This paper presents a distributed rule-based Lloyd algorithm (RBL) for multi-robot motion planning and control. The main limitations of the basic Loyd-based algorithm (LB) concern deadlock issues and the failure to address dynamic constraints effectively. Our contribution is twofold. First, we show how RBL is able to provide safety and convergence to the goal region without relying on communication between robots, nor synchronization between the robots. We considered different dynamic constraints with control inputs saturation. Second, we show that the Lloyd-based algorithm (without rules) can be successfully used as a safety layer for learning-based approaches, leading to non-negligible benefits. We further prove the soundness, reliability, and scalability of RBL through extensive simulations, comparisons with the state of the art, and experimental validations on small-scale car-like robots, unicycle-like robots, omnidirectional robots, and aerial robots on the field.

翻译：本文提出一种用于多机器人运动规划与控制的分布式基于规则的Lloyd算法（RBL）。基础Lloyd算法（LB）的主要局限在于死锁问题及未能有效处理动态约束。我们的贡献体现在两方面。首先，我们证明RBL能够在无需机器人间通信或同步的情况下，为机器人提供安全性并保证其收敛至目标区域。我们考虑了控制输入饱和情况下的多种动态约束。其次，我们证明无规则的Lloyd算法可作为基于学习方法的安全层，并带来显著优势。我们通过大量仿真实验、与现有先进技术的对比研究，以及在小型类车机器人、类独轮车机器人、全向机器人和空中机器人上的现场实验验证，进一步证明了RBL的正确性、可靠性与可扩展性。