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 neighbors control inputs, nor synchronization between the robots. We considered both case of holonomic and non-holonomic robots 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, an updated comparison with the state of the art, and experimental validations on small-scale car-like robots.

翻译：本文提出了一种分布式基于规则的Lloyd算法(RBL)，用于多机器人的运动规划与控制。基本Lloyd算法(LB)的主要局限在于死锁问题及无法有效处理动态约束。本文的贡献体现在两个方面：首先，我们展示了RBL如何在不依赖机器人间通信、相邻机器人控制输入或机器人同步的情况下，实现安全性与目标区域收敛性保障。我们同时考虑了完整约束与非完整约束机器人，并包含控制输入饱和情形。其次，我们证明了基于Lloyd的算法（不含规则）可作为学习方法的有效安全层，带来显著效益。通过大量仿真、与现有最新技术的对比更新以及基于小型类车机器人的实验验证，我们进一步证明了RBL的可靠性、鲁棒性与可扩展性。