figure 3: The robot model. The red and blue areas represent the safety area with a radius $r_\text{s}$ and the avoidance area with a radius $r_\text{a}$, respectively.
• Figure 4: An example of critical regions with the parameter $\boldsymbol{\theta}=[\theta_0\;\theta_1]$. Different colors represent different critical regions.
• Figure 5: The framework of the proposed planning method. All robots have the same controller, and only Robot 0 has the planner block. The optimal virtual tube is planned by Robot 0 and shared with other robots by ①. The states of robots are shared by the broadcast ②. Other robots receive states and the optimal virtual tube to generate the optimal trajectory by affine functions. Then, the controllers of robots achieve trajectory tracking and collision avoidance.

Theorems & Definitions (3)

• Definition 1
• Definition 2
• Remark 1