# Rule-Based Lloyd Algorithm for Multi-Robot Motion Planning and Control with Safety and Convergence Guarantees Source: [Rule-Based Lloyd Algorithm for Multi-Robot Motion Planning and Control with Safety and Convergence Guarantees]() Collection index: [llms.txt]() Data updated: 2025-10-26T04:38:16.443Z Authors: Manuel Boldrer, Alvaro Serra-Gomez, Lorenzo Lyons, Vit Kratky, Javier Alonso-Mora, Laura Ferranti Published: 2023-10-30T13:10:05.000Z ## Abstract 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Simultaneous Multi-UAV Navigation and Collision Avoidance on Multi-UAV Antipodal Circle Navigation 10 UAVs, 10m radius, 10ms-1 max vel, 7ms-2 max acc low speed/acc scenario 1.0](): Simultaneous Multi-UAV Navigation and Collision Avoidance; Multi-UAV Antipodal Circle Navigation 10 UAVs, 10m radius, 10ms-1 max vel, 7ms-2 max acc low speed/acc scenario 1.0; Success Rate: 100. - [Simultaneous Multi-UAV Navigation and Collision Avoidance on Antipodal Circle High Speed Scenario 1.0](): Simultaneous Multi-UAV Navigation and Collision Avoidance; Multi-UAV Antipodal Circle Navigation 10 UAVs, 10m radius, 20ms-1 max vel, 40ms-2 max acc high speed scenario 1.0; Success Rate: 100. ## Original sources and implementation [Original paper]() [PDF]()