🤖 AI Summary
This work addresses the susceptibility of Lloyd’s algorithm to deadlock and its inability to handle dynamic constraints in multi-robot motion planning. We propose the Regularized Broadcast Lloyd (RBL) algorithm—a distributed variant that embeds the Lloyd framework within a nonlinear dynamical system. RBL achieves provably convergent coverage over target regions while ensuring collision-free navigation, via regularized distributed optimization and explicit modeling of control input saturation—without requiring inter-robot communication or time synchronization. Crucially, RBL repurposes Lloyd’s algorithm as a safety layer for learning-based methods, bridging formal safety guarantees with practical deployability. Extensive validation across four real-world robotic platforms—car-like, bicycle-like, omnidirectional, and aerial robots—demonstrates that RBL significantly outperforms state-of-the-art approaches, exhibiting strong robustness to disturbances and scalability to varying robot numbers and environments.
📝 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.
