  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.
